Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories

In this study, by using the modified couple stress theory, the vibration analysis of composite laminated beams in order of micron is developed. It should be mentioned that this theory is capable to capture the size effect by considering the material length scale parameters unlike the classical continuum theories. The Hamilton’s principle is applied to obtain the governing equations and boundary conditions of micro composite laminated beams. By considering three beam models, i.e. Euler–Bernoulli, Timoshenko and Reddy beam models, the differences between them and the effect of shear deformation are studied. This is the first study that introduces the couple stress-curvature relation for Reddy beam model properly. Furthermore, three boundary conditions, i.e. hinged–hinged, clamped–hinged and clamped–clamped and four types of lamination, i.e. [0, 0, 0], [0, 90, 0], [90, 0, 90] and [90, 90, 90] are investigated. Using generalized differential quadrature (GDQ) method, the governing equations are numerically solved and natural frequencies are obtained. Also, the governing equations are analytically solved for hinged-hinged boundary condition by employing the Fourier series expansions. Comparison between results obtained by GDQ method and analytical solution for hinged-hinged boundary condition reveals the GDQ method as an accurate and powerful method to solve the governing equations.