Analytic Formulation for the Sound Absorption of a Panel Absorber under the Effects of Microperforation, Air Pumping, Linear Vibration and Nonlinear Vibration

Abstract

This study includes the first work about the absorption of a panel absorber under the effects of microperforation, air pumping, and linear and nonlinear vibrations. In practice, thin perforated panel absorber is backed by a flexible wall to enhance the acoustic performance within the room. The panel is easily excited to vibrate nonlinearly and the wall can vibrate linearly. However, the assumptions of linear panel vibration and no wall vibration are adopted in many research works. The development of the absorption formula is based on the classical approach and the electroacoustic analogy, in which the impedances of microperforation, air pumping, and linear and nonlinear vibrations are in parallel and connected to that of the air cavity in series. Unlike those finite element, numerical integration, and multiscale solution methods and so forth, the analytic formula to calculate the absorption of a panel absorber does not require heavy computation effort and is suitable for engineering calculation purpose. The theoretical result obtained from the proposed method shows reasonable agreement with that from a previous numerical integration method. It can be concluded that the overall absorption bandwidth of a panel absorber with an appropriate configuration can be optimized and widened by making use of the positive effects of microperforation, air pumping, and panel vibration.

Chaotic Vibration and Perforation Effects on the Sound Absorption of a Nonlinear Curved Panel Absorber

“…In the linear vibration part, these results were obtained from the numerical integration method and the analytical method, which were in reasonable agreement (the average difference is about 4%). The present three-mode approach was different from the simple and fast analytic approach in [33], which did not require any nonlinear equation solver. That is why in the nonlinear vibration part, there were more detectable discrepancies between the results from the two methods (the average difference was about 7%).…”

“…The difference between the normalized absorptions of the 1 mode and 4 mode cases was less than 1% (in the other two nonlinear cases, the differences were about 5 to 6%). Figure 2 compares the absorption results obtained from the numerical integration method and the analytical method in [33] (i.e., the solid line and orange circles). The initial center of deflection was 0, and the panel thickness was 2 mm.…”

“…These solution points were directly affected by the damping terms in the modal governing equations. The method in [33] and the proposed method were based on the classic analytic approach and numerical integration method, respectively. This is why some solution points which can be obtained from the proposed method might be missing at the ends of the solution curves obtained from the method in [33].…”

“…The method in [33] and the proposed method were based on the classic analytic approach and numerical integration method, respectively. This is why some solution points which can be obtained from the proposed method might be missing at the ends of the solution curves obtained from the method in [33]. It is because their solution forms were different.…”

UQ eSpace

“…Analytical formulae to determine absorption coefficients require heavy computational resources and require initial assumptions which hinder accurate absorption coefficient predictions (Lee, 2014). On the other hand, experimental measurements of absorption coefficients are more efficient and accurate.…”