Journal of Computational Acoustics

A stability analysis of a nonlinear plate clamped to an infinite baffle in mean flow is given. The effect of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion, and that of viscous damping are taken into account in the derivation of the plate equation. The plate flexural displacement is obtained by modal expansion based on Galerkin's method. The critical mean flow speeds at which local instabilities may occur are determined by Routh algorithm. The mechanisms that trigger the local instabilities are uncovered. The effect of structural nonlinearities, and that of plate aspect and plate length/thickness ratios on local instabilities are examined. Numerical examples of the transition from stable to locally unstable vibration, as the mean flow speed exceeds the critical values, are demonstrated. The results show that while the overall amplitude of the plate flexural displacement may be bounded when the mean flow speed exceeds the critical values, plate vibration may be locally unstable, jumping from one equilibrium position to another. Furthermore, the jumping may be random, and the plate vibration may seem chaotic. The results also show that viscous damping may stabilize plate flexural vibration and settle the plate in one of its equilibria.

An improved numerical scheme is introduced for solving a set of three-dimensional parabolic elastic wave equations. The new scheme is based on the combination of an ordinary differential equation method and a finite difference scheme. A stability analysis of the numerical method is presented along with a numerical example in which computational accuracy is verified by comparison with an exact three-dimensional analytic solution.

The optimized high-order compact (OHOC) finite difference schemes, proposed as central schemes are used for aeroacoustic computations on interior nodes. On near-boundary nodes, accurate non-central or one-sided compact schemes are formulated and developed in this paper for general computations in domains with non-periodic boundaries. The near-boundary non-central compact schemes are optimized in the wavenumber domain by using Fourier error analysis. Analytic optimization methods are devised to minimize the dispersion and dissipation errors, and to obtain maximum resolution characteristics of the near-boundary compact schemes. With the accurate near-boundary schemes, the feasibility of implementing physical boundary conditions for the OHOC schemes are investigated to provide high-quality wave solutions. Characteristics-based boundary conditions and the free-field impedance conditions are used as the physical boundary conditions for direct computations of linear and nonlinear wave propagation and radiation. It is shown that the OHOC schemes present accurate wave solutions by using the optimized near-boundary compact schemes and the physical boundary conditions.

This paper presents a new ray travel-time inversion scheme not only for localizing the source and calibrating the array position, but also for characterizing environmental parameters such as sound speed profiles (in both water column and sediment), bathymetry, etc. Special attention is given to link the unknowns to good physical observables in order to enhance robustness and efficiency. Numerical studies show the algorithm is indeed extremely efficient. The algorithm is also shown to be insensitive to model mismatch and to yield quite accurate results. This paper also focuses on specific Lincoln-Sea application and analysis of a specific data set from Iceshelf-89.

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.