Undamped nonlinear beam excited by additive L2-regular noise
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摘要
Stability of a nonlinear elastic beam excited by a space-time dependent nonrandom force or a L2-regular random noise f(x,t) (white in time, with general spatial covariance) is considered. It is supposed that the transversal displacement y of the beam with length l is governed by the quasilinear partial differential equation (PDE) ρ0hytt+Dyxxxx−[N0+ε∫0l(yx′)2dx′]yxx+ky=f(x,t),0
论文关键词：Stochastic PDE,Nonlinear beam with additive noise,Stability,Lyapunov functional,Expected energy growth,Discretization by partial-implicit methods
论文评审过程：Received 4 August 2007, Revised 21 February 2011, Available online 27 May 2011.
论文官网地址：https://doi.org/10.1016/j.cam.2011.05.039
