Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluids

Abstract

SUMMARYSuperposition principle is used to separate the incident acoustic wave from the scattered and radiated waves in a displacement-based finite element model. An absorbing boundary condition is applied to the perturbation part of the displacement. Linear constitutive equation allows for inhomogeneous, anisotropic materials, both fluids and solids. Displacement-based finite elements are used for all materials in the computational volume. Robust performance for materials with limited compressibility is achieved using assumed-strain nodally integrated simplex elements or incompatible-mode brick elements. A centereddifference time-stepping algorithm is formulated to handle general damping accurately and efficiently. Verification problems (response of empty steel cylinder immersed in water to a step plane wave, and scattering of harmonic plane waves from an elastic sphere) are discussed for assumed-strain simplex and for voxel-based brick finite element models. A voxel-based modeling scheme for complex biological geometries is described, and two illustrative results are presented from the bioacoustics application domain: reception of sound by the human ear and simulation of biosonar in beaked whales.

Morphology of the Nasal Apparatus in Pygmy (Kogia Breviceps) and Dwarf (K. Sima) Sperm Whales

“…The spermaceti organ likely serves as a sound transmitter, linking the caudal phonic lip to the melon, the latter of which forms the final portion of the kogiid sound transmission pathway. Future studies can investigate the acoustic and visco‐elastic properties of the complex, bioacoustic structures and the compositional topography of the lipids within the spermaceti organ and melon; such data could then be integrated into finite element analyses on the propagation of acoustic energy through these structures (Krysl et al, ; Cranford et al, ). Such information is necessary to further advance our understanding of the functional morphology of the echolocation system of kogiids.…”

Anatomic Geometry of Sound Transmission and Reception in Cuvier's Beaked Whale (Ziphius cavirostris)

“…Another interesting “test” of acoustic function within the head of Ziphius could make use of finite element modeling (FEM) techniques (Krysl et al, 2007). For example, one intriguing question is: What is the function of an ASO that is encased in the high‐density rostral bones?…”

“…The density disparity between compact bone and lipid tissue is the maximum attainable difference between tissues. We suspect that the very abrupt change between the low‐density ASO and the high‐density bones that embrace it are functionally significant, an idea that can be tested with finite element modeling tools (Sun et al, 2002; Richmond et al, 2005; Ross, 2005; Krysl et al, 2006, 2007).…”

Building a Virtual Model of a Baleen Whale: Phase 2

“…Our team has pioneered a suite of techniques that combine the anatomic geometry obtained from CT scans (Cranford, 1988;Cranford et al, 1996; with measurements of tissue elasticity (Soldevilla et al, 2005;Hess et al, 2006) and custom FEM software (Krysl et al, 2006), the vibroacoustic toolkit (VTk). This combination produces a versatile computational environment for vibroacoustic simulations (Krysl et al, 2008). This suite of techniques can also be used to assess acoustic exposure across a broad taxonomic spectrum.…”