• Document: Parameters design of a nonlinear membrane absorber applied to an acoustic cavity
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Parameters design of a nonlinear membrane absorber applied to an acoustic cavity Jianwang SHAO1 ; Xian WU2,∗ 1 Tongji University, China 2 Tongji University, China ∗ Corresponding author ABSTRACT The targeted energy transfer (TET) phenomenon has been demonstrated and analyzed between an acoustic medium inside a parallelepiped cavity and a thin viscoelastic membrane that is mounted on one wall of the cavity and that is working as a nonlinear absorber or a nonlinear energy sink (NES). Based on the desired working zone of the NES and the two thresholds of the zone which have been obtained, this paper investigates the parameters analysis of a nonlinear membrane absorber to design the NES. The physical parameters of the membrane and the place of the membrane on the wall of the cavity are studied. It can finally provide us to determine where is the better place for the membrane and which parameter affects mainly the desired working zone for the NES. Keywords: Acoustic cavity, Membrane absorber I-INCE Classification of Subjects Number(s): 51 1. INTRODUCTION The concept of targeted energy transfer (TET) was proposed by Vakakis and Gendelman (1, 2), in 2001, which is a new passive technique for reducing noise and vibration. A purely nonlinear absorber is often spoken of the nonlinear energy sink (NES). Firstly, the NES was used in view of applications in the field of mechanical vibrations (3, 4, 5, 6). In acoustic, the TET phenomenon has been firstly observed and analyzed inside one tube (1D acoustic system) by a membrane NES or a loudspeaker nonlinear absorber (7, 8, 9, 10). In (11),the TET phenomenon can be also observed inside an acoustic cavity (3D acoustic system) by a membrane NES. By considering one acoustic mode of 3D acoustic cavity and one membrane NES, the desired working zone for the membrane NES inside 3D acoustic cavity have been defined and the two thresholds of the zone have also been determined analytically and semi-numerically, respectively. In the paper, a parametric analysis of the membrane absorber is performed by using the system with one acoustic mode of the acoustic cavity and one membrane NES, described in (11). The parameters are the physical parameters of the membrane and the place of the membrane on the wall of the cavity. The results show the influence of each parameter firstly for the nonlinear normal modes (NNMs) and the periodic forced responses of the system, then for the value of the plateau, the desired working zone of the NES and its two thresholds. Finally, we can conclude on where is the better place for the membrane and which parameter affects mainly the desired working zone for the NES. 2. THE TET PHENOMENON OF THE SYSTEM 2.1 Description of the system The system described in (11) is composed of a primary linear system coupled by a nonlinear system NES as shown in Figure 1. The primary linear system is an acoustic medium inside a parallelepiped cavity with dimensions Lx , Ly and Lz . We assume that all the walls are rigid. The NES is a thin viscoelastic membrane that is mounted on one wall of the cavity. The eigenfrequencies of the acoustic cavity and the acoustic pressure of 1 shaojianwang@tongji.edu.cn 2 wuxian@tongji-auto.cn Inter-noise 2014 Page 1 of 10 Page 2 of 10 Inter-noise 2014 a mode marked by the integers l, m and n are described by the following form: q c0 flmn = 2 ( Llx )2 + ( Lmy )2 + ( Lnz )2 , (1) pr (x, y, z,t) = Plmn (x, y, z) p(t) = cos( lLπxx ) cos( mLπyy ) cos( nLπzz ) p(t), where Plmn is the mode shape and p(t) is the acoustic pressure amplitude. The position of the membrane center is defined as (xm , ym , zm ), (xm = Lx in Figure 1). Figure 1 – Schema of the acoustic cavity with a membrane. We assume that the first few modes of the cavity are separated in frequency, and we focus on the interaction between one mode of the acoustic cavity and the membrane. To analyze the TET phenomenon, we consider a simplified model with two DOFs system: one for the acoustic cavity and another one for the NES. The final system with two DOFs is in the following form: ρ 2 c2 s

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