This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equat...This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equations are obtained based on the first order shear deformation theory（FSDT） with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction.A semi-analytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations.And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions.Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach.Afterwards,comprehensive studies on the FG plates rested on elastic foundation are presented.The effects of parameters,such as thickness-to-radius,material distribution,foundation stiffness parameters,different combinations of constraints at edges on the frequency,mode shape and modal stress are also investigated.展开更多
The superstructures of marine structures supported by the elastic legs and located in the splash zone will subject to violent wave slamming and vibrate consequently during storms. A series of model tests are carried o...The superstructures of marine structures supported by the elastic legs and located in the splash zone will subject to violent wave slamming and vibrate consequently during storms. A series of model tests are carried out to investigate the wave impacting on the open structures supported elastically. Three kinds of models with different natural frequencies are designed. The characteristics of the wave pressures on the three models are compared. The durations of the uplift forces and the corresponding accelerations of the structure during wave impact are analyzed simultaneously. The distributions of the peak impact pressures on the subfaces of the plates with different supporting stiffness are given. The relationship between the uplift force on the three models and the relative clearance are obtained. The spectral properties of the slamming loads on the three different structures are compared, The experimental results indicate that the behaviors of the impact pressures, the uplift forces and accelerations of the plates with small natural frequencies are obviously different from those of the plates with larger natural frequencies within the range of the experimental parameters.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
This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotation. The Gram-Sch...This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotation. The Gram-Schmidt process has been used to generate two-dimensional boundary characteristic orthogonal polynomials, which have been used in the Rayleigh-Ritz method to study the problem. The lowest three frequencies have been computed for various values of nonhomogeneous parameters, thickness parameters, aspect ratio and flexibility parameters. A comparison of the results with those available in the literature has been made. Three-dimensional mode shapes for the specified plate have been presented.展开更多
An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression.Both material and geometric non-linearities were conside...An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression.Both material and geometric non-linearities were considered in finite element(FE)analysis.The initial geometric imperfection of the plate was considered,while the residual stress introduced by welding was not considered.The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions,initial imperfection and mesh size.The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented.Then a new simple empirical formula for plate ultimate strength is developed,which includes the effect of the rotational restraint stiffness,rotational restraint stiffness,and aspect ratios.By applying the new formula and FE method to ship hull plates in real ships,a good coincidence of the results between these two methods is obtained,which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.展开更多
With the introduction of Poisson's ratio in the expression of Young's modulus,nearly all the theoretical values of the various elastic moduli for the alkaline earth metals and rare earth elements can be greatl...With the introduction of Poisson's ratio in the expression of Young's modulus,nearly all the theoretical values of the various elastic moduli for the alkaline earth metals and rare earth elements can be greatly refined, with the single exception of the theoreticalvalue of Young's modulus for Pr which is slightly increased This points to the validityof the new theory, that the bulk modulus is independent of the Poisson's ratio, and further that the valency electron structures of solids as determined by Yu's theory are correct.展开更多
This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is...This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.展开更多
This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external force...This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.展开更多
To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the para...To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.展开更多
Numerical simulations are performed to study the aeroelastic responses of an elastically suspended airfoil in transonic buffet flow, by coupling the unsteady Reynolds-averaged Navier- Stokes （RANS） equations and str...Numerical simulations are performed to study the aeroelastic responses of an elastically suspended airfoil in transonic buffet flow, by coupling the unsteady Reynolds-averaged Navier- Stokes （RANS） equations and structural motion equation. The current work focuses on the char- acteristic analysis of the lock-in phenomenon. Great attentions are paid to studying the frequency range of lock-in and the effects of the three parameters, namely the structural natural frequency, mass ratio and structural damping, on lock-in characteristic of the elastic system in detail. It is found that when the structural natural frequency is close to the buffet frequency, the coupling fre- quency of the elastic system is no longer equal to the buffet frequency, but keeps the same value as the structural natural frequency. The frequency lock-in occurs and stays present until the structural nature frequency is near the double buffet frequency. It means that the lock-in presents within a broad range, of which the lower threshold is near the buffet frequency, while the upper threshold is near the double buffet frequency. Moreover, the frequency range of lock-in is affected by mass ratio and structural damping. The lower the mass ratio and structural damping are, the wider the range of lock-in will be. The upper threshold of lock-in grows with the mass ratio and structural damping decreasing, but the lower threshold always keeps the same.展开更多
Usually,the stability analysis of pipes with pulsating flow velocities is for rigidly constrained pipes or cantilevered pipes.In this paper,the effects of elastic constraints on pipe stability and nonlinear responses ...Usually,the stability analysis of pipes with pulsating flow velocities is for rigidly constrained pipes or cantilevered pipes.In this paper,the effects of elastic constraints on pipe stability and nonlinear responses under pulsating velocities are investigated.A mechanical model of a fluid-conveying pipe under the constraints of elastic clamps is established.A partial differentialintegral nonlinear equation governing the lateral vibration of the pipe is derived.The natural frequencies and mode functions of the pipe are obtained.Moreover,the stable boundary and nonlinear steady-state responses of the parametric vibration for the pipe are established approximately.Furthermore,the analytical solutions are verified numerically.The results of this work reveal some interesting conclusions.It is found that the elastic constraint stiffness in the direction perpendicular to the axis of the pipe does not affect the critical flow velocity of the pipe.However,the constraint stiffness has a significant effect on the instability boundary of the pipe with pulsating flow velocities.Interestingly,an increase in the stiffness of the constraint increases the instable region of the pipe under parametric excitation.However,when the constraint stiffness is increased,the steady-state response amplitude of the nonlinear vibration for the pipe is significantly reduced.Therefore,the effects of the constraint stiffness on the instable region and vibration responses of the fluid-conveying pipe are different when the flow velocity is pulsating.展开更多
A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory.A structure of n parallel,elastically connected rectang...A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory.A structure of n parallel,elastically connected rectangular plates is of concern,whereby the motion is explained by a set of n coupled partial differential equations.The method involves a new change in variables to uncouple equations and form an equal system of n decoupled plates,while each is assumed to be elastically connected to the ground.The differential quadrature method is adopted to solve the decoupled equations.To unravel the original system,the inverse transform is applied.Decoupling the equations enables one to solve them based on the solution methods available for a single plate system.This also diminishes the computational costs of such problems.By considering different boundary conditions,a case study is run to present the method and to validate the results with its counterparts,for which excellent agreement is observed.Assessing the influence of dimensionless thickness,aspect ratio,and stiffness coefficients on the frequencies reveals the different effects of them at the low order of dimensionless natural frequencies in comparison with high orders and for different boundary conditions.展开更多
Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of con...Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.展开更多
The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in ...The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.展开更多
In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and ...In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and boundary conditions.Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity.For each nanorod component,its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials,with the aim to make all the spatial differential sufficiently continuous across each rod.All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix.Numerical results are presented for the particular cases of twonanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model.Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature.Based on the model established,influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed.This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.展开更多
Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundar...Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundary conditions are obtained by using the weighted residual method,while the governing equations of the nonlocal Kirchhoff plate model are known.A modified Fourier series method is applied to study the vibrational behaviors of elastically constrained nonlocal Kirchhoff plate models.The convergence and reliability of the modified Fourier series method is verified via comparison with the finite element method.A comprehensive parametric study is performed to show the influences of the boundary elastic constant,nonlocal parameter and initial stress on the vibrational behaviors of single-layered M0S2.The results should be good for the design of nanoresonators.展开更多
Oxygen carriers play a fundamental role in chemical looping combustion(CLC).Iron-based carriers have been extensively investigated owing to their abundance and environmentally friendly.However,the reactivity and separ...Oxygen carriers play a fundamental role in chemical looping combustion(CLC).Iron-based carriers have been extensively investigated owing to their abundance and environmentally friendly.However,the reactivity and separability of iron-based carriers require further enhancement.This study investigates the effect of the concentration of Mn doping on reactivity,elastic properties and magnetic properties based on density functional theory(DFT)calculations.Theoretical results demonstrate that Mn doping effectively enhances reactivity by reducing the oxygen vacancy formation energy(E_(vac))from 2.33 to 0.87 eV.However,Mn doping introduces HV/EV Ms lattice distortions that deteriorate elastic properties,thereby reducing wear resistance,as evidenced by a 54.54%decrease in the hardness-to-Young's modulus ratio(H_(v)/E_(v))forα-Fe_(2)O_(3)and an 83.33%reduction for Fe_(3)O_(4).Furthermore,Mn doping also modifies magnetic properties.The maximum of saturation magnetization(M_(s))of Fe_(3)O_(4)reaches 121.02 emu/g at 33.33%Mn doping concentration.Finally,systematic evaluation identifies 33.33%as the optimal Mn doping concentration,achieving a balance in enhanced reactivity,superior magnetic performance,and retained elastic stability.展开更多
The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometr...The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.展开更多
To investigate the influence of coarse aggregate parent rock properties on the elastic modulus of concrete,the mineralogical properties and stress-strain curves of granite and dolomite parent rocks,as well as the stre...To investigate the influence of coarse aggregate parent rock properties on the elastic modulus of concrete,the mineralogical properties and stress-strain curves of granite and dolomite parent rocks,as well as the strength and elastic modulus of mortar and concrete prepared with mechanism aggregates of the corresponding lithology,and the stress-strain curves of concrete were investigated.In this paper,a coarse aggregate and mortar matrix bonding assumption is proposed,and a prediction model for the elastic modulus of mortar is established by considering the lithology of the mechanism sand and the slurry components.An equivalent coarse aggregate elastic modulus model was established by considering factors such as coarse aggregate particle size,volume fraction,and mortar thickness between coarse aggregates.Based on the elastic modulus of the equivalent coarse aggregate and the remaining mortar,a prediction model for the elastic modulus of the two and three components of concrete in series and then in parallel was established,and the predicted values differed from the measured values within 10%.It is proposed that the coarse aggregate elastic modulus in highstrength concrete is the most critical factor affecting the elastic modulus of concrete,and as the coarse aggregate elastic modulus increases by 27.7%,the concrete elastic modulus increases by 19.5%.展开更多
Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformat...Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.展开更多
文摘This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equations are obtained based on the first order shear deformation theory（FSDT） with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction.A semi-analytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations.And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions.Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach.Afterwards,comprehensive studies on the FG plates rested on elastic foundation are presented.The effects of parameters,such as thickness-to-radius,material distribution,foundation stiffness parameters,different combinations of constraints at edges on the frequency,mode shape and modal stress are also investigated.
基金supported by the National Natural Science Foundation of China(Grant No.51179030)the Innovative Research Group National Natural Science Foundation of China(Grant No.51309056)
文摘The superstructures of marine structures supported by the elastic legs and located in the splash zone will subject to violent wave slamming and vibrate consequently during storms. A series of model tests are carried out to investigate the wave impacting on the open structures supported elastically. Three kinds of models with different natural frequencies are designed. The characteristics of the wave pressures on the three models are compared. The durations of the uplift forces and the corresponding accelerations of the structure during wave impact are analyzed simultaneously. The distributions of the peak impact pressures on the subfaces of the plates with different supporting stiffness are given. The relationship between the uplift force on the three models and the relative clearance are obtained. The spectral properties of the slamming loads on the three different structures are compared, The experimental results indicate that the behaviors of the impact pressures, the uplift forces and accelerations of the plates with small natural frequencies are obviously different from those of the plates with larger natural frequencies within the range of the experimental parameters.
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This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotation. The Gram-Schmidt process has been used to generate two-dimensional boundary characteristic orthogonal polynomials, which have been used in the Rayleigh-Ritz method to study the problem. The lowest three frequencies have been computed for various values of nonhomogeneous parameters, thickness parameters, aspect ratio and flexibility parameters. A comparison of the results with those available in the literature has been made. Three-dimensional mode shapes for the specified plate have been presented.
文摘An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression.Both material and geometric non-linearities were considered in finite element(FE)analysis.The initial geometric imperfection of the plate was considered,while the residual stress introduced by welding was not considered.The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions,initial imperfection and mesh size.The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented.Then a new simple empirical formula for plate ultimate strength is developed,which includes the effect of the rotational restraint stiffness,rotational restraint stiffness,and aspect ratios.By applying the new formula and FE method to ship hull plates in real ships,a good coincidence of the results between these two methods is obtained,which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.
文摘With the introduction of Poisson's ratio in the expression of Young's modulus,nearly all the theoretical values of the various elastic moduli for the alkaline earth metals and rare earth elements can be greatly refined, with the single exception of the theoreticalvalue of Young's modulus for Pr which is slightly increased This points to the validityof the new theory, that the bulk modulus is independent of the Poisson's ratio, and further that the valency electron structures of solids as determined by Yu's theory are correct.
文摘This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.
文摘This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LR18E050003)National Natural Science Foundation of China (Grant Nos. 51975523,51905481)+1 种基金Postdoctoral Preferred Funding Project of Zhejiang Province (Grant No. zj2019019)Open Foundation of the Key Laboratory of E&M,Ministry of Education&Zhejiang Province (Grant No. EM2019120102)
文摘To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.
基金supported by the project of the National Natural Science Foundation of China(No.11272262)
文摘Numerical simulations are performed to study the aeroelastic responses of an elastically suspended airfoil in transonic buffet flow, by coupling the unsteady Reynolds-averaged Navier- Stokes （RANS） equations and structural motion equation. The current work focuses on the char- acteristic analysis of the lock-in phenomenon. Great attentions are paid to studying the frequency range of lock-in and the effects of the three parameters, namely the structural natural frequency, mass ratio and structural damping, on lock-in characteristic of the elastic system in detail. It is found that when the structural natural frequency is close to the buffet frequency, the coupling fre- quency of the elastic system is no longer equal to the buffet frequency, but keeps the same value as the structural natural frequency. The frequency lock-in occurs and stays present until the structural nature frequency is near the double buffet frequency. It means that the lock-in presents within a broad range, of which the lower threshold is near the buffet frequency, while the upper threshold is near the double buffet frequency. Moreover, the frequency range of lock-in is affected by mass ratio and structural damping. The lower the mass ratio and structural damping are, the wider the range of lock-in will be. The upper threshold of lock-in grows with the mass ratio and structural damping decreasing, but the lower threshold always keeps the same.
基金the support of the National Science Fund for Distinguished Young Scholars(No.12025204)the Shanghai Municipal Education Commission(No.2019-01-07-00-09-E00018).
文摘Usually,the stability analysis of pipes with pulsating flow velocities is for rigidly constrained pipes or cantilevered pipes.In this paper,the effects of elastic constraints on pipe stability and nonlinear responses under pulsating velocities are investigated.A mechanical model of a fluid-conveying pipe under the constraints of elastic clamps is established.A partial differentialintegral nonlinear equation governing the lateral vibration of the pipe is derived.The natural frequencies and mode functions of the pipe are obtained.Moreover,the stable boundary and nonlinear steady-state responses of the parametric vibration for the pipe are established approximately.Furthermore,the analytical solutions are verified numerically.The results of this work reveal some interesting conclusions.It is found that the elastic constraint stiffness in the direction perpendicular to the axis of the pipe does not affect the critical flow velocity of the pipe.However,the constraint stiffness has a significant effect on the instability boundary of the pipe with pulsating flow velocities.Interestingly,an increase in the stiffness of the constraint increases the instable region of the pipe under parametric excitation.However,when the constraint stiffness is increased,the steady-state response amplitude of the nonlinear vibration for the pipe is significantly reduced.Therefore,the effects of the constraint stiffness on the instable region and vibration responses of the fluid-conveying pipe are different when the flow velocity is pulsating.
基金Iran National Science Foundation(INSF)under Grant No.97021731。
文摘A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory.A structure of n parallel,elastically connected rectangular plates is of concern,whereby the motion is explained by a set of n coupled partial differential equations.The method involves a new change in variables to uncouple equations and form an equal system of n decoupled plates,while each is assumed to be elastically connected to the ground.The differential quadrature method is adopted to solve the decoupled equations.To unravel the original system,the inverse transform is applied.Decoupling the equations enables one to solve them based on the solution methods available for a single plate system.This also diminishes the computational costs of such problems.By considering different boundary conditions,a case study is run to present the method and to validate the results with its counterparts,for which excellent agreement is observed.Assessing the influence of dimensionless thickness,aspect ratio,and stiffness coefficients on the frequencies reveals the different effects of them at the low order of dimensionless natural frequencies in comparison with high orders and for different boundary conditions.
基金supported by the Portuguese Foundation for Science and Tech-nology(FCT),under the project POCI 2010 and the PhD grant SFRH/BD/44696/2008
文摘Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.
基金Project supported by the Fundamental Research Funds for the Central Universities(FRF-BR-15-026A)the National Natural Science Foundation of China(No.10972029)
文摘The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave（the P wave） and incident transverse wave（the SV wave） are considered.
文摘In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and boundary conditions.Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity.For each nanorod component,its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials,with the aim to make all the spatial differential sufficiently continuous across each rod.All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix.Numerical results are presented for the particular cases of twonanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model.Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature.Based on the model established,influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed.This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.
基金We gratefully acknowledge the support from the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0037)State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and astronautics)under Grants MCMS-E-0120G01National Natural Science Foundation of China under Grants Nos.11925205 and 51921003,and the Fundamental Research Funds for the Central Universities of China.
文摘Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundary conditions are obtained by using the weighted residual method,while the governing equations of the nonlocal Kirchhoff plate model are known.A modified Fourier series method is applied to study the vibrational behaviors of elastically constrained nonlocal Kirchhoff plate models.The convergence and reliability of the modified Fourier series method is verified via comparison with the finite element method.A comprehensive parametric study is performed to show the influences of the boundary elastic constant,nonlocal parameter and initial stress on the vibrational behaviors of single-layered M0S2.The results should be good for the design of nanoresonators.
基金Supported by National Natural Science Foundation of China(50976032,51776070)。
文摘Oxygen carriers play a fundamental role in chemical looping combustion(CLC).Iron-based carriers have been extensively investigated owing to their abundance and environmentally friendly.However,the reactivity and separability of iron-based carriers require further enhancement.This study investigates the effect of the concentration of Mn doping on reactivity,elastic properties and magnetic properties based on density functional theory(DFT)calculations.Theoretical results demonstrate that Mn doping effectively enhances reactivity by reducing the oxygen vacancy formation energy(E_(vac))from 2.33 to 0.87 eV.However,Mn doping introduces HV/EV Ms lattice distortions that deteriorate elastic properties,thereby reducing wear resistance,as evidenced by a 54.54%decrease in the hardness-to-Young's modulus ratio(H_(v)/E_(v))forα-Fe_(2)O_(3)and an 83.33%reduction for Fe_(3)O_(4).Furthermore,Mn doping also modifies magnetic properties.The maximum of saturation magnetization(M_(s))of Fe_(3)O_(4)reaches 121.02 emu/g at 33.33%Mn doping concentration.Finally,systematic evaluation identifies 33.33%as the optimal Mn doping concentration,achieving a balance in enhanced reactivity,superior magnetic performance,and retained elastic stability.
基金Project supported by the National Natural Science Foundation of China(Nos.52405095,12272089,and 92360305)the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515110557)+4 种基金the Natural Science Foundation of Liaoning Province of China(No.2023-BSBA-102)the Open Fund of National Key Laboratory of Particle Transport and Separation Technology of China(No.WZKF-2024-6)the Open Project of Guangxi Key Laboratory of Automobile Components and Vehicle Technology of China(Nos.2024GKLACVTKF07 and 2024GKLACVTKF06)the Basic Research Projects of Liaoning Provincial Department of Education of China(No.JYTQN2023162)the Fundamental Research Funds for the Central Universities of China(No.N2403022)。
文摘The testing of large structures is limited by high costs and long cycles, making scaling methods an attractive solution. However, the scaling process of elastic rings introduces complexities in multi-parameter geometric distortions, leading to a diminution in the predictive accuracy of the distorted similitude. To address this challenge, this study formulates a novel set of scaling laws, tailored to account for the intricate geometric distortions associated with elastic rings. The proposed scaling laws are formulated based on the intrinsic deformation characteristics of elastic rings, rather than the traditional systemic governing equations. Numerical and experimental cases are conducted to assess the efficacy and precision of the proposed scaling laws, and the obtained results are compared with those achieved by traditional methods. The outcomes demonstrate that the scaling laws put forth by this study significantly enhance the predictive capabilities for deformations of elastic rings.
基金Funded by State Railway Administration Research Project(No.2023JS007)National Natural Science Foundation of China(No.52438002)+1 种基金Research and Development Programs for Science and Technology of China Railways Corporation(No.J2023G003)New Cornerstone Science Foundation through the XPLORER PRIZE。
文摘To investigate the influence of coarse aggregate parent rock properties on the elastic modulus of concrete,the mineralogical properties and stress-strain curves of granite and dolomite parent rocks,as well as the strength and elastic modulus of mortar and concrete prepared with mechanism aggregates of the corresponding lithology,and the stress-strain curves of concrete were investigated.In this paper,a coarse aggregate and mortar matrix bonding assumption is proposed,and a prediction model for the elastic modulus of mortar is established by considering the lithology of the mechanism sand and the slurry components.An equivalent coarse aggregate elastic modulus model was established by considering factors such as coarse aggregate particle size,volume fraction,and mortar thickness between coarse aggregates.Based on the elastic modulus of the equivalent coarse aggregate and the remaining mortar,a prediction model for the elastic modulus of the two and three components of concrete in series and then in parallel was established,and the predicted values differed from the measured values within 10%.It is proposed that the coarse aggregate elastic modulus in highstrength concrete is the most critical factor affecting the elastic modulus of concrete,and as the coarse aggregate elastic modulus increases by 27.7%,the concrete elastic modulus increases by 19.5%.
基金Supported by the National Natural Science Foundation of China(Grant Nos.62025104,62331005,and U22A2052)the Beijing Natural Science Foundation(Grant No.L242100).
文摘Background Computed tomography(CT) and cone-beam computed tomography(CBCT) image registration play pivotal roles in computer-assisted navigation for orthopedic surgery. Traditional methods often apply uniform deformation models, neglecting the biomechanical differences between rigid structures and soft tissues, which compromises registration accuracy, especially during significant bone displacements. Method To address this issue, we introduce RE-Reg, a rigid-elastic CT-CBCT image registration framework that jointly learns rigid bone motion and soft tissue deformation. RE-Reg incorporates a rigid alignment(RA) module to estimate global bone motion and an elastic deformation(ED) module to model soft tissue deformation, preserving bony structures through bone shape preservation(BSP) loss. Result Our comprehensive evaluation on publicly available datasets demonstrates that RE-Reg significantly outperforms existing methods in terms of registration accuracy and rigid bone structure preservation, achieving a 1.3% improvement in Dice similarity coefficient(DSC) and a 23% reduction in rigid bone deformation(%Δvol) compared with the best baseline. Conclusion This framework not only enhances anatomical fidelity but also ensures biomechanical plausibility and provides a valuable tool for image-guided orthopedic surgery. This code is available athttps://github.com/Zq-Huang/RE-Reg.
