Strongly Damped Quadratic Matrix Polynomials
Copyright policy )Strongly Damped Quadratic Matrix Polynomials
Summary: We study the eigenvalues and eigenspaces of the quadratic matrix polynomial \(M\lambda^2+sD\lambda+K\) as \(s\to\infty\), where \(M\) and \(K\) are symmetric positive definite and \(D\) is symmetric positive semidefinite. This work is motivated by its application to modal analysis of finite element models with strong linear damping. Our results yield a mathematical explanation of why too strong damping may lead to practically undamped modes such that all nodes in the model vibrate essentially in phase.
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- University of Manchester United Kingdom
Numerical computation of eigenvalues and eigenvectors of matrices, principal angles, Eigenvalues, singular values, and eigenvectors, viscous damping, discrete damper, vibrating system, Systems arising from the discretization of structural vibration problems, quadratic eigenvalue problem, Free motions in linear vibration theory, Modal analysis in linear vibration theory, Matrices over function rings in one or more variables, canonical angles, Matrix pencils, matrix polynomial
Numerical computation of eigenvalues and eigenvectors of matrices, principal angles, Eigenvalues, singular values, and eigenvectors, viscous damping, discrete damper, vibrating system, Systems arising from the discretization of structural vibration problems, quadratic eigenvalue problem, Free motions in linear vibration theory, Modal analysis in linear vibration theory, Matrices over function rings in one or more variables, canonical angles, Matrix pencils, matrix polynomial
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