Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied. First, the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth, and the state equation is established by Hankel integral transform method, furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation. Secondly, by the transfer matrixes, the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of ground as well as the contact conditions. Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundaryvalue problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily. At the end of this paper, a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-Kirchhoff-Love assumption forthree dimensional elaslic plates with arbitrary shapes[1][2], the author derives afunctional of generalized variation for three dimensional elastic circular plates, therebyobtains a set of differtial equations and the relate boundary conditions to establish afirst order approximation theory for elastic circular plate with fixed boundary andunder uniform loading on one of its surface. The analytical solution of this problemwill present in another paper.

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅲ)──NUMERICAL RESULTS

ased upon the differential equations and their related boundary conditions givenin the previous papers[1, 2], using a global interpolation method, this paper presents anumerical solution to the axisymmetric bending problem of non-Kirchhoff-Love theoryfor circular plate with fixed boundary under uniform surface loading. All the numericalresults obtained in this paper are compared with that of Kirchhoff-Love classicaltheory[3] and E. Reissner's modified theory[4]

DYNAMIC INTERACTION BETWEEN ELASTIC THICK CIRCULAR PLATE AND TRANSVERSELY ISOTROPIC SATURATED SOIL GROUND

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.

Hydroelastic Response of A Circular Plate in Waves on A Two-Layer Fluid of Finite Depth

The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

A NEW TECHNIQUE FOR SOLVING NON-AXIALLY SYMMETRICALLARGE DEFLECTION OF ELASTIC AND THIN CIRCULAR PLATES

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.