Partial differential equation-constrained optimization framework for inverse design of acoustic damping layers

Abstract

We present a partial differential equation-constrained framework for the design of viscoelastic damping layer assemblies in one and two dimensions. Viscoelastic foams’ responses to loads not only provide stiffness and damping, but also vary with frequency. In a finite-element formulation, a viscoelastic solid’s structural stiffness is determined by its complex valued shear and bulk moduli. By optimally selecting the moduli values of a layered assembly, we demonstrate an effective design of graded foam that minimizes its acoustic scattering in a fluid waveguide. We define a cost functional based on the scattered field from the acoustic-structural interaction of the viscoelastic inclusion in a fluid medium. In the optimization calculations, the complex valued moduli were modified to minimize the objective functional representing the scattered field energy. Models used in numerical simulations featured circular inclusions with distinct concentric rings. This talk will focus on the convergence of optimal designs and effects of frequency and solver algorithms. Numerical results suggest the potential for optimally designed viscoelastic foams to minimize acoustic scattering. [Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL850000.]