圆柱壳振动声辐射Jacobi-Ritz时域半解析法及特性分析

Jacobi-Ritz time domain semi-analytic method and characteristic analysis of cylindrical shell vibro-acoustic radiation

针对圆柱壳结构瞬态声振特性分析研究不足,结合Newmark-β积分法和Kirchhoff时域边界积分方程,提出一种圆柱壳受迫振动声辐射Jacobi-Ritz时域半解析法。基于一阶剪切变形理论和微元法思想,建立了圆柱壳振动声辐射分析模型,采取Jacobi多项式和Fourier级数表示轴向和周向位移容许函数,基于Rayleigh-Ritz法和Newmark-β积分法计算圆柱壳的受迫振动时域响应,在此基础上,基于Kirchhoff积分方程求解辐射噪声时域响应,分析圆柱壳受迫振动声辐射特性。与有限元方法/边界元方法数值结果对比表明,该方法具备收敛性好、精度高等优点,圆柱壳结构声振响应峰值随边界条件的刚度变弱存在左移现象,振动声辐射响应随厚度的增加呈现下降趋势;当随机载荷峰值频率与结构固有频率接近时,结构声振响应出现强特征线谱。

Considering the deficiency in the research on transient vibro-acoustic characteristics of cylindrical shell structures,a Jacobi-Ritz semi-analytic method for forced vibration sound radiation of cylindrical shells in time domain was proposed by combining Newmark-βintegral method and Kirchhoff boundary element integral equation in time domain.Based on the theory of first-order shear deformation and the idea of element method,a calculation and analysis model of vibration acoustic radiation of cylindrical shell was established.Jacobi polynomial and Fourier series were used to represent the allowable functions of axial and circumferential displacement.The time domain response of forced vibration of cylindrical shell was calculated on the basis of the Rayleigh-Ritz method and Newmark-βintegral method.Based on Kirchhoff integral equation,the time domain response of radiated noise was solved,and the acoustic radiation characteristics of forced vibration of cylindrical shell were analyzed.Compared with finite element method/boundary element method numerical results,the proposed method has the characteristics of good convergence and high precision.The peak value of acoustic response of cylindrical structures shifts to the left with the weakening of the boundary condition stiffness,and the vibration acoustic response decreases with the increase of the thickness.When the peak frequency of random load is close to the natural frequency of the structure,strong characteristic line spectrum appears in the acoustic response of the structure.