An efficient multi-time step FEM–SFEM iterative coupling procedure for elastic–acoustic interaction problems

An iterative coupling methodology between the Finite Element Method (FEM) and the Spectral Finite Element Method (SFEM) for the modeling of coupled elastic-acoustic problems in the time domain is presented here. Since the iterative coupling procedure allows the use of a nonconforming mesh at the interface between the subdomains, the difference in the element sizes concerning the FEM and SFEM is handled in a straightforward and efficient manner, thereby retaining all the advantages of the SFEM. By means of the HHT time integration method, controllable numerical damping can be introduced in one of the subdomains, increasing the robustness of the method and improving the accuracy of the results; besides, independent time-step sizes can be considered within each subdomain, resulting in a more efficient algorithm. In this work, a modification in the subcycling procedure is proposed, ensuring not only an efficient and accurate methodology but also avoiding the computation of a relaxation parameter. Numerical simulations are presented in order to illustrate the accuracy and potential of the proposed methodology.CAPES, UFJF, UFSJ, FAPEMIG and CNP

An efficient analytical model for baffled, multi-celled membrane-type acoustic metamaterial panels

A new analytical model for the oblique incidence sound transmission loss prediction of baffled panels with multiple subwavelength sized membrane-type acoustic metamaterial (MAM) unit cells is proposed. The model employs a novel approach via the concept of the effective surface mass density and approximates the unit cell vibrations in the form of piston-like displacements. This yields a coupled system of linear equations that can be solved efficiently using well-known solution procedures. A comparison with results from finite element model simulations for both normal and diffuse field incidence shows that the analytical model delivers accurate results as long as the edge length of the MAM unit cells is smaller than half the acoustic wavelength. The computation times for the analytical calculations are 100 times smaller than for the numerical simulations. In addition to that, the effect of flexible MAM unit cell edges compared to the fixed edges assumed in the analytical model is studied numerically. It is shown that the compliance of the edges has only a small impact on the transmission loss of the panel, except at very low frequencies in the stiffness-controlled regime. The proposed analytical model is applied to investigate the effect of variations of the membrane prestress, added mass, and mass eccentricity on the diffuse transmission loss of a MAM panel with 120 unit cells. Unlike most previous investigations of MAMs, these results provide a better understanding of the acoustic performance of MAMs under more realistic conditions. For example, it is shown that by varying these parameters deliberately in a checkerboard pattern, a new anti-resonance with large transmission loss values can be introduced. A random variation of these parameters, on the other hand, is shown to have only little influence on the diffuse transmission loss, as long as the standard deviation is not too large. For very large random variations, it is shown that the peak transmission loss value can be greatly diminished.</p

Analytical model for low-frequency transmission loss calculation of membranes loaded with arbitrarily shaped masses

An analytical model for the transmission loss calculation of thin rectangular and circular membranes loaded with rigid masses of arbitrary shape, the so-called membrane-type acoustic metamaterials, is presented. The coupling between the membrane and the added masses is introduced by approximating the continuous interaction force with a set of discrete point forces. This results in a generalized linear eigenvalue problem that is solved for the eigenfrequencies and eigenvectors of the coupled system. The concept of the effective surface mass density is employed to calculate the low-frequency transmission loss using the obtained eigenpairs. The proposed model is verified using numerical data from a finite element model and the convergence behavior of the point matching approach is investigated using Richardson extrapolation. Finally, a method based upon the grid convergence index for estimating the error that is introduced due to the point matching approach is presented.</p

A membrane-type acoustic metamaterial with adjustable acoustic properties

A new realization of a membrane-type acoustic metamaterial (MAM) with adjustable sound transmission properties is presented. The proposed design distinguishes itself from other realizations by a stacked arrangement of two MAMs which is inflated using pressurized air. The static pressurization leads to large nonlinear deformations and, consequently, geometrical stiffening of the MAMs which is exploited to adjust the eigenmodes and sound transmission loss of the structure. A theoretical analysis of the proposed inflatable MAM design using numerical and analytical models is performed in order to identify two important mechanisms, namely the shifting of the eigenfrequencies and modal residuals due to the pressurization, responsible for the transmission loss adjustment. Analytical formulas are provided for predicting the eigenmode shifting and normal incidence sound transmission loss of inflated single and double MAMs using the concept of effective mass. The investigations are concluded with results from a test sample measurement inside an impedance tube, which confirm the theoretical predictions.</p

Perforated membrane-type acoustic metamaterials

This letter introduces a modified design of membrane-type acoustic metamaterials (MAMs) with a ring mass and a perforation so that an airflow through the membrane is enabled. Simplified analytical investigations of the perforated MAM (PMAM) indicate that the perforation introduces a second anti-resonance, where the effective surface mass density of the PMAM is much higher than the static value. The theoretical results are validated using impedance tube measurements, indicating good agreement between the theoretical predictions and the measured data. The anti-resonances yield high low-frequency sound transmission loss values with peak values over 25 dB higher than the corresponding mass-law.</p

Aeroacoustic analysis of a NACA 0015 airfoil with Gurney flap based on time-resolved PIV measurements

The present study investigates the feasibility of high-lift devices noise prediction based on measurements of time-resolved particle image velocimetry (TR-PIV). The model under investigation is a NACA 0015 airfoil with Gurney flap with height of 6% chord length. The velocity fields around and downstream the Gurney flap are measured by PIV and are used for the PIV-based noise predictions. The predictions are assessed via microphone measurements. Since the Gurney flap height is much smaller than the emitted acoustic wavelength, the source of noise can be considered compact and the integral implementation of Curle's analogy based on the unsteady aerodynamic loads can be followed. The results are compared with the simultaneous microphone measurements in terms of time histories and power spectra. The integral formulation of Curle's analogy yields acoustic sound pressure levels in good agreement with the simultaneous microphone measurements for the tonal component. All the calculated far-field noise power spectra reproduce the peak at vortex shedding frequency, which also agrees well with the microphone measurements.</p

Meteorological effects on the noise shielding by low parallel wall structures

Numerical calculations, scale model experiments and real-life implementations have shown that the insertion of a closely spaced array of low parallel walls beside a road is potentially a valuable road traffic noise abatement technique. However, all previous studies have assumed a non-refracting and non-turbulent atmosphere. This study carries out a numerical assessment of the extent to which the noise reduction is preserved in the presence of wind gradients and turbulence. Several full-wave calculation techniques have been used to model the noise reduction provided by parallel walls subject to moderate and strong winds, and in a turbulent atmosphere. While meteorological effects do not deteriorate the insertion loss of the parallel wall array in the low frequency range, higher sound frequencies are strongly negatively affected. These numerical results are compared to the noise shielding of traditional highway noise walls with different heights including refraction