In-plane vibration of a plate having an elliptical hole of arbitrary eccentricity

The in-plane vibration of a plate with an elliptic hole is studied. It is shown that standing waves whose wavelength is the same order of magnitude as the size of the hole are theoretically capable of causing microcracks which have been observed experimentally.

Several approaches were used including reduction of the mixed boundary value problem to a Fredholm equation, and to a matrix eigenvalue problem. Contour curves of various stresses and displacements were obtained numerically.

A new technique was developed for the solution of the wave equation appropriate for boundary conditions on an elliptical surface.