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 study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were i...In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were investigated. The results show that the optimal bonding strength is up to 20 MPa with a reduction ratio of 40 % and rolling temperature of 400 ℃, superior than that in other one-pass rolling studies with regard to thin lami- nated plates. In addition, a favorable property is achieved with the annealing temperature of 250-300 ℃ or annealing time of 1.5 h. When the annealing temperature exceeds 300 ℃ or annealing time exceeds 1.5 h, respectively, the bonding strength of Al/Mg/Al plate decreases. The scan- ning electron microscopy （SEM） and energy-dispersive spectroscopy （EDS） analyses suggest that the appearance of thin diffusion layers between Al and Mg interfaces is helpful to improve the bonding strength, while the presence of thick diffusion layer would reduce the bonding strength greatly.展开更多
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This fu...The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.展开更多
As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been co...As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.展开更多
The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave e...The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.展开更多
The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic f...The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic fields is proposed by taking the summation of the magnetic energy of the magnetic system and the strain energy of the elastic plates. We present a variational principle for the problem by choosing the variations of magnetic potential and deflection as independent variates each other. Based on the principle, not only are the simultaneous governing equations for magnetic fields and deformation of structures deduced, but also a general expression of magnetic force acting on the plates is gained, which makes it possible to commonly simulate the distinct two experiments of magnetoelastic interaction in a theoretical model. Thus, it can be used to theoretical prediction of the magnetoelastic interaction of ferromagnetic plates in a complex environment of applied magnetic fields.展开更多
In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of ser...In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.展开更多
We demonstrate eftlcient generation of continuous spectrum centered at 40Ohm from solid thin plates. By frequency doubling of 0.8m J, 3Ors Ti：sapphire laser pulses with a BBO crystal, 0.2m J, 33fs laser pulses at 400...We demonstrate eftlcient generation of continuous spectrum centered at 40Ohm from solid thin plates. By frequency doubling of 0.8m J, 3Ors Ti：sapphire laser pulses with a BBO crystal, 0.2m J, 33fs laser pulses at 400nm are generated. Focusing the 400-nm pulses into 7 thin fused silica plates, we obtain 0.15mJ continuous spectrum covering 350-450 nm. After compressing by 3 pairs of chirped mirrors, 0. 12 m J, 8.6 fs pulses are achieved. To the best of our knowledge, this is the first time that sub-10-fs pulses centered at 400nm are generated by solid thin plates, which shows that spectral broadening in solid-state materials works not only at 800nm but also at different wavelengths.展开更多
In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by...In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].展开更多
Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible eleme...Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.展开更多
The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compac...The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compact and economical. A pulse with a broadened spectrum from 670 to 900 nm is generated by utilizing two 0.18-mm-thick fused silica glass plates and is used to provide two input beams for the CFWM process.The new frequency components generated from the self-phase modulation effect in the two thin glass plates contribute to the broadening of the total spectral range of the generated multicolored sidebands.展开更多
A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundatio...A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence...Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.展开更多
Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sin...Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.展开更多
Vibration is a common strategy for aquatic organisms to achieve their life activities,especially at the air-water interface.For the locomotion of small creatures,the organs with plate features are often used on water ...Vibration is a common strategy for aquatic organisms to achieve their life activities,especially at the air-water interface.For the locomotion of small creatures,the organs with plate features are often used on water surfaces,which inspires relevant studies about using thin plates for robot propulsions.However,the influence of the general deformations of thin plates on the generated flow fields has not been considered.Here,a comprehensive investigation is conducted about the flow fields that arose by vibrations of thin plates and the potential as locomotion strategies are explored.It is discovered that as thin plates are subjected to vibration excitations on the water surface,the produced flow fields are mainly determined by the vibration shapes,and the influence rules of plate deformations on the flow fields are identified.The main factors producing asymmetric flow fields are analyzed to realize the morphology control of the flow fields.Then,to determine effective locomotion strategies on the water surface,the flow fields stimulated by integrated vibration exciters are explored,and 2 water surface robots are developed consequentially.which exhibit superior motion performance.This work reveals the basic rules of the vibration-induced-flow mechanism by thin plates and establishes new locomotion strategies for aquatic robots.展开更多
In this paper,we utilize Physics-Informed Neural Networks(PINNs)without any labeled data to solve the fourth-order partial differential equation governing the bending of thin plates.We meticulously formulate and apply...In this paper,we utilize Physics-Informed Neural Networks(PINNs)without any labeled data to solve the fourth-order partial differential equation governing the bending of thin plates.We meticulously formulate and apply our framework to the bending problem of elastic thin plates.Our findings indicate that defining each solution variable through an independent network,meaning without shared network parameters,yields superior performance compared to a single-network model with multiple outputs.During the training process,we discovered that more accurate results were achieved by adjusting the network architecture to strictly satisfy the boundary conditions,rather than incorporating them as part of the loss function.Remarkably,the PINNs are capable of obtaining relatively good results without the use of any labeled data during training,irrespective of whether soft or hard constraints are applied.In the end,the neural network’s predictions for plate deflection,stress,strain,bending,and shear force all have errors less than 5% compared to the analytical solutions.In the algorithm implementation phase,we leverage the Python library DeepXDE,which facilitates the training of PINNs by providing an efficient and expedited process.展开更多
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.
基金financially supported by the National Natural Science Foundation of China (Nos.51301118 and 51175363)the Specialized Research Fund for the Doctoral Program of Higher Education (No.20050112001)the Natural Science Foundation of Shanxi Province (No. 2006011051)
文摘In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were investigated. The results show that the optimal bonding strength is up to 20 MPa with a reduction ratio of 40 % and rolling temperature of 400 ℃, superior than that in other one-pass rolling studies with regard to thin lami- nated plates. In addition, a favorable property is achieved with the annealing temperature of 250-300 ℃ or annealing time of 1.5 h. When the annealing temperature exceeds 300 ℃ or annealing time exceeds 1.5 h, respectively, the bonding strength of Al/Mg/Al plate decreases. The scan- ning electron microscopy （SEM） and energy-dispersive spectroscopy （EDS） analyses suggest that the appearance of thin diffusion layers between Al and Mg interfaces is helpful to improve the bonding strength, while the presence of thick diffusion layer would reduce the bonding strength greatly.
文摘The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.
基金This project was supported in part by the National Natural Science Foundation of ChinaFoundation of the SEdC of China for Returned Chinese Scholars from Abroad
文摘As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.
基金Project (Nos 10632020 and 90715006) supported by the National Natural Science Foundation of China
文摘The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.
文摘The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic fields is proposed by taking the summation of the magnetic energy of the magnetic system and the strain energy of the elastic plates. We present a variational principle for the problem by choosing the variations of magnetic potential and deflection as independent variates each other. Based on the principle, not only are the simultaneous governing equations for magnetic fields and deformation of structures deduced, but also a general expression of magnetic force acting on the plates is gained, which makes it possible to commonly simulate the distinct two experiments of magnetoelastic interaction in a theoretical model. Thus, it can be used to theoretical prediction of the magnetoelastic interaction of ferromagnetic plates in a complex environment of applied magnetic fields.
文摘In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11434016,11574384 and 11674386the National Key Basic Research Program of China under Grant Nos 2013CB922401 and 2013CB922402
文摘We demonstrate eftlcient generation of continuous spectrum centered at 40Ohm from solid thin plates. By frequency doubling of 0.8m J, 3Ors Ti：sapphire laser pulses with a BBO crystal, 0.2m J, 33fs laser pulses at 400nm are generated. Focusing the 400-nm pulses into 7 thin fused silica plates, we obtain 0.15mJ continuous spectrum covering 350-450 nm. After compressing by 3 pairs of chirped mirrors, 0. 12 m J, 8.6 fs pulses are achieved. To the best of our knowledge, this is the first time that sub-10-fs pulses centered at 400nm are generated by solid thin plates, which shows that spectral broadening in solid-state materials works not only at 800nm but also at different wavelengths.
文摘In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].
文摘Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.
基金supported by the National Natural Science Foundation of China (NSFC) (grants 61178006, 11274327and 61221064)the Recruitment Program of Global Youth Experts
文摘The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compact and economical. A pulse with a broadened spectrum from 670 to 900 nm is generated by utilizing two 0.18-mm-thick fused silica glass plates and is used to provide two input beams for the CFWM process.The new frequency components generated from the self-phase modulation effect in the two thin glass plates contribute to the broadening of the total spectral range of the generated multicolored sidebands.
基金Project supported by the Key Laboratory of Disaster Forecast and Control in Engineering,Ministry of Education of China the Key Laboratory of Diagnosis of Fault in Engineering Structures of Guangdong Province of China
文摘A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
文摘Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.
基金The Science Foundation of Ministry of Transport of the People's Republic of China(No.200731822301-7)
文摘Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.
基金supported by the National Natural Science Foundation of China(no.52225501)the State Key Laboratory of Robotics and System(HIT)(no.SKLRS-2022-ZM-01).
文摘Vibration is a common strategy for aquatic organisms to achieve their life activities,especially at the air-water interface.For the locomotion of small creatures,the organs with plate features are often used on water surfaces,which inspires relevant studies about using thin plates for robot propulsions.However,the influence of the general deformations of thin plates on the generated flow fields has not been considered.Here,a comprehensive investigation is conducted about the flow fields that arose by vibrations of thin plates and the potential as locomotion strategies are explored.It is discovered that as thin plates are subjected to vibration excitations on the water surface,the produced flow fields are mainly determined by the vibration shapes,and the influence rules of plate deformations on the flow fields are identified.The main factors producing asymmetric flow fields are analyzed to realize the morphology control of the flow fields.Then,to determine effective locomotion strategies on the water surface,the flow fields stimulated by integrated vibration exciters are explored,and 2 water surface robots are developed consequentially.which exhibit superior motion performance.This work reveals the basic rules of the vibration-induced-flow mechanism by thin plates and establishes new locomotion strategies for aquatic robots.
基金supported by the Major scientific and technological innovation projects in Shandong Province(Grant No.2019SDZY01)the Science and Technology Innovation Development Project of Tai’an City(Grant No.2022GX075).
文摘In this paper,we utilize Physics-Informed Neural Networks(PINNs)without any labeled data to solve the fourth-order partial differential equation governing the bending of thin plates.We meticulously formulate and apply our framework to the bending problem of elastic thin plates.Our findings indicate that defining each solution variable through an independent network,meaning without shared network parameters,yields superior performance compared to a single-network model with multiple outputs.During the training process,we discovered that more accurate results were achieved by adjusting the network architecture to strictly satisfy the boundary conditions,rather than incorporating them as part of the loss function.Remarkably,the PINNs are capable of obtaining relatively good results without the use of any labeled data during training,irrespective of whether soft or hard constraints are applied.In the end,the neural network’s predictions for plate deflection,stress,strain,bending,and shear force all have errors less than 5% compared to the analytical solutions.In the algorithm implementation phase,we leverage the Python library DeepXDE,which facilitates the training of PINNs by providing an efficient and expedited process.
