Vibration of Thermally Post-Buckled Orthotropic Circular Plates

Abstract

Axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise have been studied numerically. Effects of geometric nonlinearities have been incorporated into the problem formulation. The problem is challenging because the buckled configuration is unknown a priori. By assuming that the amplitude of plate's vibration and the additional strains induced in it are infinitesimal, and its response harmonic, the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations; one for the thermal post-buckling, and the other for linear vibrations of the plate superimposed upon the post-buckled configuration. The plate's boundary is taken to be either clamped or simply supported but restrained from moving in the radial direction. The two sets of coupled boundary value problems are solved numerically by a shooting method. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and postbuckled plates, have been computed, and characteristic curves of the frequency versus temperature rise for different values of material anisotropy parameters are plotted. It is found that the three lowest frequencies of the pre-buckled plate decrease with an increase in the temperature, but those of a buckled plate increase monotonically with the temperature rise. The fundamental frequency of the deformed plate approaches zero at the onset of buckling.

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

“…Actually, in order to ensure the same discrete points for both the postbuckling solution and the vibration one fitting for the numerical integration of the fourth-order Runge-Kutta method, the two problems are solved simultaneously in the numerical computation. The procedures and programs for the numerical shooting method can be found in [4][5][6][7][8]22].…”

“…This is because they are just the bifurcation points of the corresponding equilibrium paths over which the beam goes into its secondary equilibrium configuration or the postbuckling configuration from the initial straight-line equilibrium state. They are two totally different equilibrium states so that they have totally different vibration responses [8,12,22] .…”

“…(20) are divided into two parts: the solution of static elastic deformation and that of vibration in the vicinity of the static equilibrium configurations [8,22] , i.e.,…”

Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

“…Li et al [14] analyzed thermal pre-buckled and post-buckled free vibrations behavior of orthotropic circular plate with different boundary conditions. They used von Karman's non-linear kinematics and Hamilton's principle for obtaining a system of equations.…”

On the Thermal Buckling Behavior of Laminated Hybrid Composite Plates Due to Square/Circular Cut-Outs

“…Kabir et al [3] presented an analytical solution to thermal buckling response of moderately thick symmetric angle-ply laminated, rectangular plate which is clamped from all the edges. Li et al [4] investigated the axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise. Laura and Rossit [5] worked on thermal bending of thin, anisotropic, clamped elliptic plates and their study deals with the exact analytical solution of thermal bending.…”