The vibro-acoustic behaviors of combined elliptical–cylindrical–elliptical​ shells (CECES) is studied by the spectral-energy boundary element approach. The Jacobian orthogonal polynomials and the variational principles are employed to establish the dynamic model of the CECES. The Kirchhoff–Helmholtz integral equation is used to calculate the exterior sound radiation of the CECES. The Chebyshev polynomials and the Fourier series are adopted to express the acoustic variables along the meridional direction and the circumferential direction of the CECES, respectively. In this case, the two-dimensional Helmholtz integral formulation is simplified to a one-dimensional problem. By using the spectral boundary element and Chebyshev collocation points to discretize the acoustic boundary, the mathematical difficulties of traditional boundary element method which needs physical points to integrate can be overcome. Furthermore, to solve the problem of singularity and frequency non-uniqueness in the acoustic solution, the CHIEF method is used. The full vibro-acoustic coupling model is established by considering the work due to the external field acting on the CECES surface. By comparing to the acoustic responses obtained by the coupled BEM/FEM, the present method is proved to have enough accuracy for predicting the vibro-acoustic behaviors of CECES. Furthermore, study on the influence of the circumferential wave modes, boundary condition and acoustic medium on vibro-acoustic behaviors of the CECES is made by several numerical examples, which contributes to the preliminary design of the CECES.

通过光谱-能量边界元方法研究了组合椭圆-圆柱-椭圆壳 (CECES) 的振动声学行为。采用雅可比正交多项式和变分原理建立CECES的动态模型。基尔霍夫-亥姆霍兹积分方程用于计算 CECES 的外部声辐射。分别采用切比雪夫多项式和傅里叶级数来表示沿CECES子午方向和圆周方向的声变量。在这种情况下，二维亥姆霍兹积分公式被简化为一维问题。通过使用谱边界元和切比雪夫搭配点对声学边界进行离散化，克服了传统边界元法需要物理点积分的数学难点。此外，为了解决声学解中的奇异性和频率非唯一性问题，使用了CHIEF方法。考虑外场作用于CECES表面的功，建立了完整的声振耦合模型。通过与耦合 BEM/FEM 获得的声学响应进行比较，证明本方法具有足够的精度来预测 CECES 的振动声学行为。此外，通过几个数值算例研究了圆周波模态、边界条件和声介质对CECES振声行为的影响，为CECES的初步设计做出了贡献。