This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.
The noise control at multiple tonal frequencies simultaneously, in the low frequency range, is a challenge for aerospace, ground transportation and building industries. In the past few decades, various low frequency noise control solutions based on acoustic metamaterial designs have been presented in the literature. These solutions showed promising performance and are considered a better alternative to conventional sound insulation materials. In the present investigation, it was noticed that subdividing the cavity of a Helmholtz resonator allowed the control of multi-tonal noise at several resonance frequencies simultaneously and a shift of the resonance peaks towards the low frequencies. This paper proposes concepts of Helmholtz resonators with subdivided cavities to improve the sound transmission loss (STL) performance and simultaneously control the noise at several tonal frequencies. HRs with cylindrical shaped cavities were embedded in a layer of porous material. The STL of the metamaterial noise insulation configuration was predicted using serial and parallel assemblies of transfer matrices (TMM) incorporating a thermo-viscous-acoustic approach to accurately account for the viscous and thermal losses of acoustic wave propagation within the metamaterial. The STL calculated using the proposed TMM approach were observed to be in excellent agreement with the finite element method (FEM) numerical results.
More frequently, recent low-frequency noise control techniques commonly implemented in aerospace and ground transportation as well as in building applications are based on acoustic metamaterial concepts. The technologies proposed in the literature, using layered porous materials with embedded Helmholtz resonators (HR), exhibited considerable potential when tuned at tonal, multi-tonal or narrow frequency bands. Our recent investigations have shown that the acoustical performance of these metamaterials can be further improved by the use of resonators with complex shaped necks. These necks can be designed and optimized to minimize the HR resonance frequencies (small form factor) and maximize the sound transmission loss (STL) performance. This paper presents the developed design optimization method for HRs with complex neck shapes recessed within the HR cavity. The HRs were embedded in a layer of porous material. The implemented approach was based on the transfer matrix methods (TMM) in series and in parallel coupled to a multi-objective optimization. Complex optimum neck shapes were obtained allowing for a shift towards the low frequencies of the resonator resonance with a good STL performance. Moreover the STL calculated using the TMM approach were observed to be in excellent agreement with the finite element method numerical results.
This paper examines the use of proper orthogonal decomposition (POD) and singular value decomposition (SVD) to identify zones on the surface of the source that contribute the most to the sound power the source radiates. First, computational fluid dynamics (CFD) is used to obtain the pressure field at the surface of the blade in a subsonic regime. Then the fluctuation of this pressure field is used as the input for the loading noise in the Ffowcs Williams and Hawkings (FW&H) acoustic analogy. The FW&H analogy is used to calculate the sound power that is radiated by the blade. Secondly, the most important acoustic modes of POD and SVD are used to reconstruct the radiated sound power. The results obtained through POD and SVD are similar to the acoustic power directly obtained with the FW&H analogy. It was observed that the importance of the modes to the radiated sound power is not necessarily in ascending order (for the studied case, the seventh mode was the main contributor). Finally, maps of the most contributing POD and SVD modes have been produced. These maps show the zones on the surface of the blade, where the dipolar aeroacoustic sources contribute the most to the radiated sound power. These identifications are expected to be used as a guide to design and shape the blade surface in order to reduce its radiated noise.
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