Mathematical Modeling of the Contact Interaction of Two Nanobeams Timoshenko S.P.-Reference-Cited by-同舟云学术

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

Published:2019-11-11 Issue: Volume: Page:
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Container-title:GraphiCon'2019 Proceedings. Volume 2
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Author:

Крысько Вадим¹,Krysko Vadim²,Яковлева Татьяна¹³,Yakovleva Tat'yana²⁴,Салтыкова Ольга¹,Saltykova Olga²,Кружилин Вадим⁵,Kruzhilin Vadim⁵

Affiliation:

1. Саратовский государственный технический университет имени Гагарина Ю.А.

2. Saratovskiy gosudarstvennyy tehnicheskiy universitet imeni Gagarina Yu.A.

3. Томский политехнический университет

4. Tomskiy politehnicheskiy universitet

5. Yuri Gagarin State Technical University of Saratov

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.

Publisher

Bryansk State Technical University

Reference9 articles.

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