Abstract
The paper introduces a semi-analytical approach to analyze free vibration characteristics of stepped functionally graded (FG) paraboloidal shell with general edge conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement components along axial direction are represented by Jacobi polynomials, and the Fourier series are utilized to express displacement components in circumferential direction. Based on penalty method about spring stiffness technique, the general edge conditions of doubly curved paraboloidal shell can be easily simulated. The solutions about doubly curved paraboloidal shell were solved by approach of Rayleigh–Ritz. Convergence study about boundary parameters, Jacobi parameters et al. are carried out, respectively. The comparison with published literatures, FEM and experiment results show that the present method has good convergence ability and excellent accuracy.
Highlights
The stepped functionally graded (FG) paraboloidal shells are very useful in the engineering
The stepped FG paraboloidal shells are very useful in the engineering
The vibration problems of the structures have always been the concern of the research: Fantuzzi et al [1] investigated free vibration behavior of FG cylindrical and spherical shells
Summary
The stepped FG paraboloidal shells are very useful in the engineering. The vibration problems of the structures have always been the concern of the research: Fantuzzi et al [1] investigated free vibration behavior of FG cylindrical and spherical shells. Used the GDQ approach to investigate the vibration behavior of FGM shells and panels. Based on higher-order finite element method, Pradyumna and Bandyopadhyay [3] studied the vibration behavior of FG structures. Wang et al [6,7,8,9] investigated the approach of Improved Fourier to study vibration phenomenon of various structures. Kar and Panda [14] studied vibration characteristics of FG spherical shell by FEM. Zghal [16] investigated the vibration characteristics of FG shells. Kulikov et al [17] dealt with a recently developed approach to analyze free vibration behavior of FG plates by the formulations of sampling surfaces. Kapuria et al [18] developed a four-node quadrilateral element method to analyze dynamic vibration of FGM shallow shells
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