Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

doi:10.1007/s10483-020-2670-6

摘要/Abstract

摘要： The bending and free vibrational behaviors of functionally graded (FG) cylindrical beams with radially and axially varying material inhomogeneities are investigated. Based on a high-order cylindrical beam model, where the shear deformation and rotary inertia are both considered, the two coupled governing differential motion equations for the deflection and rotation are established. The analytical bending solutions for various boundary conditions are derived. In the vibrational analysis of FG cylindrical beams, the two governing equations are firstly changed to a single equation by means of an auxiliary function, and then the vibration mode is expanded into shifted Chebyshev polynomials. Numerical examples are given to investigate the effects of the material gradient indices on the deflections, the stress distributions, and the eigenfrequencies of the cylindrical beams, respectively. By comparing the obtained numerical results with those obtained by the three-dimensional (3D) elasticity theory and the Timoshenko beam theory, the effectiveness of the present approach is verified.

关键词: higher-order beam theory, circular cross-section, bi-directional functionally graded (FG) beam, bending analysis, free vibration

Abstract: The bending and free vibrational behaviors of functionally graded (FG) cylindrical beams with radially and axially varying material inhomogeneities are investigated. Based on a high-order cylindrical beam model, where the shear deformation and rotary inertia are both considered, the two coupled governing differential motion equations for the deflection and rotation are established. The analytical bending solutions for various boundary conditions are derived. In the vibrational analysis of FG cylindrical beams, the two governing equations are firstly changed to a single equation by means of an auxiliary function, and then the vibration mode is expanded into shifted Chebyshev polynomials. Numerical examples are given to investigate the effects of the material gradient indices on the deflections, the stress distributions, and the eigenfrequencies of the cylindrical beams, respectively. By comparing the obtained numerical results with those obtained by the three-dimensional (3D) elasticity theory and the Timoshenko beam theory, the effectiveness of the present approach is verified.

Key words: higher-order beam theory, circular cross-section, bi-directional functionally graded (FG) beam, bending analysis, free vibration

中图分类号:

Yong HUANG. Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(10): 1497-1516.

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