An analytical method of free vibration analysis of elliptic cylindrical shell with ring stiffeners#br#
FANG Min1，ZHU Xiang1,2，LI Tianyun1,2,HU xiaofang3
1. School of Naval Architecture & Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, Wuhan 430074, China;
3. China Ship Development and Design Center, Wuhan 430064, China
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.
方敏1，朱翔1,2，李天匀1,2,胡晓芳3. 环肋椭圆柱壳自由振动分析的一种解析法[J]. 振动与冲击, 2018, 37(12): 138-146.
FANG Min1，ZHU Xiang1,2，LI Tianyun1,2, HU Xiaofang3. An analytical method of free vibration analysis of elliptic cylindrical shell with ring stiffeners#br#. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(12): 138-146.
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