Dynamical stability of finite anisotropic panels with elliptical cutouts and cracks

Abstract

An approximate analysis for dynamical stability of anisotropic finite panels with centrally located elliptical cutouts is presented. The analysis is divided into two parts: a plane stress analysis and a stability analysis. The plane stress distribution is determined by using Lekhnitskii’s complex variable equations of plane elastostatics combined with a Laurent series approximation constructed by the conformal mapping and a boundary collocation method. Its solutions satisfy the conditions along the interior boundary and at a discrete number of points along the exterior panel ones. The stability analysis is conducted by using the differential equations which result from the Hamilton’s principle and the classical plate theory. The relation of vibration frequency, load parameter and stability of panels is investigated by solving the fundamental equations using separation of variables, so as to obtain the critical loads. Finally, comparisons with documented experimental results and finite element analysis are made. Results of a parameter study are presented.