... that compare excellently with the numerically computed ones. nonlinear dynamical systems oscillators Duffing–van der Pol equation homotopy analysis method limit cycle computational cost Nonlinear phenomena are encountered in all areas of sciences and engineering. Even though the study...

...H. T. Zhu; G. K. Er; V. P. Iu; K. P. Kou The stationary probability density function (PDF) solution of the stochastic responses is derived for nonlinear oscillators subjected to both additive and multiplicative Poisson white noises. The PDF solution is governed by the generalized Fokker–Planck...

...S. Adhikari The characteristics of the frequency response function of a nonviscously damped linear oscillator are considered in this paper. It is assumed that the nonviscous damping force depends on the past history of velocity via a convolution integral over an exponentially decaying kernel...

... that the oscillations occur next to the resonance on frequency ω . Indeed, as shown in a lot of numerical evidence ( 2 8 ) and analytical results ( 5 6 14 ), when energy pumping occurs, u 1 and u 2 are oscillating with the same frequency. So, to validate this point we should suppose that 4...

... behavior of the structure: The number of cracks, their depth and position, as well as the amplitude, frequency, and position of the excitation. 27 12 2002 08 04 2005 chaos vibrations beams (structures) cracks numerical analysis oscillators As shown in Part I, the proposed...

... results have been reported for random excitations. Dimentberg and Menyailov ( 7 ) considered a simple linear oscillator with one or two constraints—here, the impacts are assumed instantaneous—and obtained stationary probability density under external or parametric white noise using stochastic averaging...

..., and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 29 Sept 1999 02 May 2000 nonlinear dynamical systems oscillations oscillators transient response resonance classical mechanics damping perturbation theory...

... oscillators, i.e., of one-way (irreversible) “channeling” of externally imparted energy from the linear to the nonlinear part of the system, provided that the energy is above a critical level. Clearly, no such phenomenon is possible in the linear system. To obtain a better understanding of the energy pumping...