Free in-plane vibration analysis of rectangular plates with arbitrary elastic boundaries

A Ritz method using a set of trigonometric functions is developed to obtain accurate in-plane modal properties of rectangular plates with arbitrary nonuniform elastic edge restraints. Reliability of the current approach is first assured by comparison against exact and analytical-type solutions for plates with classical boundary conditions and uniform elastic boundaries. For the first time to the author’s knowledge, the problem of free in-plane vibration of plates having triangularly and parabolically varying elastic edge supports is then considered. Accurate upper-bound solutions are tabulated to provide valuable benchmark data against which the findings of other researchers can be compared in the future. Effects of nonuniform elastic spring stiffness on the in-plane natural frequencies and modal shapes are also presented.

Research highlights▶ Upper-bound values for in-plane natural frequencies of plates with nonuniform elastic edges. ▶ A Ritz method based on admissible trigonometric functions is used. ▶ The method is rapidly convergent and computationally efficient. ▶ Effects of nonuniform stiffness along plate edges are presented and discussed.