Authors: Pavlović, Ivan
Karličić, Danilo 
Pavlović, Ratko
Janevski, Goran
Ćirić, Ivan
Title: Stochastic stability of multi-nanobeam systems
Journal: International Journal of Engineering Science
Volume: 109
First page: 88
Last page: 105
Issue Date: 1-Dec-2016
Rank: M21a
ISSN: 0020-7225
DOI: 10.1016/j.ijengsci.2016.09.006
The paper analyzes a stochastic stability problem of a multi-nanobeam system subjected to compressive axial loading. It is assumed that each pair of nanobeams is simply supported and continuously joined by a viscoelastic layer. Differential equations of nanobeams are given according to Eringen's nonlocal elasticity theory of Helmholtz and bi-Helmholtz type of kernel and Euler–Bernoulli beam theory. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. By using the moment Lyapunov exponent method, regions of almost sure stability of a multi-nanobeam system are obtained in a function of different parameters of the viscoelastic medium, axial loadings and number of nanobeams. Using the regular perturbation method, an approximated analytical solution of the moment Lyapunov exponent is obtained for a single nanobeam subjected to the white noise process, where the results are successfully confirmed with numerical results using the Monte Carlo simulation method. Numerical determination of the moment Lyapunov exponents is further performed for a higher number of nanobeams and different models of wideband processes.
Keywords: Almost sure stability | Moment lyapunov exponent | Multi-nanobeam | Nonlocal elasticity | Stochastic stability | Viscoelastic medium | Wideband process
Publisher: Elsevier
Project: Dynamic stability and instability of mechanical systems subjected to stochastic excitations 
Ministry of Education and Science of the Republic of Serbia, Project No. 1614022

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