Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro/nanolaminated composite Euler–Bernoulli beam under thermal loading

Abstract

In this paper, the effect of finite strain on the nonlinear free vibration and bending of the symmetrically micro/nanolaminated composite beam under thermal environment within the framework of the Euler-Bernoulli and modified couple stress theory is studied. The governing equation of motion and boundary conditions are obtained using Hamilton's principle, and then they are solved by generalized differential quadrature method. The bending and free vibration of the beam are investigated for both carbon/epoxy and glass/epoxy materials based on the finite strain and von Karman assumptions subjected to different boundary conditions. Also, two different fiber orientations including unidirectional and cross-ply are considered in this research. Comparison of the bending results show that there is a significant difference between the finite strain and von Karman particularly for L ¼ 10h. Furthermore, it is found that the natural frequencies predicted by the finite strain are more than the von Karman. Also, when the microbeam is inserted under thermal loading, the natural frequencies increase.

The Response of Nanobeams with Temperature-Dependent Properties Using State-Space Method via Modified Couple Stress Theory

“…The material scale parameter of the MCS theory had a great influence on the considered fields. It is noted that the current work results were in good agreement with the results of [47,53,54]. Note, for example, that the values of deflection w in the MCS model were higher compared to classical theory.…”

A new approach for determination of interlaminar normal/shear stresses in micro and nano laminated composite beams

“…Therefore, in order to consider the size-dependent effect, various non-classical continuum theories are offered, which include the material length scale parameter, such as micropolar theory (Eringen, 1967), strain gradient theory (Lam et al, 2003), nonlocal elasticity theory (Eringen, 1972), surface elasticity theory (Gurtin et al, 1976), and modified couple stress theory (MCST) (Park and Gao, 2006). The couple stress and strain gradient theories are applied for the micro-and nanoscale structures (Farokhi and Ghayesh, 2015;Jung et al, 2014;Kahrobaiyan et al, 2014;Mohandes and Ghasemi, 2017;Park and Gao, 2006;Salamat-talab et al, 2012;Shaat et al, 2014;Wang et al, 2013Wang et al, , 2015). There is a difference between these two theories so that the rotation and strain are applied as a variable to describe curvature in the couple stress and strain gradient theories, respectively.…”

“…There is a difference between these two theories so that the rotation and strain are applied as a variable to describe curvature in the couple stress and strain gradient theories, respectively. Therefore, it is known that the couple stress theory is as a special format of the strain gradient theory (Mohandes and Ghasemi, 2017). Yin et al (2010) applied the MCST to analyze the vibration of micro-plates.…”

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

“…The governing equation was solved using the Laplace transform technique and Adomian decomposition method. Mohandes and Ghasemi (2017) presented the vibration and bending analysis of laminated beams subjected to thermal loading. The governing equation derived from Hamilton’s principle was numerically solved using the generalized differential quadrature method.…”