Free vibrations of rectangular cantilever plates. Part 2: in-plane motion

An analysis of the free in-plane vibrations of a cantilevered rectangular plate is performed by means of a variational approximation procedure. The problem is treated by first obtaining the exact solution for waves in the plate satisfying the equations of plane stress including in-plane inertia with two opposite edges traction free. The solution results in a set of dispersion curves. A number of the resulting waves are used in what remains of the variational equation, in which all conditions occur as natural conditions. Roots of the resulting transcendental equation are calculated, which yield the eigensolutions and associated eigenfrequencies. The results are compared with results obtained using FEM, and good agreement is shown.