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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In this paper the problem of randomly excited vibration of a Bernoulli-Euler beam with an elastic support is considered. The pointwise, stationary random in time force effects on the beam in a fixed point, exciting its transverse vibration. The statistical properties of the response are described in terms of covariance of the random excitation. The effect of position of the random force as well the rigidity of the elastic support on the standard deviation of the beam deflection has been numerically investigated.
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