# Strongly damped quadratic matrix polynomials

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

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.