周向加肋非圆柱壳谐振分析的一个新矩阵方法

A New Matrix Method for Response Analysis of Circumferentially Stiffened Non-Circular Cylindrical Shells Under Harmonic Pressure

基于一类柱壳谐振控制方程呈一阶常微分矩阵方程形式以及傅立叶级数展开,提出了一种新矩阵方法,求解两端简支具有环肋加强非圆柱壳在谐外压作用下的稳态响应.该方法和以往同类方法相比,有两个突出的优点:1)矩阵微分方程的解采用齐次扩容精细积分法替代龙格-库塔法,提高了精度;其中传递矩阵能实现计算机精确计算.2)环肋作用力借助Dirac-δ函数和三角级数逼近可以解析求出;除法向作用力外,还考虑了切向作用力.通过数值计算,还研究了外激励频率对壳体位移和应力的影响规律.对比有限元分析与其它方法的计算结果,表明了该方法的正确性和有效性.

Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady state vibration analysis of a non-circular cylindrical shell simply supported at two ends and circumferentially stiffened by rings under harmonic pressure. Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration approach rather than the Runge-Kutta-Gill integration method. The transfer matrix can easily be determined by a high precision integration scheme. In addition, besides the normal interacting forces, which were commonly adopted by researchers before, the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function. The effects of the exciting frequencies on displacements and stresses responses have been invesigated. Numerical results show that the proposed method is more efficient than the above mentioned method.