Influence of the pre-stress of the nonlinear membrane absorber for targeted energy transfer applied to 3D acoustic cavit
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(2020) 42:557
TECHNICAL PAPER
Influence of the pre‑stress of the nonlinear membrane absorber for targeted energy transfer applied to 3D acoustic cavity Jianwang Shao1 · Tao Zeng1 · Xian Wu1 · Jinmeng Yang1 Received: 3 January 2020 / Accepted: 25 September 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract The targeted energy transfer (TET) technique could be applied to reduce the low frequency noise by a nonlinear membrane absorber as nonlinear energy sink (NES) inside a tube or an acoustic cavity. The pre-stress of the nonlinear membrane can affect the desired working zone for the TET and also the suppressed amplitude of noise. In order to design the nonlinear membrane according to a given acoustic medium, the influence of the pre-stress of the nonlinear membrane is quantitatively studied in this paper. The analytical formulae over the pre-stress of the membrane are established based on a general model of the system with an acoustic mode of 3D acoustic cavity and one membrane. Meanwhile, the suppressed frequency bandwidth of noise is investigated under different pre-stress levels of the membrane by using harmonic balance method and numerical method. For convenient applications, the radial deformation analysis and the modal analysis of the membrane with the prestress are finally performed by finite element method (FEM) to obtain the relationship between the radial displacement and the first mode. It can be helpful to guide design of the pre-stress of the membrane NES according to the desired working zone for the practice engineering application in acoustic field. Keywords Nonlinear membrane absorber · Pre-stress · Targeted energy transfer · Modal analysis · 3D acoustic cavity
1 Introduction The nonlinear energy sink (NES) as a nonlinear vibration absorber was first proposed by Vakakis and Gendelman [1, 2] in 2001, and then has become a research hotspot in recent years by using the target energy transfer (TET) phenomenon to achieve vibration suppression. NES is usually an additional mass with strong nonlinear stiffness and viscous damping connected to the primary system. With the advantages of simplicity, high efficiency, strong robustness, short time needed for vibration reduction, it owns high application value in the field of mechanical vibrations [3–7]. In addition, by using a rubber membrane with nonlinear stiffness as a NES to control low-frequency noise in one tube (1D acoustic system), Cochelin et al. [8] took the lead in applying NES to acoustic filed in 2006. Subsequently, Bellet Technical Editor: Pedro Manuel Calas Lopes Pacheco, D.Sc.. * Xian Wu [email protected] 1
School of Automotive Studies, Tongji University, Shanghai, China
et al. [9, 10] demonstrated that the membrane as nonlinear absorber could tune itself to any linear system and operate in a large frequency band. Mariani et al. [11] verified that a loudspeaker working outside its linear regime could be an efficient NES. Cote et al. [12] found that an introduced second excitation frequency was benefic
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