Mathematical Modeling of the Contact Interaction of Two Nanobeams Timoshenko S.P.

Abstract

The mathematical model of the contact interaction of two nanobeams obeying the kinematic hypothesis of the second approximation S.P. Timoshenko is constructed. There is a small gap between the nanobeams; an external alternating transverse load acts on the upper nanobeam. Nanobeams are isotropic, elastic, and they are connected through boundary conditions. Modified couple stress theory has been applied to describe the size-dependent effects of a beam nanostructure. Contact interaction is accounted for by the model B.Ya. Cantor. The paper studies the effect of the size-dependent coefficient. The system of differential equations is reduced to the Cauchy problem by the finite-difference method with an approximation of 0(h2) in the spatial coordinate. Further, the solution was carried out by the Runge-Kutta methods of the 4th order of accuracy in time. The convergence of numerical methods is investigated. The visualization of the results obtained by the methods of nonlinear dynamics and using wavelet transforms.