Dynamics of Plate Structures

Deterministic and random vibrations of linear elastic plate structures are discussed. At first polygonally shaped thin plates according to Kirchhoff s theory are considered. The undamped frequency response function is calculated by a powerful boundary element method (BEM) with Green’s functions of rectangular domains, which was developed in [3.4–1] for static loading of plates in a first stage. An extension of the method to eigenvalue problems of membranes and plates is given in [3.4–2], forced vibrations are analysed in [3.4–3,4,5,6], and plates with particular orthotropy are treated in [3.4–7,8]. Embedding the actual polygonal domain properly into a rectangular plate, the boundary conditions (b.c.s) are possibly satisfied exactly at the coinciding boundaries. The remaining prescribed b.c.s of the actual problem lead to a pair of coupled integral equations for a density function vector whose components are line loads and moments distributed in the basic domain along the actual boundary. Considering time-harmonic excitation and sweeping the forcing frequency stepwise the undamped frequency response function results, where the roots of the reciprocal yield the eigenfrequencies with high numerical accuracy.