Search

Abstract: Vibration of a circular plate internally concentrically supported is basic in structural mechanics. The complete first six frequencies and mode shapes are determined for clamped, simply-supported, sliding, and ring supports using exact characteristic frequency equations. Complex mode switches occur as the support radius is varied. Asymptotic formulas for large support radii are derived. Different types of singularities as the support radius shrinks to zero are distinguished and classified. [Copyright &y& Elsevier]

Abstract: Fundamental frequencies of vibrating circularly periodic plates with a circular core have been determined analytically. A boundary perturbation method is developed to extract the fundamental eigenvalue of the governing biharmonic boundary value problem. The method is then applied to wavy and polygonal plates with clamped and simply supported outer boundary conditions. Clamped, simply supported, and free circular cores are considered. Approximate analytical formulations of the fundamental frequency for such plates with core are obtained. [Copyright &y& Elsevier]

The vibration of a rectangular plate under self-weight (or acceleration) is studied. The vertical edges are simply supported and a semi-analytic Levy-integration method is used. The fundamental frequencies are determined for various top and bottom boundary conditions. It is found that self-weight has considerable effect on both the frequency and the mode shape. [Copyright &y& Elsevier]

Abstract: A boundary perturbation method is developed to determine the fundamental frequency of vibrating plates. The method is then applied to wavy, star shape and polygonal plates with clamped boundary conditions. Approximate analytical solutions of the fundamental frequency are obtained with an accuracy of O(ε 4), where ε is the deviation from the unit circle. [Copyright &y& Elsevier]

Abstract: Vibrations of thin annular plates with at least one sliding or movable edge are considered. The fundamental frequencies for the seven cases may correspond to axisymmetric or non-axisymmetric modes. [Copyright &y& Elsevier]

Abstract: The fundamental frequency of a thin circular plate supported by a concentric partial foundation is studied. For free or sliding edge conditions, the fundamental mode may not be axisymmetric. [Copyright &y& Elsevier]

We present the direct formulation of the two-dimensional boundary element method (BEM) for time-harmonic dynamic problems in solids of general anisotropy. We split the fundamental solution, obtained by Radon transform, into static singular and dynamics regular parts. We evaluate the boundary integrals for the static singular part analytically and those for the dynamic regular part numerically over the unit circle.We apply the developed BEM to eigenvalue analysis. We determine eigenvalues of full non-symmetric complex-valued matrices, depending non-linearly on the frequency, by first reducing them to the generalized linear eigenvalue problem and then applying the QZ algorithm. We test the performance of the QZ algorithm thoroughly in comparison with the FEM solution. The proposed BEM is not only a strong candidate to replace the FEM for industrial eigenvalue problems, but it is also applicable to a wider class of two-dimensional time-harmonic problems. [Copyright &y& Elsevier]

Abstract: For an isotropic circular plate with constant thickness and free edges, its fundamental vibration mode takes the form of a twisting mode with two nodal diameters, i.e. n=2. In certain applications, it may be necessary to have an axisymmetric shape for the fundamental vibration mode (i.e. mode shape with no nodal diameter, n=0). In this paper, we show that such an axisymmetric vibration mode can be realized by increasing the bending rigidity of the outer rim of the circular plate by using a larger thickness or by using a material with a larger Young''s modulus or both. We also determine the critical flexural rigidity of the outer rim that will trigger this vibration mode change from n=2 type to n=0 type for a given rim width. The ability to alter the mode shape of circular plates with free edges has useful applications in sensing and actuating devices and large pontoon-type floating circular structures. [Copyright &y& Elsevier]