In order to solve the vibration and acoustic characteristics of spherical shell in light fluid environment, based on Jacobi-Ritz-spectral BEM, a unified analysis formula for acoustic vibration of spherical shell under arbitrary boundary conditions is established. Based on the First-order shear deformation theory (FSDT) and domain decomposition method (DDM), the theoretical model of spherical shell structure is established. The improved Jacobi polynomial is innovatively used to construct the displacement tolerance function of the spherical shell. Based on the spectral Kirchhoff-Helmholtz integral formula, the theoretical model of the acoustic fluid outside the spherical shell is established. The special form of Jacobi polynomial Chebyshev polynomial is used to describe the excitation sound pressure on the spherical shell segment, so as to ensure that the generalized coordinates of the structure can be perfectly matched with the acoustic boundary element nodes. In addition, the integration along the meridian of the shell is used to control the movement of the fluid, which simplifies the surface integration. The CHIEF method is used to solve the problem of non-unique solution of acoustic variables of rotary structure. Compared with the published literature, numerical simulation results and experimental results, the proposed method has higher calculation accuracy. In addition, based on this method, the influence of boundary conditions, geometric dimensions and other factors on the acoustic and vibration characteristics of spherical shells is discussed, which accumulates data for analyzing the acoustic and vibration behavior of spherical shells.

中文翻译：

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用于球壳振动声学行为的统一 Jacobi-Ritz 频谱边界元法


为解决球壳在轻流体环境下的振动和声学特性，基于Jacobi-Ritz-spectral BEM，建立了任意边界条件下球壳声振动的统一分析公式。基于一阶剪切变形理论 （FSDT） 和域分解法 （DDM），建立了球壳结构的理论模型。创新性地将改进的 Jacobi 多项式用于构建球壳的位移容差函数。基于谱 Kirchhoff-Helmholtz 积分公式，建立了球壳外声流体的理论模型。采用雅可比多项式切比雪夫多项式的特殊形式来描述球壳段上的激励声压，从而保证结构的广义坐标能够与声学边界元节点完美匹配。此外，沿壳体子午线的积分用于控制流体的运动，从而简化了表面积分。采用 CHIEF 方法解决旋转结构声学变量不唯一解的问题。与已发表的文献、数值模拟结果和实验结果相比，所提方法具有更高的计算精度。此外，基于该方法，讨论了边界条件、几何尺寸等因素对球壳声学和振动特性的影响，为分析球壳的声学和振动行为积累了数据。