Index of content:
Volume 125, Issue 1, January 2009
- STRUCTURAL ACOUSTICS AND VIBRATION 
Fuzzy structure theory modeling of sound-insulation layers in complex vibroacoustic uncertain systems: Theory and experimental validation125(2009); http://dx.doi.org/10.1121/1.3035827View Description Hide Description
The fuzzy structure theory was introduced 20 years ago in order to model the effects of complex subsystems imprecisely known on a master structure. This theory was only aimed at structural dynamics. In this paper, an extension of that theory is proposed in developing an elastoacoustic element useful to modelsound-insulation layers for computational vibroacoustics of complex systems. The simplified model constructed enhances computation time and memory allocation because the number of physical and generalized degrees of freedom in the computational vibroacoustic model is not increased. However, these simplifications introduce model uncertainties. In order to take into account these uncertainties, the nonparametric probabilistic approach recently introduced is used. A robust simplified model for sound-insulation layers is then obtained. This model is controlled by a small number of physical and dispersion parameters. First, the extension of the fuzzy structure theory to elastoacoustic element is presented. Second, the computational vibroacoustic model including such an elastoacoustic element to modelsound-insulation layer is given. Then, a design methodology to identify the model parameters with experiments is proposed and is experimentally validated. Finally, the theory is applied to an uncertain vibroacoustic system.
125(2009); http://dx.doi.org/10.1121/1.3021418View Description Hide Description
This paper describes a wavefinite element method for the numerical prediction of wavecharacteristics of cylindrical and curved panels. The method combines conventional finite elements and the theory of wave propagation in periodic structures. The mass and stiffness matrices of a small segment of the structure, which is typically modeled using either a single shell element or, especially for laminated structures, a stack of solid elements meshed through the cross-section, are postprocessed using periodicity conditions. The matrices are typically found using a commercial FE package. The solutions of the resulting eigenproblem provide the frequency evolution of the wavenumber and the wave modes. For cylindrical geometries, the circumferential order of the wave can be specified in order to define the phase change that a wave experiences as it propagates across the element in the circumferential direction. The method is described and illustrated by application to cylinders and curved panels of different constructions. These include isotropic, orthotropic, and laminated sandwich constructions. The application of the method is seen to be straightforward even in the complicated case of laminated sandwich panels. Accurate predictions of the dispersion curves are found at negligible computational cost.
125(2009); http://dx.doi.org/10.1121/1.3021312View Description Hide Description
The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analysis methods. Particular attention is paid to the coupled waves. The problem is formulated directly in terms of displacements which leads to a Sturm–Liouville system. The resolvent kernel (Green’s function) is expressed in terms of simple plane-wave solutions. Application of Stone’s formula leads naturally to eigenfunction expansions in terms of generalized eigenvectors with oscillatory behavior at infinity. The generalized eigenfunction expansion is employed to define a diffuse field as a white noise process in modal space. By means of a Wigner transform, we calculate vertical to horizontal kinetic energy ratios in layered media, as a function of depth and frequency. Several illustrative examples are considered including energy ratios near a free surface, in the presence of a soft layer. Numerical comparisons between the generalized eigenfunction summation and a classical locked-mode approximation demonstrate the validity of the approach. The impact of the local velocity structure on the energy partitioning of a diffuse field is illustrated.