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了分析，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。
Abstract
The free vibration equations of elliptic cylindrical shell are derived based on Flügge shell theory. Vibration equations are not decoupled about the circumferential wave number due to the varied circumferential curvature. The shell’s displacements are expanded in double Fourier series in wave propagation method and the circumferential curvature is expanded in single Fourier series. The partial differential equations with variable coefficients are converted into a set of linear equations which couple with each other about circumferential wave numbers. The natural frequencies of elliptic cylindrical shell are obtained by solving the coupled equations. The influences of main parameters of elliptic cylindrical shell, such as ellipticity parameter and shell length ratio, on the vibration characteristics are discussed in detail. The symmetric and anti-symmetric modes of elliptic cylindrical shell are both considered.
关键词
椭圆柱壳 /
自由振动 /
固有频率 /
椭圆度参数 /
反对称模态
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Key words
elliptic cylindrical shell /
free vibration /
natural frequency /
ellipticity parameters /
anti-symmetric mode
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