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Size-dependent coupled bending-torsional vibration of functionally graded carbon nanotube reinforced composite Timoshenko microbeams

Dehkordi Hamid Reza Balali, Beni Yaghoub Tadi

Archives of Civil and Mechanical Engineering

2023

Vol. 23, no. 3

art. no. e186, 2023

This paper investigates the free vibration of a carbon nanotube-reinforced composite Timoshenko microbeam considering the effect of axial load and bending-torsion coupling. The microbeam properties are developed based on the micromechanical model concerning the extended rule of mixtures. The governing equations of motion are derived using the modified couple stress theory and Hamilton’s principle. The uniform nanotube distribution and three functionally graded distributions are considered for the carbon nanotube-reinforced composite microbeam. The generalized differential quadrature method is applied to the governing equations for deriving the natural frequency under different boundary conditions. Next, the effects of different parameters, including nanotube distribution, geometric characteristics of microbeam, material length scale, and nanotube volume fraction, on the natural frequency are demonstrated through different tables and diagrams. Among obtained results is the significant effect of the carbon nanotube volume fraction on the natural frequency of the microbeam. Also, the nonconformity between the mass and elastic axes leads to the natural frequency reduction. The comparison between obtained results and results of other credible papers confirms the validity of obtained results.

Size‑dependent coupled bending-torsional vibration of Timoshenko microbeams

Balali Dehkordi Hamid Reza, Tadi Beni Yaghoub

Archives of Civil and Mechanical Engineering

2022

Vol. 22, no. 3

art. no. e124

In this paper, the coupled bending and torsional vibration analysis of microbeams under axial force based on Timoshenko’s beam theory is investigated. Modified non-classic coupled stress theory and the Hamilton principle used to establish the motion equations of the system. The generalized differential quadratures method is used to solve the obtained set of differential equations. After establishment of eigenvalue problem, two comparison studies are conducted to assure the validity and accuracy of the present solution and excellent agreement observed with the present results and those reported by other researchers in some specific cases by analytical solutions and classical beam theory. Afterwards, parametric studies are developed to examine the influences of boundary conditions, size effect, and various geometric characteristics of the beam on natural frequencies and the associated mode shapes are discussed. The results show that the non-compliance of the mass axis with the elastic axis reduces the natural frequency. Also, Poisson’s ratio have an opposite effect on the natural frequency.