Nonlinear energy pumping in Acoustics using multistable absorbers - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2019

Nonlinear energy pumping in Acoustics using multistable absorbers

Résumé

This work addresses the development of a vibroacoustics nonlinear absorber based on the concept of a Nonlinear Energy Sink (NES) under multi-stable configuration. Numerical experiments show that adding a bistable property to a NES permits to lower its activation threshold compared to NESs with only one stable position. Since the seminal papers by Vakakis et al [1, 2], energy pumping has become a subject of growing interest. Despite highly efficient energy dissipation, the main drawback is that the higher the frequency of the primary linear system to control, the higher the amplitude for activation of non linear passive dissipation. Recent theoretical and numerical works by Manevitch et al [3], Romeo et al [4] and experimental work by Mattei et al [5] showed that a bi-stable NES (B-NES) provides improved robustness in frequency and amplitude range over existing NESs by lowering the activation threshold. This work aims at improving the absorber developed by R. Bellet et al [6]. The developed absorber is made of a high amplitude vibrating membrane that is described by linear and cubic stiffnesses and a dissipation described by linear and quadratic terms. The bistable NES developed in this work can be described by linear quadratic and cubic stiffness terms. The presence of this quadratic damping conplexifies the theoretical analysis but doesn't prevent numerical experiments. The absorber equation developed in [6] is written as m mq (t) + k 1 [(1 + χ)q(t) + ηq(t)] + k 3 (2ηq 2 (t)q(t) + q 3 (t)) = S m /(2h)p(t) (1) where m m = ρ m hS m /3 is the dynamic membrane mass, S m its section, η its viscous damping and p(t) is the forcing term. The parameter χ = 3R 2 e 0 /h 2 is the ratio between the pre-strain e 0 and the (strain) buckling load of the membrane and the coefficients k 1 and k 3 that respectively stand for the linear and nonlinear stiffnesses are defined as k 1 ≈ 1.015 4 π 5 12 Eh 3 3(1−ν 2)R 2 , k 3 = 8π Eh 3 3(1−ν 2)R 2. It is worth noting that 1.015 4 π 5 /12 = 8.24 ≈ 8 and thus k1 ≈ k 3. By denoting 1 + χ = −ζ with ζ > 0 for a buckled membrane, the Eq. (1) is then written as m mq (t) + k 1 [−ζq(t) + q 3 (t) + η(1 + 2q 2 (t))q(t)] = S m /(2h)p(t). By the change of variable q m (t) = √ ζ(y(t) + 1), one obtains a Helmholtz-Duffing like nonlinear equation for the buckled membrane, very similar to that obtained in [5] y(t)+f 2 1 y(t) + 3/2 y 2 (t) + 1/2 y 3 (t) + η 1/(2ζ) + (1 + y(t)) 2 ẏ(t) = S m /(2 ζhm m)p(t) (2) where f 1 = 2ζk 1 /m m is the linear frequency of the buckled membrane. Such an equation with a non-linearity of the form y + 3/2y 2 + 1/2y 3 possesses two stable equilibrium points (0 and-2) and one unstable (-1). We investigated the targeted energy transfer occurring between the acoustic medium (the one-dimensional tube of length L around its first acoustic mode) and the bistable membrane during both the sinusoidal forced regime and the free oscillations as proposed in [6]. Using non-dimensional quantities defined as τ = ωt, ω = c 0 π/L, and
Fichier principal
Vignette du fichier
NNM2019_Marseille_Bouzid-Cote-Mattei.pdf (106.54 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02370365 , version 1 (19-11-2019)

Identifiants

  • HAL Id : hal-02370365 , version 1

Citer

Islem Bouzid, Renaud Côte, Pierre-Olivier Mattei. Nonlinear energy pumping in Acoustics using multistable absorbers. 7 th International Conference on Nonlinear Vibrations, Localization and Energy Transfer, Jul 2019, Marseille, France. ⟨hal-02370365⟩
39 Consultations
43 Téléchargements

Partager

Gmail Facebook X LinkedIn More