A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

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

“…us, the stochastic instantaneous frequency ](A, θ) can be displaced to be the averaged frequency ω(A) in equations ( 18) and (19). is approach has been proved to be effective in dealing with single-degree-of-freedom strongly nonlinear stochastic equations by Ge [23].…”

“…Zhu and Huang [20,21] extended Xu and Chung's [22] method to handle strongly nonlinear oscillators with lightly linear and/or nonlinear damping subject to weakly external and/or parametric excitations of wideband random processes. Ge and Li [23] have simplified Zhu and Huang's method [20,21] with a cost of slightly reducing the prediction accuracy.…”

“…Although the improved energy envelope stochastic averaging methods [20][21][22][23] are effective on randomly excited oscillators with strong geometric nonlinearities, it cannot offer effective approach to solve randomly excited systems with inertia nonlinearity in the form of…”

Bursting dynamics and the bifurcation mechanism of a modified Rayleigh-van der Pol-Duffing oscillator

“…Recently, the behavior of Rayleigh-van der Pol-Duffing oscillator has been also investigated extensively by many researchers. For instance, it can be applied in several mathematic and mechanic problems, such as the ship roll damping [22], sensitivity of dynamic characteristics of system to changing parameters [23] and the stationary response of the probability density of amplitude and energy [24]. However, generalizations of MRPDO, have not been received much attention.…”

“…By observing the roots of characteristic polynomials equation (12), it is not difficult to find that the type of equilibrium points from supH2 to point P are focus, and there is no turning point between node and focus, so the asymptotic theory can be used to solve equation (24). By substituting equation (25) into equation (24) and making the coefficients of each order of ω zero, we can get Omitting the higher order infinitesimal, we have…”