Research Report: Manuscript CMCU-95-05, July 1995
A Multi-Field Space-Time
Finite Element Method for Structural Acoustics
Lonny L. Thompson
Computational Mechanics at Clemson University
Department of Mechanical Engineering
Clemson, South Carolina 29634-0921
Abstract
A Computational Structural Acoustics (CSA) capability for solving scattering,
radiation, and other problems related to the acoustics of submerged
structures has been developed by employing some of the recent
algorithmic trends in Computational Fluid Dynamics (CFD), namely
time-discontinuous Galerkin Least-Squares finite element methods.
Traditional computational methods toward simulation of acoustic
radiation and scattering from submerged elastic bodies
have been primarily based on frequency domain
formulations. These classical time-harmonic approaches
(including boundary element,
finite element, and finite difference methods)
have been successful for problems
involving a limited range of frequencies
(narrow band response) and scales (wavelengths) that are large
compared to the characteristic dimensions of the elastic structure.
Attempts at solving large-scale structural acoustic systems
with dimensions that are much larger
than the operating wavelengths and which are complex, consisting of many
different components with different scales and broadband frequencies,
has revealed limitations of many of the classical methods. As a result,
there has been renewed interest in new innovative
approaches, including time-domain approaches. This paper describes recent
advances in the development of
a new class of high-order accurate and unconditionally stable
space-time methods for structural acoustics which employ
finite element discretization of
the time domain as well as the usual discretization of the spatial domain.
The formulation is based on a space-time variational equation for both
the acoustic fluid and
elastic structure together with their interaction.
Topics to be discussed include the
development and implementation of higher-order accurate
non-reflecting boundary conditions based on the exact impedance relation
through the Dirichlet-to-Neumann (DtN) map, and a
multi-field representation for the acoustic fluid based
on independent pressure and velocity potential variables.
Numerical examples involving
radiation and scattering of acoustic waves
are presented to illustrate the high-order
accuracy achieved by the new methodology for CSA.
Postscript file of Manuscript CMCU-95-05