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November  2010, 14(4): 1279-1292. doi: 10.3934/dcdsb.2010.14.1279

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, United States
2. 

Department of Mathematics, Iowa State University, Ames, IA 50011, United States

Received  October 2009 Revised  March 2010 Published  August 2010

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: structural damping., analytic semigroup, Sandwich beam, optimal damping.
Mathematics Subject Classification: Primary: 93D99, 74K10; Secondary: 49K2.
Citation: Aaron A. Allen, Scott W. Hansen. Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1279-1292. doi: 10.3934/dcdsb.2010.14.1279
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