Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam

Aaron A. Allen; Scott W. Hansen

doi:10.3934/dcdsb.2010.14.1279

Article Contents

2010, Volume 14, Issue 4: 1279-1292. Doi: 10.3934/dcdsb.2010.14.1279

This issue Previous Article A robust well-balanced scheme for multi-layer shallow water equations Next Article Low complexity shape optimization & a posteriori high fidelity validation

Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam

Aaron A. Allen^1, and
Scott W. Hansen^2,

1.
Area of Scientific Learning, Milligan College, Milligan College, TN 37682
2.
Department of Mathematics, Iowa State University, Ames, IA 50011

Received: September 30, 2009

Revised: February 28, 2010

Published: May 2010

Abstract Related Papers Cited by

Abstract

The classical Mead-Markus sandwich beam consists of two stiff outer layers modeled under Euler-Bernoulli beam assumptions and a compliant "core layer" that is elastic in shear. In this article we consider a multilayer analog consisting of $n = 2m + 1$ layers of alternating stiff and compliant beam layers ($m+1$ stiff and $m$ compliant) with viscous damping proportional to the shear in the compliant layers. We prove that the associated semigroup is analytic and describe the sector of analyticity. We also consider the problem of how to choose the damping parameters to optimize the angle of analyticity. We obtain an analytical solution to the optimization problem.

Keywords:

Mathematics Subject Classification: Primary: 93D99, 74K10; Secondary: 49K20.

Citation:

Article Metrics

HTML views() PDF downloads(71) Cited by(0)

Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content