Thomas L. Geers

Doubly asymptotic approximations for transient motions of submerged structures

Doubly asymptotic approximations (DAA) are differential equations for simplified analysis of the transient interaction between a flexible structure and a surrounding infinite medium. These surface interaction approximations approach exactness in the limit of low‐ and high‐frequency motions and effect a smooth transition in the intermediate frequency range. A finite‐element DAA formulation for an acoustic medium is presented herein, with attention focused on the first and second members of the DAA hierarchy. The free‐vibration and forced‐response characteristics of the first and second approximations are examined through specialization to a spherical geometry.

Residual Potential and Approximate Methods for Three‐Dimensional Fluid‐Structure Interaction Problems

A method developed previously for an analysis of the two‐dimensional excitation of an elastic cylindrical shell by a transverse, transient acoustic wave is extended to three‐dimensional applicability. In addition, some fluid‐structure interaction approximations are presented that follow naturally from the rigorous development. Application to finite element analysis of the transient response of submerged structures is discussed.

An integrated wave-effects model for an underwater explosion bubble

A model for a moderately deep underwater explosion bubble is developed that integrates the shock wave and oscillation phases of the motion. A hyperacoustic relationship is formulated that relates bubble volume acceleration to far-field pressure profile during the shock-wave phase, thereby providing initial conditions for the subsequent oscillation phase. For the latter, equations for bubble-surface response are derived that include wave effects in both the external liquid and the internal gas. The equations are then specialized to the case of a spherical bubble, and bubble-surface displacement histories are calculated for dilational and translational motion. Agreement between these histories and experimental data is found to be substantially better than that produced by previous models.

Excitation of a fluid‐filled, submerged spherical shell by a transient acoustic wave

A mathematical formulation and method of solution for the title problem are developed, and numerical results are presented for excitation by a plane step wave. The formulation is based on the familiar equations of motion for a thin spherical shell and the wave equation for the internal and external fluid domains. The Laplace transform is invoked, and the usual separation of variables method produces modal equations for each component of the Fourier–Legendre series solution. The modal equations are then restructured to facilitate transform inversion, yielding delayed differential equations in time for each response mode of the shell‐fluid system, which are integrated numerically in time. Complete response solutions then follow by modal superposition, with special techniques being employed to improve modal convergence. Transient response histories are shown for a step‐wave‐excited steel shell containing water and submerged in water. Also, these results are compared with their counterparts for an empty submerged steel shell.

Scattering of a Transient Acoustic Wave by an Elastic Cylindrical Shell

A plane acoustic step wave traveling through an infinite fluid medium is scattered by an infinite, elastic, circular cylindrical shell whose axis is parallel to the wavefront of the incident wave. The resulting transient acoustic field is studied through the use of temporal convolution techniques in conjunction with wave front analysis. Computed pressure histories are presented for various points in the fluid. The field produced by the cylindrical shell is compared with those produced by a fixed rigid cylinder and a cylindrical cavity. Attention is given to the nearfield pressure reduction capability of the cavity.

Modal impedances for two spheres in a thermoviscous fluid

A modal impedance matrix is formulated for two spheres undergoing axisymmetric oscillations in a thermoviscous acoustic medium. The formulation utilizes the governing equations of Epstein and Carhart [J. Acoust. Soc. Am. 25, 553–565 (1953)] and the analysis method of Guz and Golovchan [Diffraction of Elastic Waves in Multiply Connected Bodies (U.S. Department of Commerce, Washington, DC, 1973)]. The impedance matrix is used to generate dilatational and translational surface‐force curves for dilatational and translational surface motion. Three models of the acoustic medium are examined: full thermoviscous, thin boundary layer, and ideal acoustic. Numerical results for water and air display the limitations of the last two models.

Response of an Elastic Cylindrical Shell to a Transverse Acoustic Shock Wave in a Light Fluid Medium

A plane acoustic step‐wave traveling through a light fluid medium impinges upon an infinite, elastic, circular cylindrical shell whose axis is parallel to the wavefront of the incident wave. Approximate analytical expressions are given for the post‐envelopment response of the first three modes of the shell appropriate to both a rigorous treatment of the fluid‐shell interaction and a treatment that disregards the effects of the scattered wave. These analytical expressions, plus numerical computations of modal pressures and of displacement and strain responses for an aluminum shell in air, show why neglect of the scattered wave is a poor approximation.

Axisymmetric free vibration of a submerged spherical shell

Previous studies of the title problem have produced only partial solutions for this classical configuration. The present study shows how complete solutions are readily obtained from simple polynomial expressions. Numerical results in graphical form are presented for a steel shell submerged in water as functions of a parameter related to the shell’s thickness‐to‐radius ratio. It is found that descriptions based upon added‐mass and added‐damping perturbations of the shell’s in vacuo free‐vibration characteristics can be misleading.

Doubly asymptotic approximations for transient poroelastodynamics

A doubly asymptotic approximation (DAA) is an approximate temporal impedance relation at the boundary of a continuous medium. Here, first- and second-order DAAs are formulated for an infinite external poroelastic medium described by Biot’s equations. As with their acoustic, elastodynamic, and electromagnetic predecessors, the poroelastodynamic DAAs approach exactness in both the early-time (high-frequency) and late-time (low-frequency) limits, effecting a smooth transition between. They also lend themselves to straightforward boundary-element discretization, producing matrix ordinary differential equations in time that are readily solved by numerical integration. An initial examination of poroelastodynamic DAA accuracy is presented for two problems with spherical symmetry.

Transient response analysis of complex submerged structures

Through the continuing development of discrete element methods of structural analysis, great progress has been made during the past decade in the static and dynamic analysis of complex structures. The transient response analysis of such structures submerged in a dense fluid, however, is severely complicated by the intrusion of important fluid‐structure interaction effects. Following a brief review of the nature of these effects, a variety of techniques for the treatment of the fluid‐structure interaction are examined. Specifically, standing wave (modal), traveling wave, brute‐force numerical, modified numerical, retarded potential, and surface interaction approximation techniques are discussed. The characteristics of each of these techniques are studied and the compatibility of each with present discrete element methods of structural analysis is assessed.