Abstract
The aim of this paper is to propose a unified formulation for the free in-plane vibration of arbitrarily-shaped straight-sided quadrilateral and triangular plates with arbitrary boundary conditions by means of improved Fourier series method (IFSM). The arbitrarily-shaped straight-sided quadrilateral and triangular plates are all mapped into a unit square plate uniformly, and accordingly, the problem can be solved directly by the existing vibration modeling method of rectangular plates. The displacement admissible function is generally expressed as the combinations of Fourier cosine and sine series. All the series expansion coefficients can be determined by the Rayleigh-Ritz procedure. A number of numerical examples of the quadrilateral and triangular plate with various shapes and boundary conditions are presented to assess the convergence and accuracy of the current solution method by comparing with those of literature or the finite element method (FEM). Furthermore, comprehensive studies on the influence of parameters of triangular plates on its in-plane vibration frequency characteristics are given, based on the angle of the isosceles triangular plate, the ratio of the length of the side of right-angled triangular plates and boundary restraint parameters.
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