A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and Shear

Abstract

The minimum principle and step-by-step iteration method are generalized for coupled simultaneous differential equations in order to obtain an approximate solution for the flexural vibration frequencies of a wedge with rotatory inertia and shear effects. This procedure avoids the difficulty of solving the nonself-adjoint equation which results when the simultaneous equations for bending slope and displacement are combined into a single differential equation. The upper and lower bounds of the first two eigenvalues are established and a comparison is made with the classical Kirchhoff solution where the rotatory inertia and shear are neglected.