Vol 71, No 2 (2019)

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Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory

I.R. Pavlovic, R. Pavlović, G. Janevski

Arch. Mech. 71 (2), 137-153, 2019, DOI: 10.24423/aom.3139

Keywords: stochastic vibrations; strain gradient theory; Liapunov method; Gaussian and harmonic process; Monte Carlo simulation


This paper analyzes stochastic vibrations of a viscoelastic nanobeam under axial loadings. Based on the higher-order nonlocal strain gradient theory and the Liapunov functional method, bounds of the almost sure asymptotic stability of a nanobeam are obtained as a function of retardation time, variance of the stochastic force, higher-order and lower-order scale coefficients, strain gradient length scale, and intensity of the deterministic component of axial loading. Analytical results from this study are first compared with those obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian and harmonic non-white processes as models of axial forces.

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