The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear osc...

In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé approximants. This modified homotopy perturbation method (MHPM) utilizes an alternative framework to capture the periodic behavior of the solution, which is characteristic of oscillator equations, and to give a ...

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always...

Energy balance method EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the firstand second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreemen...

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In process solving, explicit effect matrix time delay term was derived. The stability periodic determined by method which combines continuous approximation and multivariable Floquet theory. On this basis, frequency–amplitude response curve...

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

In this paper, interpolated variational iteration method (IVIM) is applied to investigate the vibration period and steady-state response for motion of rigid rod rocking back forth on a circular surface without slipping. The problem can be considered as strongly nonlinear oscillator. solution procedure, analytical technique utilized by evaluating integrals numerically. approximate results produc...

Abstract: A straightforward method to simulate high–Q quartz crystal oscillator is derived in this paper. The oscillator circuit is expressed under a canonical 5–terminal network which can be easily handled. The oscillator behavior is then described under the form of a nonlinear characteristic polynomial whose coefficients are functions of the circuit components and of the oscillation amplitude...