A monotonicity analysis theory for the dependent eigenvalues of the vibrating systems

This paper presents and discusses the monotonicity analysis theory for the generalized eigenvalues of the nonlinear structural eigensystems. The analysis is based on investigating the mass and stiffness matrices which are associated with both the mixed and exact finite element models. These models can be distinguished by the shape functions derived from the choice of displacement field which plays a crucial role in the accuracy and efficiency of the solution. The main emphasis of this contribution is the derivation and the investigation of this analysis for large scale eigenproblems.