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Sound radiation of a vibrating elastically supported circular plate embedded into a flat screen revisited using the Zernike circle polynomials

机译:振动弹性支撑的圆形板的声辐射嵌入到使用Zernike圆多项式重新介绍的平板上

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This study deals with the problem of sound radiation by an elastically supported thin circular plate. The plate is excited asymmetrically. In such cases, usually different approximate methods are used to calculate the acoustic power. These methods are time-consuming, and some of them are applicable only to axisymmetric problems. They work only for the lowest and the highest frequencies. Consequently, their applications are limited. Another shortcoming of such methods is that they work only for either clamped circular plates or simply supported plates. In practical applications, the boundary conditions of circular plates are often required. Therefore, the model of an elastically supported plate is of a great interest in this regard. Finally, the methods presented in the literature are time-consuming and not highly accurate. They often incorporate numerical integration to calculate the acoustic pressure and the acoustic power. The use of the radial polynomials leads to much more accurate and efficient results. The acoustic power is expressed in terms of the modal impedance coefficients. The coefficients are calculated without numerical integration and with arbitrary precision in a wide low-frequency band. They are expressed in terms of a rapidly converging expansion series. The formulas presented are useful to solve the problem of vibration of a plate including arbitrary excitation, material damping, and fluid-structure interactions. This results in a system of three coupled differential equations. The first one is the Helmholtz equation governing the fluid vibrations in the upper half-space, the second one is also the Helmholtz equation governing the fluid vibrations in the lower half-space, and the third one deals with the motion of the plate. Consequently, it leads to a system of algebraic equations. Finally, the effects of the plate's boundary conditions on the acoustic power, the far field, and the near field are analyzed numerically.
机译:本研究涉及弹性支撑的薄圆板的声辐射问题。板材很兴奋。在这种情况下,通常使用不同的近似方法来计算声功率。这些方法是耗时的,其中一些方法仅适用于轴对称问题。它们仅适用于最低频率和最高频率。因此,他们的应用是有限的。这种方法的另一种缺点是它们仅适用于夹紧的圆形板或简单的支撑板。在实际应用中,通常需要圆形板的边界条件。因此,在这方面,弹性支撑板的模型非常兴趣。最后,文献中呈现的方法是耗时的,而不是高度准确的。它们通常包含数值集成以计算声压和声电源。径向多项式的使用导致更准确和有效的结果。声功率以模态阻抗系数表示。计算系数在没有数值积分并在宽的低频带中具有任意精度。它们以快速融合的膨胀系列表示。所呈现的公式可用于解决包括任意激发,材料阻尼和流体结构相互作用的板的振动问题。这导致三个耦合微分方程的系统。第一个是控制上半空间中的流体振动的亥姆霍兹方程,第二个是控制下半空间中的流体振动的亥姆霍兹方程,第三个是涉及板的运动。因此,它导致代数方程的系统。最后,在数值上分析了板的边界条件对声电源,远场和近场的影响。

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