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Nonlinear eigenvalue analysis for spectral element method
- Source :
- Computers & Structures. 242:106367
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
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.
- Subjects :
- Mechanical Engineering
Numerical analysis
Modal analysis using FEM
Spectral element method
MathematicsofComputing_NUMERICALANALYSIS
02 engineering and technology
01 natural sciences
Finite element method
Computer Science Applications
010101 applied mathematics
Matrix (mathematics)
020303 mechanical engineering & transports
0203 mechanical engineering
Linearization
Modeling and Simulation
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Applied mathematics
General Materials Science
0101 mathematics
Root-finding algorithm
Eigenvalues and eigenvectors
Civil and Structural Engineering
Mathematics
Subjects
Details
- ISSN :
- 00457949
- Volume :
- 242
- Database :
- OpenAIRE
- Journal :
- Computers & Structures
- Accession number :
- edsair.doi...........76252edfc2d441af85d59ce0673f88f9