Scientific Visualization of the Results of a Numerical Experiment of the Nonlinear Dynamics of a Nanoscale Beam Structure

Abstract

The paper presents the results of scientific visualization of the nonlinear dynamics of contact interaction of a nanoscale beam structure under the action of an external harmonic load. The beam structure consists of two beams obeying the kinematic hypotheses of Euler-Bernoulli and S.P. Timoshenko. The constructed mathematical model takes into account geometric and constructive nonlinearities. The size-dependent behavior of the structure is implemented on the basis of the modified moment theory of elasticity. The resulting system of partial differential equations is reduced to a system of ordinary differential equations by the second order finite difference method. The Cauchy problem is solved by the fourth order Runge-Kutta method. In this work, using the methods of scientific visualization of the results of applying the methods of nonlinear dynamics, the influence of the size-dependent parameter and external load on the vibrations of the beam structure is investigated. As methods for studying nonlinear dynamics, the work uses wavelet spectra based on the mother Morlet, Fourier power spectra, signals. The use of scientific visualization methods makes it possible to develop specific recommendations for the operating conditions of the beam structure. This, in turn, makes it possible to avoid unwanted vibration modes of beam nanostructures, which are widely used as sensitive elements of sensors of micro and nano electromechanical systems.