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