Odd elasticity introduces active moduli to the antisymmetric components of the elastic tensor,which describe the asymmetric coupling between different deformation modes in a medium and quantify the work extracted duri...Odd elasticity introduces active moduli to the antisymmetric components of the elastic tensor,which describe the asymmetric coupling between different deformation modes in a medium and quantify the work extracted during quasi-static strain cycles.The introduction of active moduli renders the elastic tensor non-Hermitian,breaking the Maxwell-Betti reciprocity and enabling the observation of phenomena that cannot occur in traditional passive media.Here,we develop an analytical dynamic model for odd elastic circular plates to investigate the effects of odd elasticity on motion in rotationally symmetric geometries.We report a novel nonreciprocal rotating wave and explore the effects of different odd elastic moduli on chiral deformation.Nonreciprocal rotating waves represent a distinct dynamic mode,exhibiting unidirectional propagation with amplitude increasing or decreasing exclusively along a specific direction.The amplitude change during motion reveals the system’s non-conservation of energy.展开更多
A new dimensionless number is proposed for dynamic plastic deformation analysis of clamped circular plates under underwater explosion loads by introducing dimensional analysis method to the basic dynamical governing e...A new dimensionless number is proposed for dynamic plastic deformation analysis of clamped circular plates under underwater explosion loads by introducing dimensional analysis method to the basic dynamical governing equations of circular plates.The relation between dimensionless final plastic deformation of circular plates and the new dimensionless number is established based on massive underwater explosion test data.Meanwhile,comparative analysis was discussed with two other published dimensionless parameters which indicated the new dimensionless number proposed in this paper is more effective and extensive to predict the dynamic plastic response of circular plates under underwater explosion condition.展开更多
New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bendin...New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.展开更多
The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurca...The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.展开更多
A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetr...A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and procedure of the technique mentioned here. The technique given here can also be used to solve large deflection problem of circular plates under other non-axisymmetrical loads and boundary conditions.展开更多
Based on the general theory of elastic plates which abandons Kirchhoff-Loveassunption in the classical theory. this paper establishes a first order approximationtheory of elastic circular plates with non-Kirchhoff-Lov...Based on the general theory of elastic plates which abandons Kirchhoff-Loveassunption in the classical theory. this paper establishes a first order approximationtheory of elastic circular plates with non-Kirchhoff-Love assumption, and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clampedboundary under uniformly distributed load. By comparing with the classical solution ofthe thin circular plates, it is verified that the new solution is closer to the experimentresults than the classical solution. By virtue of the new theory. the influence of thediameter-to=thickness ratio upon the precision of the classical theory is examined.展开更多
By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary co...By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.展开更多
In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for ci...In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed.展开更多
The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The supp...The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.展开更多
By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of...By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made.展开更多
By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. ...By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented.展开更多
Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact so...Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.展开更多
In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of partic...In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.展开更多
The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge condit...The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.展开更多
Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied...Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.展开更多
Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded an...Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the Corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.展开更多
Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engi...Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engineering disciplines.Based on the nonlinear theory of electroelasticity and its linearized version for incremental fields,we derive the state-space formulations for small-amplitude free vibrations of an SEAM circular plate under large predeformation due to static biasing fields.An exact three-dimensional solution is then obtained by adopting the finite Hankel transform for the plate with an elastic simple support at the circular boundary.The exact solution for an isotropic linear elastic circular plate can be obtained as a particular and degenerated case.The model of generalized neo-Hookean compressible material is considered in numerical simulations.It is found that the natural frequency,while depending on the intrinsic parameters of the plate(e.g.,initial thickness and electromechanical coupling coefficients),can be controlled effectively by the extrinsic factors(e.g.,pre-stretch and biasing electric displacement).Results further indicate that Euler’s instability will occur under a certain combination of the biasing electric displacement and pre-stretch,which should be of practical importance when one intends to tune the dynamic characteristics of a plate by means of external loading.展开更多
Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform t...Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.展开更多
This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible...This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.展开更多
In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed...In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.展开更多
基金The Innovative Projects of Key Disciplines of Civil Engineering of Changsha University of Science and Technology,24ZDXK07,Andi Lai。
文摘Odd elasticity introduces active moduli to the antisymmetric components of the elastic tensor,which describe the asymmetric coupling between different deformation modes in a medium and quantify the work extracted during quasi-static strain cycles.The introduction of active moduli renders the elastic tensor non-Hermitian,breaking the Maxwell-Betti reciprocity and enabling the observation of phenomena that cannot occur in traditional passive media.Here,we develop an analytical dynamic model for odd elastic circular plates to investigate the effects of odd elasticity on motion in rotationally symmetric geometries.We report a novel nonreciprocal rotating wave and explore the effects of different odd elastic moduli on chiral deformation.Nonreciprocal rotating waves represent a distinct dynamic mode,exhibiting unidirectional propagation with amplitude increasing or decreasing exclusively along a specific direction.The amplitude change during motion reveals the system’s non-conservation of energy.
基金supported by the National Natural Science Foundation of China(12402444)。
文摘A new dimensionless number is proposed for dynamic plastic deformation analysis of clamped circular plates under underwater explosion loads by introducing dimensional analysis method to the basic dynamical governing equations of circular plates.The relation between dimensionless final plastic deformation of circular plates and the new dimensionless number is established based on massive underwater explosion test data.Meanwhile,comparative analysis was discussed with two other published dimensionless parameters which indicated the new dimensionless number proposed in this paper is more effective and extensive to predict the dynamic plastic response of circular plates under underwater explosion condition.
文摘New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.
文摘The method of averaging is applied in this paper to deal with primary resonance of a three circular plates torsion vibration system having cubic nonlinearities which is excited by a simple-harmonic excitation. Bifurcation equation of the steady state response is obtained and its singularity analysis is given. The results of theoretical analysis are shown to be in good agreement with experimental ones.
文摘A new technique for solving large deflection problem of circular plates flexural non-axisymmetrically is proposed in this paper. The large deflection problem of a circular plate with built-in edge under non-axisymmetrical load is taken as an example to clarify the principle and procedure of the technique mentioned here. The technique given here can also be used to solve large deflection problem of circular plates under other non-axisymmetrical loads and boundary conditions.
文摘Based on the general theory of elastic plates which abandons Kirchhoff-Loveassunption in the classical theory. this paper establishes a first order approximationtheory of elastic circular plates with non-Kirchhoff-Love assumption, and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clampedboundary under uniformly distributed load. By comparing with the classical solution ofthe thin circular plates, it is verified that the new solution is closer to the experimentresults than the classical solution. By virtue of the new theory. the influence of thediameter-to=thickness ratio upon the precision of the classical theory is examined.
文摘By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.
文摘In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed.
文摘The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.
基金the National Natural Science Foundation of China(No.19872060)
文摘By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made.
基金The project supported by the National Natural Science Foundation of China (No. 19872060)
文摘By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented.
基金the National Natural Science Foundation of Chinathe Zhejiang Provincial Natural Science Foundation
文摘Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.
基金Partially Supported by the National Natural Science Foundation of China
文摘In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.
文摘The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.
基金Project supported by the National Natural Science Foundation of China(No.11621062)the Natural Science Foundation of Zhejiang Province(No.LY18A020009)+1 种基金the Science and Technology Project of Ministry of Housing and Urban and Rural Development(No.2016-K5-052)the Science Foundation of Zhejiang Sci-Tech University(No.16052188-Y)
文摘Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.
基金supported by the National Natural Science Foundation of China (Nos. 10872180 and10725210)
文摘Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the Corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.
基金This work was supported by the National Natural Science Foundation of China(Nos.11872329 and 11621062).
文摘Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engineering disciplines.Based on the nonlinear theory of electroelasticity and its linearized version for incremental fields,we derive the state-space formulations for small-amplitude free vibrations of an SEAM circular plate under large predeformation due to static biasing fields.An exact three-dimensional solution is then obtained by adopting the finite Hankel transform for the plate with an elastic simple support at the circular boundary.The exact solution for an isotropic linear elastic circular plate can be obtained as a particular and degenerated case.The model of generalized neo-Hookean compressible material is considered in numerical simulations.It is found that the natural frequency,while depending on the intrinsic parameters of the plate(e.g.,initial thickness and electromechanical coupling coefficients),can be controlled effectively by the extrinsic factors(e.g.,pre-stretch and biasing electric displacement).Results further indicate that Euler’s instability will occur under a certain combination of the biasing electric displacement and pre-stretch,which should be of practical importance when one intends to tune the dynamic characteristics of a plate by means of external loading.
基金Project supported by the National Natural Science Foundation of China (No. 10572049).
文摘Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.
文摘This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.
文摘In this paper, nonlinear forced vibration of symmetrically laminated rectilinearly orthotropic circular plates excited by a harmonic force q(0)cos omega t including effects of transverse shear deformation is discussed. The analytical solution for the relationship between forcing frequency and amplitude of vibration is obtained by Galerkin's method. Finally, the paper analyses the effect of the transverse shear on the vibration of the plate and gives the ratio of nonlinear period to linear period for nonlinear free vibration of the plate.
