Trefftz's Method for Vibration of Rigid Plate

Trefftz's method is applied to study the vertical vibration of a rigid rectangular plate of infinite length resting on an elastic half‐space. The problem is formulated as one of diffraction of elastic waves. The method consists in using c‐complete or T‐complete (T after Trefftz) families of solutions of the governing equations in the medium to construct the diffracted displacement fields as linear combinations of such solutions. Coefficients are obtained from the treatment of boundary conditions using a collocation least‐square scheme. The relationship between the vertical contact force applied to the plate and vertical displacement is given in terms of a complex stiffness that depends on the frequency. Numerical values are given for different Poisson's ratios. They are compared with those obtained by an analytical method.