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(a) Vibration amplitude ratio versus frequency ratio (in-phase mode, nine acoustic modes, two harmonic terms). (b) Vibration amplitude ratio versus frequency ratio (out of phase mode, nine acoustic modes, two harmonic terms). (c) Axial forces and moments acting on a plate element (side view). When the vibration amplitude is large, θ is large, the axial force acting on the panel is significant, and the nonlinear stiffness due to the axial deformation must be considered. When the vibration amplitude is small, sin θ ≈ 0 and the axial force is neglectable (the linear vibration theory is valid for small deflection), where N is the axial force; M is the bending moment; θ is the slope.
Source publication
The nonlinear structural acoustic problem considered in this study is the nonlinear natural frequency analysis of flexible double panels using the elliptic integral solution method. There are very limited studies for this nonlinear structural-acoustic problem, although many nonlinear plate or linear double panel problems have been tackled and solve...
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Citations
... However, frequency-amplitude analysis was not included in [10] or in any other related works. In the work of [11], two governing equations for two identical panels with same vibration amplitude coupled with a cavity were simplified to become just one governing equation. This is the equivalent of a governing equation for a panel-cavity problem with only one flexible panel (not two). ...
... It is assumed that the panel absorber and flexible wall are simply supported. According to [10,11], the governing equations of the nonlinear symmetric panel and flexible wall are shown in the following, ...
... Thus, the residual terms, R c and R o , are considered on the right side of Equations (3) and (4). ω is the nonlinear resonant frequency of the whole structural acoustic system and given by [11] ...
This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.
