Abstract
In this paper, quadratic nonlinear oscillators under stochastic excitation are considered. The Wiener-Hermite expansion with perturbation (WHEP) method and the homotopy perturbation method (HPM) are used and compared. Different approximation orders are considered and statistical moments are computed in the two methods. The two methods show efficiency in estimating the stochastic response of the nonlinear differential equations.
Highlights
Quadrate oscillation arises through many applied models in applied sciences and engineering when studying oscillatory systems [1]
Since Meecham and his co-workers [2] developed a theory of turbulence involving a truncated Wiener-Hermite expansion (WHE) of the velocity field, many authors studied problems concerning turbulence [3,4,5,6,7,8]
The WHEP technique uses the following expansion for its deterministic kernels as corrections made under each approximation order
Summary
Quadrate oscillation arises through many applied models in applied sciences and engineering when studying oscillatory systems [1]. These systems can be exposed to a lot of uncertainties through the external forces, the damping coefficient, the frequency and/or the initial or boundary conditions. The nonlinear oscillators were considered as an opened area for the applications of WHE as can be found in [17,18,19,20,21,22,23]. The main goal of this paper is to consider the quadratic nonlinear oscillator under stochastic excitation.
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