Nonlinear structure-extended cavity interaction simulation using a new version of harmonic balance method

Abstract

This study addresses the nonlinear structure-extended cavity interaction simulation using a new version of the multilevel residue harmonic balance method. This method has only been adopted once to solve a nonlinear beam problem. This is the first study to use this method to solve a nonlinear structural acoustic problem. This study has two focuses: 1) the new version of the multilevel residue harmonic balance method can generate the higher-level nonlinear solutions ignored in the previous version and 2) the effect of the extended cavity, which has not been considered in previous studies, is examined. The cavity length of a panel-cavity system is sometimes longer than the panel length. However, many studies have adopted a model in which the cavity length is equal to the panel length. The effects of excitation magnitude, cavity depth, damping and number of structural modes on sound and vibration responses are investigated for various panel cases. In the simulations, the present harmonic balance solutions agree reasonably well with those obtained from the classical harmonic balance method. There are two important findings. First, the nonlinearity of a structural acoustic system highly depends on the cavity size. If the cavity size is smaller, the nonlinearity is higher. A large cavity volume implies a low stiffness or small acoustic pressure transmitted from the source panel to the nonlinear panel. In other words, the additional volume in an extended cavity affects the nonlinearity, sound and vibration responses of a structural acoustic system. Second, if an acoustic resonance couples with a structural resonance, nonlinearity is amplified and thus the insertion loss is adversely affected.

The effect of large amplitude vibration on the pressure-dependent absorption of a structure multiple cavity system

“…By putting Eqs (10–13) into Eq (1), the general expression for the acoustic pressure in the three cases is given by [7,28] where ω is the excitation frequency; A(t) is the modal response of the panel; ρ a is the air density; U and V are the numbers of acoustic modes used; and where ω uv is the acoustic resonant frequency of the ( u , v ) mode…”

“…The normalized impedance of the large-amplitude vibrating panel is derived here. The governing equation of a large-amplitude vibrating panel subject to harmonic excitation is given by [7,28] where where E = Young’s modulus; ν = Poisson’s ratio; ρ = density per unit thickness; τ = panel thickness; g = gravity acceleration (9.81ms -2 ); and κ = dimensionless excitation parameter.…”