111 research outputs found
Fast computation of optimal damping parameters for linear vibrational systems
We formulate the quadratic eigenvalue problem underlying the mathematical
model of a linear vibrational system as an eigenvalue problem of a
diagonal-plus-low-rank matrix . The eigenvector matrix of has a
Cauchy-like structure. Optimal viscosities are those for which is
minimal, where is the solution of the Lyapunov equation .
Here is a low-rank matrix which depends on the eigenfrequencies that need
to be damped. After initial eigenvalue decomposition of linearized problem
which requires operations, our algorithm computes optimal viscosities
for each choice of external dampers in operations, provided that the
number of dampers is small. Hence, the subsequent optimization is order of
magnitude faster than in the standard approach which solves Lyapunov equation
in each step, thus requiring operations. Our algorithm is based on
eigensolver for complex symmetric diagonal-plus-rank-one matrices and
fast multiplication of linked Cauchy-like matrices.Comment: 14 pages, 1 figur
Optimization of damping positions in a mechanical system
This paper deals with damping optimization of the mechanical system based on the minimization of the so-called "average displacement amplitude". Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples
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