A theoretical modelling approach is proposed for the vibroacoustic problem of sound transmission across a rectangular double-wall panel clamp mounted on an infinite rigid baffle with magnetically connected stiffness. The magnetic stiffness is derived based on interaction energy between the two rectangular magnets attached to the clamped plates. The exact solution for the vibration of the clamped double plates is taken into account by the method of modal function, and the dynamic response of the structures is obtained by employing the weighted residual (Galerkin) method. This method enabled the coupling of the acoustic and the magnetic stiffness of the link to be done effectively. The accuracy of the theoretical predictions is checked against existing experimental data, with good agreement achieved. The model is then compared with the theoretical formulation in a duct based on a low-frequency range with and without magnetic stiffness. The sound transmission loss (STL) of the two models agrees perfectly in the first resonance, but the mass–air–mass resonance frequency for the current model tends to shift towards a higher value. Furthermore, the influence of magnetic stiffness on the elevation angle and azimuth angle of the STL is investigated. The present method is suitable for double-panel systems with connecting stiffness for practical plates and is applicable for both low- and high-frequency ranges.

中文翻译：

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有限的带磁性联动刚度的双夹层墙板传声的解析模型

提出了一种理论上的建模方法，用于通过安装在无限刚性挡板上的矩形双壁面板夹的声波传播的振动声问题。磁刚度是基于附着在夹紧板上的两个矩形磁体之间的相互作用能得出的。通过模态函数的方法考虑了被夹住的双板振动的精确解，并通过加权残差（Galerkin）方法获得了结构的动力响应。这种方法可以有效地完成链节的声学刚度和磁刚度的耦合。根据现有的实验数据检查了理论预测的准确性，并取得了良好的一致性。然后将该模型与基于具有和不具有磁刚度的低频范围的管道中的理论公式进行比较。两种模型的声传输损耗（STL）在第一次共振时完全吻合，但是当前模型的质量-空气-质量共振频率趋于向更高的值偏移。此外，研究了磁刚度对STL仰角和方位角的影响。本方法适用于具有实用板连接刚度的双面板系统，并且适用于低频和高频范围。但是当前模型的质量-空气-质量共振频率趋于向更高的值偏移。此外，研究了磁刚度对STL仰角和方位角的影响。本方法适用于具有实用板连接刚度的双面板系统，并且适用于低频和高频范围。但是当前模型的质量-空气-质量共振频率趋于向更高的值偏移。此外，研究了磁刚度对STL仰角和方位角的影响。本方法适用于具有实用板的连接刚度的双面板系统，并且适用于低频和高频范围。