Abstract
In this paper, post-buckling and free nonlinear vibration of microbeams resting on nonlinear elastic foundation subjected to axial force are investigated. The equations of motion of microbeams are derived by using the modified couple stress theory. Using Galerkin’s method, the equation of motion of microbeams is reduced to the nonlinear ordinary differential equation. By using the equivalent linearization in which the averaging value is calculated in a new way called the weighted averaging value, approximate analytical expressions for the nonlinear frequency of microbeams with pinned–pinned and clamped–clamped end conditions are obtained in closed-forms. Comparisons with previous solutions are showed accuracy of the present solutions. Effects of the material length scale parameter and the axial compressive force on the frequency ratios of microbeams; and effect of the material length scale parameter on the buckling load ratios of microbeams are investigated in this paper.
Highlights
With the development of science and technology, micro/ nanostructures have become increasingly important in our life and technology
Buckling analysis of functionally graded microbeams based on the modified couple stress theory was investigated by Nateghi et al [13]; in the work, it can be observed that buckling loads deviate significantly from classical elastic theory, especially for thin beams
A nonclassical beam theory was developed for static and nonlinear vibration analysis of microbeams resting on a three-layered nonlinear elastic foundation based on the modified couple stress theory and Euler–Bernoulli beam theory together with the von-Karman’s geometric nonlinearity; the work was done by Simsek [20]
Summary
With the development of science and technology, micro/ nanostructures have become increasingly important in our life and technology. Mathematical Problems in Engineering of supported laminated composite beams subjected to transverse loads Lou and He [17] used the modified couple stress theory and the Kirchhoff/Mindlin plate theory together with the von Karman’s geometric nonlinearity to study the nonlinear bending and free vibration responses of a supported FG microplate resting on an elastic foundation. A nonclassical beam theory was developed for static and nonlinear vibration analysis of microbeams resting on a three-layered nonlinear elastic foundation based on the modified couple stress theory and Euler–Bernoulli beam theory together with the von-Karman’s geometric nonlinearity; the work was done by Simsek [20]. Analytical solutions of stability problem for axially loaded nanobeams based on strain gradient elasticity and modified couple stress theories were presented by Akgoz and Civalek [21]. Effects of the material length scale parameter and the axial compressive load on nonlinear responds of Pinned – Pinned (P-P) and Clamped-Clamped (C-C) microbeams are investigated in this work
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
