Eigenvalue Sensitivity Analysis for a Combined Beam Structure with Varying Constraints

Abstract

An eigenvalue sensitivity formula for a combined beam structure due to the variation of its shape or joint coordinates is proposed based on the Lagrange multiplier technique for a free vibration equation of the structure. The shape variation is decomposed into the length and the orientation variation of each beam to obtain individual effects on the total sensitivity. The sensitivity equations due to the length and the orientation variations are expressed as an energy density form and the cross product of joint forces and displacements respectively. Several numerical examples are also presented to validate the proposed formulation and to show how to implement the idea.