This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
Ceramic thin plates were prepared using kaolin,potassium sodium feldspar and quartz powder as the main raw materials and kaolin,α-Al_(2)O_(3),MoO_(3) and AlF_(3)·3H_(2)O as additives.The experiment examined the ...Ceramic thin plates were prepared using kaolin,potassium sodium feldspar and quartz powder as the main raw materials and kaolin,α-Al_(2)O_(3),MoO_(3) and AlF_(3)·3H_(2)O as additives.The experiment examined the effects of different additives on mullite formation,as well as the microstructure and properties of the ceramic thin plates.Additionally,the study explored the toughening and strengthening mechanisms induced by the additives,providing a theoretical foundation for further optimizing the toughness of ceramic thin plates.The results showed that the D4 sample fired at 1220℃(with an addition of 20 wt% α-Al_(2)O_(3))exhibited the best performance,with a water absorption rate of 0.07%,apparent porosity of 0.18%,bulk density of 2.75 g·cm^(-3),firing shrinkage of 12.76%,bending strength reaching 101.93 MPa,and fracture toughness of 2.51 MPa·m^(1/2).As the amount ofα-Al_(2)O_(3) additive increased,the ceramic thin plates exhibited a greater abundance of short rod-like mullite and corundum grains,which were tightly packed together,forming a framework for the ceramic thin plates.This microstructure enhanced pathways for crack propagation,dispersed internal stresses,and increased fracture surface energy,resulting in significant improvements in both strength and fracture toughness of the ceramic thin plates.展开更多
In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete...A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete components.Each channel consists of an integrator,a pole-zero cancellation net,and a linear amplification stage,which can be adapted to accommodate either positive or negative input signals.The RMS equivalent input noise charges are 3.3 fC,the conversion gains are approximately±2 mV∕fC,and the intrinsic time resolution reaches 32 ps.In the prototype PPAC application,the CSA performs as well as the commercial FTA820A amplifier,providing a position resolution as good as 0.17 mm,and exhibiting reliable stability during several hours of continuous data acquisition.展开更多
High-Mg andesites(HMAs)typically originate in subduction-related tectonic settings,including active continental margins and island arcs,and studies of HMAs can constrain the tectonic evolution of the South China Block...High-Mg andesites(HMAs)typically originate in subduction-related tectonic settings,including active continental margins and island arcs,and studies of HMAs can constrain the tectonic evolution of the South China Block and Paleo-Tethyan Ocean.This paper presents new chronological and geochemical data for high-Mg gabbroic diorites in the Funing area,southern South China.The gabbroic diorites yield ages of 254-249 Ma,and have moderate SiO2 contents(51.3%-57.8%),high MgO contents(4.6%-10.2%)and Mg^(#)values(52-75),enrichment in large-ion lithophile elements and light rare earth elements,and depletion in high-field-strength elements-collectively displaying geochemical signatures typical of sanukites.The gabbroic diorites have radiogenic initial Sr and Pb isotopic compositions,and negativeεNd(t)andεHf(t)values.These characteristics distinguish the Funing gabbroic diorites from subduction-related igneous rocks in the Paleo-Pacific tectonic domain.Instead,they are isotopically similar to HMAs and basalts along the Paleo-Tethys suture.We propose the high-Mg gabbroic diorites and basaltic andesites in Funing area share a common mantle source,linked to subduction and rollback of the Paleo-Tethyan plate beneath the South China Block,which triggered back-arc rifting and partial melting of the metasomatized lithospheric mantle during the Late Permian to Early Triassic.展开更多
A wealth of geological and geochemical evidence indicates that plate tectonics was initiated in the Archean,though its style differing from that in the Phanerozoic,largely due to higher temperatures of convective mant...A wealth of geological and geochemical evidence indicates that plate tectonics was initiated in the Archean,though its style differing from that in the Phanerozoic,largely due to higher temperatures of convective mantle.Understanding the specific characteristics for the operation of ancient plate tectonics is critical for deciphering the formation and evolution of continental crust on early Earth,as well as the progressive development of Earth’s habitability.Through an in-depth analysis of geology and geochemistry for two events of late Archean crustal growth in the North China Craton,this study suggests that Archean plate tectonics would likely undergo the gradual evolution from immature to mature phases.The North China Craton experienced two major episodes of crustal growth at~2.9-2.7 and~2.6-2.5 Ga,respectively,represented by peaks in isotopic model ages of Archean felsic gneisses and widespread mafic rocks in greenstone belts.Although the preserved mafic rocks in greenstone belts generally exhibit arc-like trace element signatures,the early mafic crust formed at~2.9-2.7 Ga is limited in volume,with most of it having been reworked within several hundred million years.Tonalite-trondhjemite-granodiorite(TTG),produced by partial melting of such mafic crust,show zircon Hf-O isotope compositions indicative of sources consisting of seawater-hydrothermally altered oceanic crustal rocks with varying ages,suggesting that the early mafic crust was likely dominated by oceanic basalts.The medium-to low-pressure signatures of TTG rocks further imply that the oceanic crust was not subducted deeply to mantle depths,but instead was accreted to the margin of proto-continental nuclei due to aborted subduction.In contrast,the~2.6-2.5 Ga crustal growth event preserved a greater volume of mafic rocks.For these mafic rocks,the enrichment of incompatible elements correlates with water contents estimated from whole-rock major elements,indicating that their arc-like trace element features were associated with fluid metasomatism of the source region.Integrated with regional geological evidence from~2.5 Ga,such as ophiolites containing ultrahigh-pressure mineral inclusions and eclogite-facies remnants of oceanic crust,these observations suggest that modern-style plate subduction was likely in operation by the end of the Late Archean.Therefore,the modern plate tectonics regime did not emerge abruptly,but underwent a gradual evolution controlled by the thermal state of plate margins.It is this evolving tectonic regime that drove the significant crustal growth during the Archean.The two distinct episodes of crustal growth ultimately led to the formation of the North China Craton.展开更多
A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The resu...A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The results show that cold-pressing produces intense plastic deformation near the corrugated surface of the Al plate,which promotes dynamic recrystallization of the Al substrate near the interface during the subsequent hot-pressing.In addition,the initial corrugation on the surface of the Al plate also changes the local stress state near the interface during hot pressing,which has a large effect on the texture components of the substrates near the corrugated interface.The construction of the corrugated interface can greatly enhance the shear strength by 2−4 times due to the increased contact area and the strong“mechanical gearing”effect.Moreover,the mechanical properties are largely depended on the orientation relationship between corrugated direction and loading direction.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
We investigate the effects of projectile material on high-speed penetration/perforation of Inconel 718 alloy(IN718)plates.High-speed ballistic impact tests are conducted on 2 mm-thickness IN718 plates with 5-mm-diamet...We investigate the effects of projectile material on high-speed penetration/perforation of Inconel 718 alloy(IN718)plates.High-speed ballistic impact tests are conducted on 2 mm-thickness IN718 plates with 5-mm-diameter stainless steel 304(SS304),Ti alloy TC4,and Al alloy AA1060 spherical projectiles.The impact processes are captured with high-speed photography.Optical and scanning electron microscopy and laser scan are conducted on recovered projectiles and targets.Finite element models of the ballistic impact are established based on the coupled Eulerian-Lagrangian algorithm with the Johnson-Cook constitutive model and failure criterion,and can well reproduce the experimental results.The experimental and simulated data related to projectile dynamics,and the geometries of postmortem projectiles and bullet holes are analyzed with phenomenological models.Projectile velocity evolution can be described with hydrodynamic models of penetration.Dimensional analysis reveals a universal relationship between the bullet hole expansion coefficient and the normalized dynamic pressure,regardless of the projectile material.However,the projectile material does affect projectile deformation,bullet hole size,and energy absorption of target.展开更多
A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order ...A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order time derivatives.The proposed scheme attains third-order temporal accuracy and is rigorously validated through stability and convergence analyses for both scalar and coupled systems.Its effectiveness is demonstrated by simulating unsteady Eyring-Prandtl non-Newtonian nanofluid flow over a Riga plate with coupled heat and mass transfer under electromagnetic actuation.The physical model accounts for Brownian motion and thermophoresis,and the nanofluid considered is a Prandtl-type non-Newtonian base fluid containing suspended nanoparticles,with heat and mass transport governed by coupled momentum,energy,and concentration equations.Numerical simulations are performed over practically relevant parameter ranges,with the Reynolds number fixed at Re=5 and the Prandtl number set to Pr=3 to represent moderate inertial and thermal diffusion effects typical of nanofluid transport systems.To enhance computational efficiency,an artificial neural network(ANN)-based surrogate model is developed to predict the skin friction coefficient and local Sherwood number as functions of Reynolds number,Prandtl number,Schmidt number,Brownian motion,and thermophoresis parameters.The training dataset is generated entirely from high-fidelity numerical simulations produced by the proposed hybrid scheme.The data are systematically partitioned into 70%for training,15%for validation,and 15%for testing,ensuring reliable generalization.Regression analysis yields a near-unity correlation coefficient(R≈0.99),while error histograms exhibit tightly clustered residuals around zero,confirming high predictive accuracy.Furthermore,a benchmark convergence study using Stokes’first problem demonstrates that the proposed scheme consistently achieves lower global error norms than the classical Runge–Kutta method for identical spatial and temporal resolutions.Overall,this study introduces a novel computational intelligence framework that integrates high-order numerical solvers with machine learning,offering a robust and time-efficient tool for advanced modeling and real-time prediction of non-Newtonian nanofluid transport phenomena under electromagnetic flow control.展开更多
With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristi...With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristics has become critical.This paper puts forward a dynamic model for a rotating functionally graded graphenereinforced(FG-GPR)sandwich metal porous cantilever pre-twisted plate(PTP),aiming to analyze its natural vibration characteristics.To this end,the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer.With the classical plate theory,the Rayleigh-Ritz method,and the polynomials,the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP.The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations.The bending stiffnesses are analyzed.Finally,the effects of different graphene/pore distributions,length-to-thickness/width ratios,layer thickness ratios,twist angles,and rotational speeds on the natural frequencies of the system are systematically investigated.展开更多
In order to investigate the penetration performance of Linear-Shaped Charge(LSC),Embowed LinearShaped Charge(ELSC),and Embowed Linear Explosively Formed Projectile(ELEFP)on T-shaped stiffened plates,a series of near-f...In order to investigate the penetration performance of Linear-Shaped Charge(LSC),Embowed LinearShaped Charge(ELSC),and Embowed Linear Explosively Formed Projectile(ELEFP)on T-shaped stiffened plates,a series of near-field air-burst experiments are conducted.The damage modes and characteristics of the target plates are compared and analyzed.Each flat plate section is completely punctured,resulting in a penetration hole.The damage modes induced by the three charge types on the stiffened plate structure are consistent,characterized by shear failure in the central region of the flat plate due to penetration by the penetrator,localized plastic deformation of the flat plate,and local penetration failure resulting from partial perforation of the central stiffener.The penetration lengths caused by ELSC and ELEFP are 45.1%and 46.1% larger than that of LSC,while the half-width of the penetration hole generated by ELEFP is 54.2% and 24.7% smaller than that of ELSC and LSC,respectively.The penetration height caused by ELEFP are 17.5%and 62.1% larger than that of ELSC and LSC,respectively.The stiffener effectively segments the damage area,enhancing the local structural strength and limiting the extent of plastic deformation in the flat plate section.The comparative results show that the ELSC proves to be more effective for efficient large-scale damage,and ELEFP is more suitable for achieving efficient localized damage.展开更多
Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding str...Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.展开更多
Proton exchange membrane water electrolysis(PEMWE)is one of the most promising strategies to pro-duce green hydrogen energy,and it is crucial to exploit highly conductive and good corrosion-resistant coatings on bipol...Proton exchange membrane water electrolysis(PEMWE)is one of the most promising strategies to pro-duce green hydrogen energy,and it is crucial to exploit highly conductive and good corrosion-resistant coatings on bipolar plates(BPs),one of the core components in PEMWE cells.In this work,NbN coatings are deposited on Ti BPs by magnetron sputtering to improve the corrosion resistance and conductivity,for which the critical process parameters,such as the working pressure,partial nitrogen pressure and de-position temperature are well optimized.It is found that the compact microstructure,highly conductive δ-NbN and uniform nanoparticles play a dominant role in the synergistic improvement of the corrosion resistance and electrical conductivity of NbN coatings.The optimized NbN coatings exhibit excellent cor-rosion resistance with the low corrosion current density of 1.1×10^(-8) A cm^(-2),a high potential value of-0.005 V vs.SCE and a low ICR value of 15.8 mΩcm2@1.5 MPa.Accordingly,NbN coatings can be a promising candidate for the development of the low-cost and high-anti-corrosion Ti BPs of PEMWE.展开更多
Zirconium-titanium-steel composite plate with the size of 2500 mm×7800 mm×(3+0.7+22)mm was prepared by explosive welding+rolling method,and its properties were analyzed by ultrasonic nondestructive testing,p...Zirconium-titanium-steel composite plate with the size of 2500 mm×7800 mm×(3+0.7+22)mm was prepared by explosive welding+rolling method,and its properties were analyzed by ultrasonic nondestructive testing,phased array waveform shape,interface structure shape,electronic scanning,and mechanical property testing.Results show that the rolling temperature of zirconiumtitanium complex should be controlled at 760°C,and the rolling reduction of each pass should be controlled at 10%–25%.The explosive velocity to prepare zirconium-titanium-steel composite plates should be controlled at 2450–2500 m/s,the density should be 0.78 g/cm3,the stand-off height should be 12 mm,and the explosive height of Zone A and Zone B should be 45–50 mm.Explosive welding combined with rolling method reduces the impact of explosive welding and multiple heat treatment on material properties.Meanwhile,the problems of surface wrinkling and cracking,which occur during the preparation process of large-sized zirconiumtitanium-steel composite plate,can be solved.展开更多
Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer ...Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.展开更多
7039 Al alloys are widely used in armor vehicles,given the material’s high specific strength and fracture toughness.However,laminar tearing in the thickness plane of the base metal(BM),specifically in the normal dire...7039 Al alloys are widely used in armor vehicles,given the material’s high specific strength and fracture toughness.However,laminar tearing in the thickness plane of the base metal(BM),specifically in the normal direction(ND)and rolling direction(RD)plane,was occasionally observed after the welding of thick plates,resulting in premature material failure.A vertically metal-inert gas(MIG)-welded laminar tearing component of a 30 mm thick plate was analyzed to determine the factors associated with this phenomenon.The texture,residual stress,microhardness,and tensile properties were also investigated.The results indicated that the crack extended along the RD as a transcrystalline fracture and terminated at the BM.The grains near the crack grew preferentially in the(001)crystal direction.Furthermore,the tensile strength(83 MPa)and elongation(6.8%)in the RD were relatively higher than those in the ND.In particular,the primary factors for crack initiation include stronger texture,higher dislocation density,increased Al_(7)Cu_(2)Fe phases,lower proportion of small-angle grain boundaries,and varying grain sizes in different regions,leading to the fragile microstructure.The higher residual stress of the BM promotes the formation and extension of cracks.The restraining force due to fixation and welding shrinkage force transformed the crack into laminar tearing.Preventive measures of laminar tearing were also proposed.展开更多
In this paper,the work hardening and softening behavior of AZ31 magnesium alloy sheets by hard plate accumulative roll bonding(HP-ARB)process in a specific temperature range was studied for the first time,and the cycl...In this paper,the work hardening and softening behavior of AZ31 magnesium alloy sheets by hard plate accumulative roll bonding(HP-ARB)process in a specific temperature range was studied for the first time,and the cyclic stress relaxation test,EBSD,TEM and other characterization methods were used.When the rolling temperature is 350℃,the grain size of magnesium sheets is refined to 4.32(±0.36)μm on average,and it shows an excellent combination of strength and plasticity.The tensile strength reaches 307(±8.52)MPa and the elongation is 12.73(±0.84)%.At this time,the curve of work hardening rate decreases smoothly and the degree of hardening is the lowest,and the amplitude of stress drop △σ_(p) in work softening test is the smallest with the increase of cycle times,which shows that the well coordination between work hardening and softening behavior has been achieved.Research has found that the combined effect of grain boundary strengthening and fine grain strengthening enhances the yield and tensile strength of magnesium sheets after three passes HP-ARB process at 350℃.This is attributed to the high degree of dislocation slip opening in the pyramidal surfaceand<c+a>,which not only coordinates the c-axis strain of the entire grain,but also promotes the slip transfer of dislocations in the fine-grained region,significantly improving the elongation of the sheets.This study provides a new idea for the forming and manufacturing of high performance magnesium alloy sheets.展开更多
On January 7,2025,01:05:15 UTC(9:05 a.m.local time)southern Tibet was rocked by a M_(W)7.1 earthquake(M_(W)=moment magnitude,USGS)centered(28.639°N 87.361°E)in the Lhasa Block north of the India/Eurasia Plat...On January 7,2025,01:05:15 UTC(9:05 a.m.local time)southern Tibet was rocked by a M_(W)7.1 earthquake(M_(W)=moment magnitude,USGS)centered(28.639°N 87.361°E)in the Lhasa Block north of the India/Eurasia Plate boundary,in a remote area about 180 km SW of Xigaze,in Dingri County of Shigatse of the Xizang Autonomous Region(Figure 1).展开更多
For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattic...For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it.For this purpose,the partial differential equations of motion have been derived based on the first-order shear deformation theory,employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations.Then,the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation(Duffing equation)by applying the Galerkin method.From the solution of this equation,the natural frequencies are extracted.Then,to calculate the non-linear frequencies of the plate,the non-linear equation of the plate has been solved analytically using the method of multiple scales.Finally,the effect of some critical parameters of the system,such as the thickness,height,and different angles of the stiffeners on the linear and nonlinear frequencies,has been analyzed in detail.To confirmthe solution method,the results of this research have been compared with the reported results in the literature and finite elements in ABAQUS,and a perfect match is observed.The results reveal that the geometry and configuration of core ribs strongly affect the natural frequencies of the plate.展开更多
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
基金Funded by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(No.2023YFB4204302)。
文摘Ceramic thin plates were prepared using kaolin,potassium sodium feldspar and quartz powder as the main raw materials and kaolin,α-Al_(2)O_(3),MoO_(3) and AlF_(3)·3H_(2)O as additives.The experiment examined the effects of different additives on mullite formation,as well as the microstructure and properties of the ceramic thin plates.Additionally,the study explored the toughening and strengthening mechanisms induced by the additives,providing a theoretical foundation for further optimizing the toughness of ceramic thin plates.The results showed that the D4 sample fired at 1220℃(with an addition of 20 wt% α-Al_(2)O_(3))exhibited the best performance,with a water absorption rate of 0.07%,apparent porosity of 0.18%,bulk density of 2.75 g·cm^(-3),firing shrinkage of 12.76%,bending strength reaching 101.93 MPa,and fracture toughness of 2.51 MPa·m^(1/2).As the amount ofα-Al_(2)O_(3) additive increased,the ceramic thin plates exhibited a greater abundance of short rod-like mullite and corundum grains,which were tightly packed together,forming a framework for the ceramic thin plates.This microstructure enhanced pathways for crack propagation,dispersed internal stresses,and increased fracture surface energy,resulting in significant improvements in both strength and fracture toughness of the ceramic thin plates.
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
基金supported by the National Natural Science Foundation of China(Nos.U2167202,12225504,12005276)the Natural Science Foundation of Shandong Province(No.ZR2024QA172)the Fundamental Research Funds of Shandong University.
文摘A 32-channel charge-sensitive amplifier(CSA)is designed for fast timing in the delay-line readout of a parallel plate avalanche counter(PPAC)array.It is realized on a PCB with operational amplifiers and other discrete components.Each channel consists of an integrator,a pole-zero cancellation net,and a linear amplification stage,which can be adapted to accommodate either positive or negative input signals.The RMS equivalent input noise charges are 3.3 fC,the conversion gains are approximately±2 mV∕fC,and the intrinsic time resolution reaches 32 ps.In the prototype PPAC application,the CSA performs as well as the commercial FTA820A amplifier,providing a position resolution as good as 0.17 mm,and exhibiting reliable stability during several hours of continuous data acquisition.
基金supported by the National Natural Science Foundation of China (42473063)Guike AD24010023, the Seventh Guangxi Zhuang Autonomous Region Bagui Scholars Program (to LIU Xijun)the Guangxi Natural Science Foundations of China (2025GXNSFBA069054)
文摘High-Mg andesites(HMAs)typically originate in subduction-related tectonic settings,including active continental margins and island arcs,and studies of HMAs can constrain the tectonic evolution of the South China Block and Paleo-Tethyan Ocean.This paper presents new chronological and geochemical data for high-Mg gabbroic diorites in the Funing area,southern South China.The gabbroic diorites yield ages of 254-249 Ma,and have moderate SiO2 contents(51.3%-57.8%),high MgO contents(4.6%-10.2%)and Mg^(#)values(52-75),enrichment in large-ion lithophile elements and light rare earth elements,and depletion in high-field-strength elements-collectively displaying geochemical signatures typical of sanukites.The gabbroic diorites have radiogenic initial Sr and Pb isotopic compositions,and negativeεNd(t)andεHf(t)values.These characteristics distinguish the Funing gabbroic diorites from subduction-related igneous rocks in the Paleo-Pacific tectonic domain.Instead,they are isotopically similar to HMAs and basalts along the Paleo-Tethys suture.We propose the high-Mg gabbroic diorites and basaltic andesites in Funing area share a common mantle source,linked to subduction and rollback of the Paleo-Tethyan plate beneath the South China Block,which triggered back-arc rifting and partial melting of the metasomatized lithospheric mantle during the Late Permian to Early Triassic.
基金supported by the National Natural Science Foundation of China(Grant No.42472258)the Shandong Provincial Natural Science Foundation for Excellent Young Scholars(Grant No.ZR2023YQ036).
文摘A wealth of geological and geochemical evidence indicates that plate tectonics was initiated in the Archean,though its style differing from that in the Phanerozoic,largely due to higher temperatures of convective mantle.Understanding the specific characteristics for the operation of ancient plate tectonics is critical for deciphering the formation and evolution of continental crust on early Earth,as well as the progressive development of Earth’s habitability.Through an in-depth analysis of geology and geochemistry for two events of late Archean crustal growth in the North China Craton,this study suggests that Archean plate tectonics would likely undergo the gradual evolution from immature to mature phases.The North China Craton experienced two major episodes of crustal growth at~2.9-2.7 and~2.6-2.5 Ga,respectively,represented by peaks in isotopic model ages of Archean felsic gneisses and widespread mafic rocks in greenstone belts.Although the preserved mafic rocks in greenstone belts generally exhibit arc-like trace element signatures,the early mafic crust formed at~2.9-2.7 Ga is limited in volume,with most of it having been reworked within several hundred million years.Tonalite-trondhjemite-granodiorite(TTG),produced by partial melting of such mafic crust,show zircon Hf-O isotope compositions indicative of sources consisting of seawater-hydrothermally altered oceanic crustal rocks with varying ages,suggesting that the early mafic crust was likely dominated by oceanic basalts.The medium-to low-pressure signatures of TTG rocks further imply that the oceanic crust was not subducted deeply to mantle depths,but instead was accreted to the margin of proto-continental nuclei due to aborted subduction.In contrast,the~2.6-2.5 Ga crustal growth event preserved a greater volume of mafic rocks.For these mafic rocks,the enrichment of incompatible elements correlates with water contents estimated from whole-rock major elements,indicating that their arc-like trace element features were associated with fluid metasomatism of the source region.Integrated with regional geological evidence from~2.5 Ga,such as ophiolites containing ultrahigh-pressure mineral inclusions and eclogite-facies remnants of oceanic crust,these observations suggest that modern-style plate subduction was likely in operation by the end of the Late Archean.Therefore,the modern plate tectonics regime did not emerge abruptly,but underwent a gradual evolution controlled by the thermal state of plate margins.It is this evolving tectonic regime that drove the significant crustal growth during the Archean.The two distinct episodes of crustal growth ultimately led to the formation of the North China Craton.
基金supported by Guangdong Major Project of Basic and Applied Basic Research, China (No. 2020B0301030006)Fundamental Research Funds for the Central Universities, China (No. SWU-XDJH202313)+1 种基金Chongqing Postdoctoral Science Foundation Funded Project, China (No. 2112012728014435)the Chongqing Postgraduate Research and Innovation Project, China (No. CYS23197)。
文摘A new method was proposed for preparing AZ31/1060 composite plates with a corrugated interface,which involved cold-pressing a corrugated surface on the Al plate and then hot-pressing the assembled Mg/Al plate.The results show that cold-pressing produces intense plastic deformation near the corrugated surface of the Al plate,which promotes dynamic recrystallization of the Al substrate near the interface during the subsequent hot-pressing.In addition,the initial corrugation on the surface of the Al plate also changes the local stress state near the interface during hot pressing,which has a large effect on the texture components of the substrates near the corrugated interface.The construction of the corrugated interface can greatly enhance the shear strength by 2−4 times due to the increased contact area and the strong“mechanical gearing”effect.Moreover,the mechanical properties are largely depended on the orientation relationship between corrugated direction and loading direction.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by National Natural Science Foundation of China(No.12402465)Sichuan Science and Technology Program(No.2023NSFSC1284)。
文摘We investigate the effects of projectile material on high-speed penetration/perforation of Inconel 718 alloy(IN718)plates.High-speed ballistic impact tests are conducted on 2 mm-thickness IN718 plates with 5-mm-diameter stainless steel 304(SS304),Ti alloy TC4,and Al alloy AA1060 spherical projectiles.The impact processes are captured with high-speed photography.Optical and scanning electron microscopy and laser scan are conducted on recovered projectiles and targets.Finite element models of the ballistic impact are established based on the coupled Eulerian-Lagrangian algorithm with the Johnson-Cook constitutive model and failure criterion,and can well reproduce the experimental results.The experimental and simulated data related to projectile dynamics,and the geometries of postmortem projectiles and bullet holes are analyzed with phenomenological models.Projectile velocity evolution can be described with hydrodynamic models of penetration.Dimensional analysis reveals a universal relationship between the bullet hole expansion coefficient and the normalized dynamic pressure,regardless of the projectile material.However,the projectile material does affect projectile deformation,bullet hole size,and energy absorption of target.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2603).
文摘A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order time derivatives.The proposed scheme attains third-order temporal accuracy and is rigorously validated through stability and convergence analyses for both scalar and coupled systems.Its effectiveness is demonstrated by simulating unsteady Eyring-Prandtl non-Newtonian nanofluid flow over a Riga plate with coupled heat and mass transfer under electromagnetic actuation.The physical model accounts for Brownian motion and thermophoresis,and the nanofluid considered is a Prandtl-type non-Newtonian base fluid containing suspended nanoparticles,with heat and mass transport governed by coupled momentum,energy,and concentration equations.Numerical simulations are performed over practically relevant parameter ranges,with the Reynolds number fixed at Re=5 and the Prandtl number set to Pr=3 to represent moderate inertial and thermal diffusion effects typical of nanofluid transport systems.To enhance computational efficiency,an artificial neural network(ANN)-based surrogate model is developed to predict the skin friction coefficient and local Sherwood number as functions of Reynolds number,Prandtl number,Schmidt number,Brownian motion,and thermophoresis parameters.The training dataset is generated entirely from high-fidelity numerical simulations produced by the proposed hybrid scheme.The data are systematically partitioned into 70%for training,15%for validation,and 15%for testing,ensuring reliable generalization.Regression analysis yields a near-unity correlation coefficient(R≈0.99),while error histograms exhibit tightly clustered residuals around zero,confirming high predictive accuracy.Furthermore,a benchmark convergence study using Stokes’first problem demonstrates that the proposed scheme consistently achieves lower global error norms than the classical Runge–Kutta method for identical spatial and temporal resolutions.Overall,this study introduces a novel computational intelligence framework that integrates high-order numerical solvers with machine learning,offering a robust and time-efficient tool for advanced modeling and real-time prediction of non-Newtonian nanofluid transport phenomena under electromagnetic flow control.
基金Project supported by the National Natural Science Foundation of China(Nos.12272056 and 11832002)。
文摘With the continuous increase in performance requirements for power systems in the aerospace and low-altitude economy sectors,designing lightweight and highstrength blade structures with excellent dynamic characteristics has become critical.This paper puts forward a dynamic model for a rotating functionally graded graphenereinforced(FG-GPR)sandwich metal porous cantilever pre-twisted plate(PTP),aiming to analyze its natural vibration characteristics.To this end,the mixture principle and the revised Halpin-Tsai model are used to determine the parameters of graphene and porosity distributions in the core layer.With the classical plate theory,the Rayleigh-Ritz method,and the polynomials,the dynamic equations are derived to solve for the free vibration mode shapes and frequencies of the rotating FG-GPR sandwich metal porous cantilever PTP.The comparison of natural frequencies and mode shapes with available literature results confirms the precision of the theoretical formulation and numerical computations.The bending stiffnesses are analyzed.Finally,the effects of different graphene/pore distributions,length-to-thickness/width ratios,layer thickness ratios,twist angles,and rotational speeds on the natural frequencies of the system are systematically investigated.
基金supported by the National Natural Science Foundation of China(Grant Nos.52271307,52061135107,52192692,11802025)the Liao Ning Excellent Youth Fund Program(Grant No.2023JH3/10200012)+1 种基金the Liao Ning Revitalization Tal-ents Program(Grant No.XLYC1908027)the Fundamental Research Funds for the Central Universities(Grant Nos.DUT20RC(3)025,DUT20TD108,DUT20LAB308)。
文摘In order to investigate the penetration performance of Linear-Shaped Charge(LSC),Embowed LinearShaped Charge(ELSC),and Embowed Linear Explosively Formed Projectile(ELEFP)on T-shaped stiffened plates,a series of near-field air-burst experiments are conducted.The damage modes and characteristics of the target plates are compared and analyzed.Each flat plate section is completely punctured,resulting in a penetration hole.The damage modes induced by the three charge types on the stiffened plate structure are consistent,characterized by shear failure in the central region of the flat plate due to penetration by the penetrator,localized plastic deformation of the flat plate,and local penetration failure resulting from partial perforation of the central stiffener.The penetration lengths caused by ELSC and ELEFP are 45.1%and 46.1% larger than that of LSC,while the half-width of the penetration hole generated by ELEFP is 54.2% and 24.7% smaller than that of ELSC and LSC,respectively.The penetration height caused by ELEFP are 17.5%and 62.1% larger than that of ELSC and LSC,respectively.The stiffener effectively segments the damage area,enhancing the local structural strength and limiting the extent of plastic deformation in the flat plate section.The comparative results show that the ELSC proves to be more effective for efficient large-scale damage,and ELEFP is more suitable for achieving efficient localized damage.
基金supported by the National Key R&D Program of China (No. 2018YFA0707300)the National Natural Science Foundation of China (No. 52374376)the Introduction Plan for High end Foreign Experts, China (No. G2023105001L)。
文摘Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective.
基金supported by the National Key Re-search and Development Program of China(No.2022YFB4002100)the National Natural Science Foundation of China(No.52271136)the Natural Science Foundation of Shaanxi Province(Nos.2019TD-020 and 2021JC-06).
文摘Proton exchange membrane water electrolysis(PEMWE)is one of the most promising strategies to pro-duce green hydrogen energy,and it is crucial to exploit highly conductive and good corrosion-resistant coatings on bipolar plates(BPs),one of the core components in PEMWE cells.In this work,NbN coatings are deposited on Ti BPs by magnetron sputtering to improve the corrosion resistance and conductivity,for which the critical process parameters,such as the working pressure,partial nitrogen pressure and de-position temperature are well optimized.It is found that the compact microstructure,highly conductive δ-NbN and uniform nanoparticles play a dominant role in the synergistic improvement of the corrosion resistance and electrical conductivity of NbN coatings.The optimized NbN coatings exhibit excellent cor-rosion resistance with the low corrosion current density of 1.1×10^(-8) A cm^(-2),a high potential value of-0.005 V vs.SCE and a low ICR value of 15.8 mΩcm2@1.5 MPa.Accordingly,NbN coatings can be a promising candidate for the development of the low-cost and high-anti-corrosion Ti BPs of PEMWE.
基金Key R&D Plan of Shaanxi Province(2021LLRH-05-09)Shaanxi Province Youth Talent Support Program Project(CLGC202234)Sponsored by Innovative Pilot Platform for Layered Metal Composite Materials(2024CX-GXPT-20)。
文摘Zirconium-titanium-steel composite plate with the size of 2500 mm×7800 mm×(3+0.7+22)mm was prepared by explosive welding+rolling method,and its properties were analyzed by ultrasonic nondestructive testing,phased array waveform shape,interface structure shape,electronic scanning,and mechanical property testing.Results show that the rolling temperature of zirconiumtitanium complex should be controlled at 760°C,and the rolling reduction of each pass should be controlled at 10%–25%.The explosive velocity to prepare zirconium-titanium-steel composite plates should be controlled at 2450–2500 m/s,the density should be 0.78 g/cm3,the stand-off height should be 12 mm,and the explosive height of Zone A and Zone B should be 45–50 mm.Explosive welding combined with rolling method reduces the impact of explosive welding and multiple heat treatment on material properties.Meanwhile,the problems of surface wrinkling and cracking,which occur during the preparation process of large-sized zirconiumtitanium-steel composite plate,can be solved.
基金Opening Foundation of Key Laboratory of Explosive Energy Utilization and Control,Anhui Province(BP20240104)Graduate Innovation Program of China University of Mining and Technology(2024WLJCRCZL049)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_2701)。
文摘Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.
基金supported by the National Key Research and Development Program of China(No.SQ2021YFF 0600011).
文摘7039 Al alloys are widely used in armor vehicles,given the material’s high specific strength and fracture toughness.However,laminar tearing in the thickness plane of the base metal(BM),specifically in the normal direction(ND)and rolling direction(RD)plane,was occasionally observed after the welding of thick plates,resulting in premature material failure.A vertically metal-inert gas(MIG)-welded laminar tearing component of a 30 mm thick plate was analyzed to determine the factors associated with this phenomenon.The texture,residual stress,microhardness,and tensile properties were also investigated.The results indicated that the crack extended along the RD as a transcrystalline fracture and terminated at the BM.The grains near the crack grew preferentially in the(001)crystal direction.Furthermore,the tensile strength(83 MPa)and elongation(6.8%)in the RD were relatively higher than those in the ND.In particular,the primary factors for crack initiation include stronger texture,higher dislocation density,increased Al_(7)Cu_(2)Fe phases,lower proportion of small-angle grain boundaries,and varying grain sizes in different regions,leading to the fragile microstructure.The higher residual stress of the BM promotes the formation and extension of cracks.The restraining force due to fixation and welding shrinkage force transformed the crack into laminar tearing.Preventive measures of laminar tearing were also proposed.
基金supported by the Natural Science Foundation of Heilongjiang Province(No.JQ2022E004).
文摘In this paper,the work hardening and softening behavior of AZ31 magnesium alloy sheets by hard plate accumulative roll bonding(HP-ARB)process in a specific temperature range was studied for the first time,and the cyclic stress relaxation test,EBSD,TEM and other characterization methods were used.When the rolling temperature is 350℃,the grain size of magnesium sheets is refined to 4.32(±0.36)μm on average,and it shows an excellent combination of strength and plasticity.The tensile strength reaches 307(±8.52)MPa and the elongation is 12.73(±0.84)%.At this time,the curve of work hardening rate decreases smoothly and the degree of hardening is the lowest,and the amplitude of stress drop △σ_(p) in work softening test is the smallest with the increase of cycle times,which shows that the well coordination between work hardening and softening behavior has been achieved.Research has found that the combined effect of grain boundary strengthening and fine grain strengthening enhances the yield and tensile strength of magnesium sheets after three passes HP-ARB process at 350℃.This is attributed to the high degree of dislocation slip opening in the pyramidal surfaceand<c+a>,which not only coordinates the c-axis strain of the entire grain,but also promotes the slip transfer of dislocations in the fine-grained region,significantly improving the elongation of the sheets.This study provides a new idea for the forming and manufacturing of high performance magnesium alloy sheets.
文摘On January 7,2025,01:05:15 UTC(9:05 a.m.local time)southern Tibet was rocked by a M_(W)7.1 earthquake(M_(W)=moment magnitude,USGS)centered(28.639°N 87.361°E)in the Lhasa Block north of the India/Eurasia Plate boundary,in a remote area about 180 km SW of Xigaze,in Dingri County of Shigatse of the Xizang Autonomous Region(Figure 1).
文摘For the first time,the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work.The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it.For this purpose,the partial differential equations of motion have been derived based on the first-order shear deformation theory,employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations.Then,the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation(Duffing equation)by applying the Galerkin method.From the solution of this equation,the natural frequencies are extracted.Then,to calculate the non-linear frequencies of the plate,the non-linear equation of the plate has been solved analytically using the method of multiple scales.Finally,the effect of some critical parameters of the system,such as the thickness,height,and different angles of the stiffeners on the linear and nonlinear frequencies,has been analyzed in detail.To confirmthe solution method,the results of this research have been compared with the reported results in the literature and finite elements in ABAQUS,and a perfect match is observed.The results reveal that the geometry and configuration of core ribs strongly affect the natural frequencies of the plate.
