Response of Cantilever Model with Inertia Nonlinearity under Transverse Basal Gaussian Colored Noise Excitation | Zendy

Bo Li | Zendy; Kai Hu | Zendy; Guoguang Jin | Zendy; YanYan Song | Zendy; Gen Ge | Zendy

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Response of Cantilever Model with Inertia Nonlinearity under Transverse Basal Gaussian Colored Noise Excitation

Author(s) -

Bo Li,

Kai Hu,

Guoguang Jin,

YanYan Song,

Gen Ge

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/1823596

Subject(s) - nonlinear system , cantilever , curvature , mathematical analysis , mathematics , amplitude , displacement (psychology) , stochastic differential equation , probability density function , differential equation , physics , classical mechanics , geometry , optics , quantum mechanics , structural engineering , psychology , statistics , engineering , psychotherapist

Considering the curvature nonlinearity and longitudinal inertia nonlinearity caused by geometrical deformations, a slender inextensible cantilever beam model under transverse pedestal motion in the form of Gaussian colored noise excitation was studied. Present stochastic averaging methods cannot solve the equations of random excited oscillators that included both inertia nonlinearity and curvature nonlinearity. In order to solve this kind of equations, a modified stochastic averaging method was proposed. This method can simplify the equation to an Ito differential equation about amplitude and energy. Based on the Ito differential equation, the stationary probability density function (PDF) of the amplitude and energy and the joint PDF of the displacement and velocity were studied. The effectiveness of the proposed method was verified by numerical simulation.

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