The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved b...The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.展开更多
An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isot...An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil＇s anisotropy on the foundation＇s vibrations.展开更多
A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this...A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this interaction problem is reduced to a problem of dynamic plastic response of the plate in vacuum.The closed-form solutions are derived for both middle and high pressure loads by solving the equations of motion with the large deflection in the range where both bending moments and membrane forces are important.Some numerical results are given.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
Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considere...Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 50478081).
文摘The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.
基金Project supported by the National Natural Science Foundation of China (No.50478081)
文摘An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil＇s anisotropy on the foundation＇s vibrations.
基金The study is supported by National Natural Science Foundation of China.
文摘A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this interaction problem is reduced to a problem of dynamic plastic response of the plate in vacuum.The closed-form solutions are derived for both middle and high pressure loads by solving the equations of motion with the large deflection in the range where both bending moments and membrane forces are important.Some numerical results are given.
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Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.
