The problem of the aperiodic vibration of a thick non-prismatic circular plate resting on an inertial elastic half-space

The problem of the vibration of an axially symmetrical thick circular non-prismatic plate subjected to an axially symmetrical aperiodic normal load is solved in this paper. The plate rests on an inertial elastic half-space and is joined to the foundation by bilateral constrains. The problem is solved by the approximation method, using Chebyshev series. As a result, closed analytical formulas for the coefficients of an infinite system of equations for calculating the Laplace transforms of the sought solution's coefficients – the passive foundation pressure function and the displacement function – are obtained. In order to illustrate the proposed method, the problem of the vibration of the plate under a uniformly distributed aperiodic load is solved. The inverse transform is calculated using the Zakian method.