Efficient finite element methods/reduced-order modeling for structural acoustics with applications to transduction

Efficient finite element techniques for time harmonic structural acoustics are developed and examined in the context of applications where high frequencies/wavenumbers are present.; In the first portion of this thesis, discrete dispersion analysis on a regular rectangular mesh is developed for the Helmholtz equation and applied to four finite element methods (basic Galerkin method, two Galerkin least-squares methods, and a related residual-based method). The goal of the modified FEM techniques is to reduce problem size by allowing coarse mesh modeling of the fluid domain while retaining solution accuracy. The efficacy of these schemes is assessed analytically then verified numerically for high frequency applications in a therapeutic medical ultrasound model problem. Numerical experiments on a simple 2D beam-forming problem show that GLS methods can reduce matrix storage requirements by a factor of five and solution time by a factor of eight over basic Galerkin FEM.; The remainder of this dissertation deals with development and validation of an improved FEM technique for structural acoustics. A novel hybrid analytical/FEM method (known as 2.5D FEM) for fluid-coupled, variable-width plates (linear and exponential variation) is presented. This modeling technique achieves computational savings by reducing the physical dimensionality of a problem via a priori specification of a limited set of structural and fluid modes in the condensed dimension. Consequently, 2.51) FEM models can be 10–20 times smaller than comparable full 3D FEM models. This method, in conjunction with an analytical technique (WKB), is applied to the design of a transducer which employs mammalian cochlea-like behavior. The design process of this so-called cochlear-based transducer is illucidated with discussion of design guidelines. Finally, experimental results are shown which validate the 2.51) FEM method for both isotropic and orthotropic plate models. To facilitate the comparison of numerical results and experimental data, an alternate modal basis (utilizing a static “mode” approximation) for the lateral plate structural modeshape was implemented. Experimental and numerical data correlated well across the operational range of the experimental setup with average L₂-error levels of 17% for the isotropic plate material (aluminum) and 32% for the orthotropic plate material (graphite-epoxy). Various other composite plate materials are examined experimentally to explore plate dynamics of orthotropic materials.