The image source method for calculating the vibrations of simply supported convex polygonal plates

The aim of this paper is to show that the image source method (ISM) can be used both for analytically calculating Greenʹs functions of particular simply supported convex polygonal plates and for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates with controllable precision. In the first part of the paper, the method for obtaining the Greenʹs function of a polygonal plate by ISM is developed. Examples for plates of different geometries (rectangle, isosceles right triangle, half-equilateral triangle and equilateral triangle) are given. In the second part of the paper, the pertinence of ISM for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates is investigated. An approximation based on the exclusion of image sources beyond a certain distance from the receiver is used in order to take advantage of the dissipation of vibrational energy through wave propagation. We investigate the influence of structural damping and truncation distance on the accuracy of such approximation. The computed responses are in good agreement with reference solutions, which are analytically known or obtained by the finite element method.