Abstract This study used the wave based method (WBM) to investigate the optimum layout of an absorbing material on a vibrating surface. The structural dynamic behavior was examined using the finite element model, and the acoustic response was computed using the WBM. The thickness of the absorbing material on each structural element was considered as the design variable. The sensitivity of the acoustic response to the acoustic impedance was derived using wave based system matrices, and a polynomial function was used to describe the impedance variation with respect to the thickness of the absorbing material. Thereafter, the final design sensitivity of a vibro-acoustic model was derived with respect to the thickness of the damping material using the chain rule. The design sensitivity results were found to be in good agreement with the results of the central finite difference methods. The design optimization of the absorbing material layout was applied to a vibrating surface using the design sensitivity results under various excitations, and the results of the optimization showed a layout similar to the active intensity plot of the vibrating surface. The proposed method can easily be applied to reduce the noise produced by a vibrating structure.

中文翻译：

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使用基于波的方法定义吸波材料布局的声阻抗灵敏度方法

摘要 本研究使用基于波的方法 (WBM) 来研究振动表面上吸波材料的最佳布局。使用有限元模型检查结构动态行为，并使用 WBM 计算声学响应。每个结构元件上吸收材料的厚度被视为设计变量。声学响应对声阻抗的敏感性是使用基于波的系统矩阵得出的，并且使用多项式函数来描述相对于吸收材料厚度的阻抗变化。此后，使用链式法则推导出与阻尼材料厚度相关的振动声学模型的最终设计灵敏度。发现设计灵敏度结果与中心有限差分法的结果非常一致。利用各种激励下的设计灵敏度结果，将吸波材料布局的设计优化应用于振动表面，优化结果显示出类似于振动表面活性强度图的布局。所提出的方法可以很容易地应用于减少振动结构产生的噪音。