A two-dimensional mathematical model has been developed to analyze the scattering of plane acoustic waves from an infinite, uniform, plane grating of compliant tubes. It relies upon the finite element method and uses the ATILA code [J. N. Decarpigny et al., J. Acoust. Soc. Am. 78, 1499 (1985) ]. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, thanks to the Bloch-Floquet theorem, and the effects of the remaining fluid domain are accounted for by matching the pressure field in the fi'nite element mesh with simple plane wave expansions of the ingoing and outgoing waves. This paper describes results obtained for the scattering of a plane wave from different tube gratings, including internal losses, at oblique incidence. Comparing finite element results to analytical or experimental results allows for the validation of the model. Then, various compliant tube gratings are considered to demonstrate the efficiency and versatility of this approach. Finally, the generalization to doubly periodic gratings is emphasized. PACS numbers' 43.20.Fn, 43.20.Bi, 43.30.Gv
Substructuring approaches are nowadays widely used to predict numerically the vibroacoustic behavior of complex mechanical systems. Some of these methods are based on admittance or mobility frequency transfer functions at the coupling interfaces. They have already been used intensively to couple subsystems linked by point contacts and enable to solve problems at higher frequency while saving computation costs. In the case of subsystems coupled along lines, a Condensed Transfer Function method is developed in the present paper. The admittances on the coupling line are condensed in order to reduce the number of coupling forces evaluated. Three variants are presented, where the transfer functions are condensed using three different functions. After describing the principle of the CTF method, simple structures will be given as test cases for validation.
The effect of uncertainties in material and geometric parameters on the acoustic performance of a viscoelastic coating is investigated. The model of the coating comprises a structure conventionally used in underwater applications, namely a soft elastic matrix embedded with periodic arrangements of voids. To investigate the effect of uncertainties on the acoustic performance of the coating, stochastic models based on the non-intrusive polynomial chaos expansion (PCE) method and Monte Carlo (MC) simulations are developed. The same analytical formulation of the acoustic coating is employed in both stochastic models. In the PCE method, the analytical model is transformed into a computationally efficient surrogate model using stochastic collocation. The effect of uncertainty in an individual geometric or material parameter on the acoustic performance of the coating is investigated by examining the mean, envelopes, and probability distribution of the monopole resonance frequency and sound transmission through the coating. The effect of variation in combinations of geometric and material parameters is then examined. Uncertainty in the geometric parameters is observed to have greater impact on the resonance frequency of the voids and sound transmission through the coating compared to uncertainty in the material properties.
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