Nonlinear eigenvalue analysis for spectral element method. (1st January 2021)

• Record Type: Journal Article
• Authors: Mukherjee, Avisek; Sarkar, Soumyadipta; Banerjee, Arnab
• Is Part Of: Computers & structures. Volume 242(2020)
• Publication Date: 2021-01-01
• Subjects: Spectral element -- Nonlinear Eigenvale problem -- Matrix polynomials -- Modal analysis -- Rational polynomial approximation -- Linearization; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106367
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Novel techniques to solve nonlinear eigenvalue problem for spectral elements method. Robust algorithms to identify eigenvalues in presence of singularities. Numerical examples showing efficiency and accuracy of the proposed algorithms. Applicable for structural health monitoring, soil-structure interaction etc. Abstract: Spectral element method (SEM) is a robust and efficient mathematical technique for dynamic analysis of structures in frequency domain. Unlike finite element method (FEM), in SEM, the dynamic stiffness matrix forms a nonlinear eigenvalue problem (NLEP) to compute the natural frequencies and vibration modes of the structure which cannot be solved using linear numerical eigen-solvers. In this paper, two distinct numerical methods, i.e. (1) a root finding method of rational polynomial functions and (2) a linearization of Lagrange matrix interpolating polynomials, have been used to compute the eigenvalues of a problem more efficiently employing SEM. These proposed methods can solve NLEP in a stable, efficient and accurate way even in the presence of singularities. The accuracy of these methods are numerically evaluated by comparing with the solutions from the modal analysis using FEM.