Abdel-Aziz, Mohammedi R.2018-06-182018-06-181993-07Abdel-Aziz, Mohammedi R.. "A Monotonicity Analysis Theory for the Dependent Eigenvalues of the Vibrating Systems in Structural Dynamics." (1993) <a href="https://hdl.handle.net/1911/101804">https://hdl.handle.net/1911/101804</a>.https://hdl.handle.net/1911/101804This paper presents and discusses the monotonicity analysis theory for the generalized eigenvalues of the nonlinear structural eigensystems. This analysis is based on investigating the mass and stiffness matrices which are associated with 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 both the accuracy and efficiency of the solution. This strategy is sufficiently general that it holds for any problem associated with the mixed finite element formulation involving a frequency independent stiffness matrix and a frequency dependent mass matrix. The main emphasis of this contribution is the derivation and investigation of this analysis for large scale eigenproblems.29 ppengTechnical reportTR93-28