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Stability of a shallow arch under action of deterministic and stochastic load taking into account nonlocalness of elasticity and damping

Research paper by V. D. Potapov

Indexed on: 11 Oct '13Published on: 11 Oct '13Published in: Acta mechanica



Abstract

On the example of a shallow arch, the geometrically nonlinear problem concerned with oscillations of systems excited by a deterministic or stochastic load is considered. The dynamic stability problem is solved for the arch, made from micro- and nanomaterials. The equation, describing the motion of the Euler–Bernoulli arch, is based on the nonlocal elasticity theory and nonlocal damping, taking into account finite deflections. Asymptotic stability and almost sure asymptotic stability criteria involving a damping coefficient, structure and loading parameters are derived using the method of the maximum Liapunov exponent.