功能梯度圆柱壳-内声场耦合系统振声预测

Vibro-acoustic prediction of functionally graded cylindrical shell coupled with internal acoustic field

针对功能梯度(FGM)圆柱壳与其内声场的振声特性分析需求,采用特征正交-里兹法研究圆柱壳厚度、材料梯度指数、边界支撑刚度、阻抗边界和简谐力位置等因素对振声系统的影响。圆柱壳的位移及内部声压变量通过特征正交多项式与周向傅里叶谐波函数构建,并以声压做功的方式考虑结构与声场之间耦合条件,进而结合里兹法得到耦合系统的振声模态和稳态响应。研究表明,由该模型所得到的数值解与文献及有限元结果具有较好的一致性。对参数的研究发现,壳体厚度、梯度指数、边界刚度、阻抗边界和激励位置等对振声系统的耦合特性均有较为明显影响,这为该类结构的低噪声设计及其内部声场优化提供了有益的参考。

To satisfy the requirements for the vibro-acoustic analysis of a functionally graded(FGM)cylindrical shell and its internal sound field,the characteristic orthogonal-Ritz method is employed to investigate the influence of some factors,such as shell’s thickness,the material gradient index,the stiffness of the boundary support,impedance boundary,and the position of the harmonic force on the vibro-acoustic system.The displacement components of the cylindrical shell and its internal sound pressure are constructed by the characteristic orthogonal polynomials and the circumferential Fourier harmonic functions,when the coupling conditions between the structure and the sound field are considered by means of the work done by sound pressure.And then,the Ritz method is introduced to obtain the vibro-acoustic modes and steady-state response of the coupled system.This research shows that the numerical solution obtained by the current model is in good agreement with the results of the literature and the finite element method.Parametric studies reveal that shell’s thickness,gradient index,boundary stiffness,impedance boundary,and excitation position play significant roles on the coupling characteristics of the vibro-acoustic system,which provides a useful reference for the low-noise design of this type of structure as well as optimization of their internal sound field.