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

Pages: 1279 - 1292, Volume 14, Issue 4, November 2010

doi:10.3934/dcdsb.2010.14.1279       Abstract        Full Text (217.2K)       Related Articles

Aaron A. Allen - Area of Scientific Learning, Milligan College, Milligan College, TN 37682, United States (email)
Scott W. Hansen - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)

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:  Sandwich beam, analytic semigroup, optimal damping, structural damping.
Mathematics Subject Classification:  Primary: 93D99, 74K10; Secondary: 49K20.

Received: October 2009;      Revised: March 2010;      Published: August 2010.