提出了求解环肋椭圆柱壳自由振动的一种解析法。基于Flügge壳体理论建立了环肋椭圆柱壳的自由振动方程，采用“刚度均摊”法将环肋纳入方程，将位移沿壳体轴向和周向展开成双Fourier级数形式，将椭圆截面的变曲率沿壳体周向展开成单Fourier级数形式，使得变系数的偏微分方程组转变成常系数的线性方程组，进而求得环肋椭圆柱壳的自由振动固有频率。为了验证方法的准确性，将环肋椭圆柱壳退化成环肋圆柱壳和不加肋的椭圆柱光壳，两个退化模型的计算结果与已有参考文献吻合良好。同时也与有限元法进行对比直接验证了本文求解方法的准确性，并给出了方法的适用范围。随后详细讨论了椭圆度、环肋间距和环肋高度对环肋椭圆柱壳自由振动的影响。
Abstract
An analytical solution about the free vibration behaviors of a finite elliptic cylindrical shell with ring stiffeners was proposed. The vibration equations of the shell were derived based on the Flügge shell theory and the effects of ring stiffeners were evaluated via the “smeared” stiffener theory whereby the properties of the stiffeners were averaged over the shell surface. The displacements of the shell were expanded in double Fourier series in the axial and circumferential directions and the circumferential curvature was expanded in single Fourier series in the circumferential direction. A set of partial differential equations with variable coefficients was transformed into a set of linear equations with constant coefficients and then the natural frequencies of free vibration of elliptic cylindrical shell with ring stiffeners were obtained. To verify the accuracy of the present method, the finite elliptic cylindrical shell with ring stiffeners was degenerated into two models, one of which is a ringstiffened circular cylindrical shell and the other of which is an elliptic cylindrical shell without ring stiffeners. The present results of the two degenerated shells show good agreements with available results from literature. At the same time, compared with the finite element method, the accuracy of the method was verified directly, and the application scope of the method was given. The influences of main parameters of the shell and ring stiffeners on the vibration characteristics, such as ellipticity parameter, stiffeners interval ratio and height of the stiffeners, were also discussed in detail.
关键词
环肋椭圆柱壳 /
自由振动 /
Fourier级数 /
刚度均摊
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Key words
elliptic cylindrical shell with ring stiffeners /
free vibration /
Fourier series /
“smeared&rdquo /
stiffener theory
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