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- Title
Dynamic stability and instability of nanobeams based on the higher-order nonlocal strain gradient theory.
- Authors
Pavlović, Ivan R; Pavlović, Ratko; Janevski, Goran
- Abstract
This paper investigates a dynamic stability and instability problem of a nanobeam. For that purpose, the stochastic parametric vibrations of a nanobeam are considered based on the higher-order nonlocal strain gradient theory. The nanobeam is subjected to the compressive axial load, which consists of a constant and a stochastic part. According to the direct Liapunov method, bounds of the almost sure asymptotic stability and instability of the nanobeam are obtained as a function of the damping coefficient, variance of the stochastic force, higher-order and lower-order nonlocal scale coefficients, strain gradient length scale parameter and intensity of the deterministic component of axial loading. The obtained analytical results are firstly verified by numerical results using the Monte Carlo simulation method. Detailed numerical calculations are performed for the Gaussian and harmonic processes as models of stochastic axial loads.
- Subjects
BEAM dynamics; STRAINS &; stresses (Mechanics); DYNAMIC stability; GIRDER vibration; LYAPUNOV functions; MONTE Carlo method
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2019, Vol 72, Issue 2, p157
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hby024