基于级数变换法的椭圆柱壳受迫振动分析

摘要

由于椭圆柱壳周向曲率的变化,壳体振动方程中状态变量的系数是关于周向曲率的变系数,造成振动方程在周向波数域内不解耦,为求解带来困难.本文基于Flügge壳体理论推导出椭圆柱壳体的受迫振动方程,采用波传播法将椭圆柱壳位移以双Fourier级数形式展开,周向曲率以单Fourier级数形式展开,通过级数变换将变系数的偏微分方程组转换为周向波数相互耦合的有限阶常系数线性方程组,通过求解耦合方程得到椭圆柱壳受迫振动下的位移响应.通过与数值仿真及已有文献结果进行对比,验证了本文方法的准确性,同时具有较高的求解效率.通过对影响壳体振动的主要参数进行分析,得出激励力沿长半轴方向激励的输入功率流较小,沿短半轴方向激励的输入功率流较大;椭圆度对壳体输入功率流的影响主要在低频域;壳厚比减小,椭圆柱壳输入功率流峰值向低频偏移且幅值增大.%Due to its varied circumferential curvature,the coefficients of the state variables in the vibration equations of the elliptic cylindrical shell also vary with the circumferential curvature.Vibration equations are difficult to solve because they are coupled in the domain of the circumferential wave numbers.We derived the forced vibration equations of the elliptic cylindrical shell based on the Flügge shell theory.We then expanded the displacements of the elliptic cylindrical shell in the form of the double Fourier series using the wave propagation method and expanded the circumferential curvature in a single Fourier series.We then converted the partial differential equations with variable coefficients into a set of linear equations that were coupled to each other with respect to the circumferential wave numbers.We obtained the forced vibration responses of the elliptic cylindrical shell by solving the coupled equations.The results show good agreement with published and FEM results.In addition,our method has higher calculation efficiency.Through the analysis of the influences of the main parameters on the vibration of the elliptic cylindrical shell,we can draw the following conclusions: the input power flow is smaller when the exciting force is activated along the semi-major axis,and the input power flow is larger along the semi-minor axis.The influence of the ellipticity on the input power flow is mainly in the low-frequency domain.The peak of the input power flow has a lower frequency and the amplitude also increases with a decrease in the shell thickness ratio.