Convexity analysis of the largest dependent eigenvalue functions of eigensystems

摘要

This paper presents and discusses the convexity of the largest eigenvalue functions of nonlinear structural eigensystems. The analysis is based on investigating the entries of the mass and stiffness matrices which are associated with the mixed finite element formulation. The mass and stiffness matrices are symmetric positive definite and the entries of the mass matrix are continuously differentiable functions. The main emphasis of our contribution is the derivation and the investigation of this analysis for the frequency dependent eigensystems.