# Strongly damped quadratic matrix polynomials

Taslaman, Leo (2014) Strongly damped quadratic matrix polynomials. [MIMS Preprint]

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## Abstract

We study the eigenvalues and eigenspaces of the quadratic matrix polynomial \allowbreak $M\lambda^2+sD\lambda+K$ as $s\rightarrow\infty$, where $M$ and $K$ are symmetric positive definite and $D$ is symmetric positive semi-definite. The 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.

Item Type: MIMS Preprint quadratic eigenvalue problem, principal angles, canonical angles, matrix polyno- mial, viscous damping, discrete damper, vibrating system MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysisMSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems Leo Taslaman 03 Mar 2014 08 Nov 2017 18:18 http://eprints.maths.manchester.ac.uk/id/eprint/2108

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