Dynamic stability of a nonlinear multiple-nanobeam system

Abstract

We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen's nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler-Bernoulli beam theory and D' Alembert's principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the sta- method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude-frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems.

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Contact Dynamics and Stress Field of Fluid-Conveying GRC Nanotubes

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Linear and nonlinear dynamics of hybrid systems

“…12,13,20,24,27,31,33,35,[39][40][41] In Hedrih (Stevanovi c) and Simonovi c [42][43][44][45][46][47][48][49][50][51] published in period in 2008-2013, and late published Simonovi c [52][53][54] as well as in monographs published by Kluwer and Springer and other contributions of author and coauthors to linear and nonlinear dynamics of deformable bodies (rods, beams, plates, moving strips) can be classified as systems of coupled subsystems and deformable bodies. [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] After the first published scientific papers by Hedrih (Stevanovi c) K.R. in the newly opened field of coupled deformable bodies and the dynamics of hybrid systems of complex structures, Hedrih (Stevanovi c) K.R.…”

“…31 The presenter and project leader and manager publicly suggested ideas for research in these seminars in area of linear and nonlinear oscillations of coupled deformable bodies as well as hybrid systems nonlinear dynamics. Then a large volume of published papers of researchers from the project team and their PhD advisors at the Faculty of Mechanical Engineering in Ni s and Belgrade and Faculty of Technical sciences in Kosovska Mitrovica appeared in world known scientific journals (see literature, e.g., [52][53][54][66][67][68][69]74 and other). Based on these facts and the content of the published scientific papers in period 1966-2019, and The transversal vibration beam problem is classical, but in current university books on vibrations, we can find only the Euler-Bernoulli's classical partial differential equation for describing transversal beam vibrations.…”