This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equatio...This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equations can be solved by using an iterative method,a Galerkin's approach and a perturbation method.Detailed solutions and numerical results are given for two kinds of boundary conditions,the clamped edge and the supported edge.The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case.The effect of various thickness parameters is investigated in detail.Also,a Runge Kutta method is used to solve the free and forced vibrations of plates with variable thickness,and the results are obtained firstly.It has shown that the adoption of variable thickness plate would be useful in engineering design.展开更多
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bendin...Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.展开更多
To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the met...To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.展开更多
By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi...By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.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
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
文摘This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equations can be solved by using an iterative method,a Galerkin's approach and a perturbation method.Detailed solutions and numerical results are given for two kinds of boundary conditions,the clamped edge and the supported edge.The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case.The effect of various thickness parameters is investigated in detail.Also,a Runge Kutta method is used to solve the free and forced vibrations of plates with variable thickness,and the results are obtained firstly.It has shown that the adoption of variable thickness plate would be useful in engineering design.
文摘Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.
文摘To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.
文摘By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.
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.
