基于波传播法的椭圆柱壳自由振动特性研究

Free vibration characteristics of an elliptic cylindrical shell based on the wave propagation method

基于Flügge壳体理论推导出椭圆柱壳的自由振动方程。由于椭圆柱壳周向曲率的变化,造成振动方程在周向模态阶数域内不解耦,采用波传播法将壳体位移以双Fourier级数形式展开,椭圆截面曲率半径以单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关于周向模态阶数相互耦合的有限阶常系数线性方程组,通过求解耦合振动方程得到椭圆柱壳的固有频率。随后对影响壳体固有频率的主要参数进行分析,得到椭圆柱壳对称和反对称模态频率随椭圆度、壳长比等参数的变化规律。

The free v ibrat ion equations of anellipticcy lindrical shell were derived based on the Fliigge shell theory. Vibration equations about the c ircumfe ren tial wave number are not decoupled due to the varied c ircumfe ren tial curvature. The shel l,s displacements were expanded in double Fourier series in the wave propagation method and the circumferential curvature was expanded in single Fourier series. The p a r t ia l d if fe re n t ia l equations w i th variable coefficients were converted into a set of l inear equations w h ich couple w ith each other about c ircum fe ren tial wave numbers. The natural frequencies of the el l ipt ic cyl indr ic al shell were obtained by solving the coupled equations. The influences o f main parameters of the el l ipt ic cyl indr ical s hel l, such as e l l ip t ic i ty parameter and shell length ra t io , on the v ib rat io n characteristics were discussed. The symmetric and ant i-symmetric modes o f the e l l ip t ic c y l in d r ic a l shell were both considered.