Free vibration characteristics analysis of a porous functionally graded material rotating Timoshenko beam in thermal environment

Abstract

Abstract: For the porous functionally graded materials beam model with uniform pore distribution, the temperature dependence of material properties is considered and the physical neutral surface of the beam is determined firstly, then the governing differential equation of the transverse free vibration of porous functionally graded material Timoshenko beam is derived by using Hamilton principle when it rotates in thermal environment, and the dimensionless form of the governing differential equation is also obtained. Secondly, differential transformation method (DTM) is used to transform the dimensionless governing differential equations and its boundary conditions, and the equivalent algebraic characteristic equations including the dimensionless natural frequencies are obtained. The dimensionless natural frequencies of transverse free vibration of a porous functionally graded material rotating Timoshenko beam under four boundary conditions of clamped-clamped (C-C), clamped-simply supported (C-S), simply supported-simply supported (S-S) and clamped-free (C-F) in thermal environment are calculated. After degrading it the dimensionless natural frequencies obtained are compared with the calculated results in existing literatures, the validity and correctness of which are verified. Finally, the effects of boundary conditions, porosity, rotating speed, temperature, elongation ratio and gradient index on the natural frequencies of rotating porous functionally graded material Timoshenko beams are analyzed.

Key words: porous functionally graded materials, Timoshenko beams, rotating, porosity, free vibration, natural frequency, differential transformation method (DTM)

CLC Number:

O343

TENG Zhao-chun, MA Ling-quan. Free vibration characteristics analysis of a porous functionally graded material rotating Timoshenko beam in thermal environment[J]. Journal of Lanzhou University of Technology, 2022, 48(6): 164-171.

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