The results of a recent study of fluid-borne waves on plates with one-sided fluid loading [M. Talmant, Ph.D. thesis, University of Paris VII (1987)] allow the prediction of the corresponding waves and their resonances (as well as of the Lamb-wave resonances) on thin submerged spherical shells. Similar fluid waves and the ensuing ‘‘bifurcation’’ in the dispersion curves of the first antisymmetric vibration mode on cylindrical shells were previously described [J. V. Subrahmanyam, Ph.D. thesis, Catholic University of America (1983); J. L. Rousselot, Acustica 58, 291 (1985)] and the fluid waves were observed by Talmant et al. [J. Acoust. Soc. Am. 84, 681–688 (1988)]. The resonances predicted by the plate model for spherical shells are confirmed here by comparison with scattering cross-section calculations using surface integral equation radiation and scattering (SIERRAS) and T-matrix codes.
The steady state analysis of the scattering of plane acoustic waves from submerged rigid and elastic bodies using two approaches is presented. The first approach uses a combined finite element/boundary element (FE/BE) methodology. The NASA structural analysis (NASTRAN) program is used to formulate the structural matrices based on the finite element method (FEM). The surface integral equation radiation and scattering (SIERRAS) program creates the fluid matrices based on the boundary element method (BEM) and solves the coupled fluid-structure interaction problem. A superparametric boundary element (BE) with nine nodes is employed. The combined Helmholtz integral equation formulation (CHIEF) is employed to provide a unique solution for all frequencies. In the second approach, the superposition method (SUP) is used for modeling the fluid. The SUP method is an off-boundary approach that employs a number of point sources moved inside the body to represent the fluid response at the surface. This allows the fluid matrices to be formed without surface integration. Formulations for the SUP method are introduced for both the radiation and scattering problems. The program SUPER reads the NASTRAN structural matrices and solves the combined FE/SUP fluid-structure equations. The FE/BEM and FE/SUP methods are applied to the scattering of an infinite set of plane waves from a submerged rigid sphere, rigid prolate spheroid, right cylinder, and from an elastic cylindrical shell with hemispherical endcaps. The SUP method is found to be easier to implement and to provide an accurate result at internal resonance frequencies where the BEM requires additional equations to ensure an accurate solution.
The steady-state analysis of submerged rigid and elastic bodies using two approaches is presented. In the first approach, a combined finite element/boundary element approach is used. The finite element program NASTRAN (NASA structural analysis) is used to formulate the structural matrices. The SIERRAS (surface integral equation radiated noise and analysis) program is then used to solve the coupled fluid-structure interaction problem. A superparametric boundary element with nine nodes is used. In the second approach, the superposition method is employed for modeling the fluid. The superposition method employs a number of point sources moved inside the body to represent the fluid response at the surface. This allows the fluid matrices to be formed without surface integration. Formulations for the superposition method are given for both the radiation and scattering problems. The methodologies are demonstrated for the scattering of an infinite set of plane waves from a submerged rigid sphere, prolate spheroid, and elastic spherical shell.
A recent study of fluid-borne waves on plates with one-sided fluid loading [M. Talmant, Ph.D thesis, University of Paris VII (1987)] allows the prediction of the corresponding waves and their resonances (as well as of the Lamb-wave resonances) on thin submerged spherical shells. Similar fluid waves and the ensuing bifurcation in the dispersion curves of the first antisymmetric vibration mode (reminiscent of the repulsion of atomic levels) on cylindrical shells were previously described [Breitenbach et al., J. Acoust. Soc. Am. 74, 1267 (1983); J. V. Subrahmanyam, Ph.D. thesis, Catholic University (1983)] and observed [Talmant et al., J. Acoust. Soc. Am. (in press)]. The predicted resonances were confirmed by scattering cross section calculations using SIERRAS (R.D.M.) and T-matrix (M.F.W.) codes.
A typical structure-borne noise control configuration consists of a vibrating machine, a set of resilient isolation mounts, a foundation supporting structure, and a building floor or deck. If the floor is represented by an infinite flat plate and the foundation is comprised of structural beam elements, the acoustic power transmitted to the floor can be calculated in exact fashion using the dynamic direct stiffness technique. This analysis approach involves the representation of beam segment properties in terms of dynamic frequency-dependent stiffness coefficients. The solution of dynamic displacement response to a harmonic input force parallels the solution of static deflections to an applied constant load. Calculations of transmitted acoustic power were made for a range of foundation structural parameters and resilient mounting configurations. The results indicate the sensitivity to such design parameters on structure-borne noise transmission.
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