In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi-periodic dynamics of the undamped system forced by a single impulse on the linear oscillator and being initially at rest, by considering separately low-, moderateand high-energy impulsive motions....

When a nonlinear oscillator with an amplitude dependent frequency is driven by a swept frequency drive, the oscillator’s amplitude will, in some circumstances, automatically adjust itself so that the oscillator’s nonlinear frequency closely matches the drive frequency. This phenomenon is called autoresonance, and allows the amplitude of the oscillator to be controlled simply by sweeping the dri...

This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations ...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

This paper provides the investigation of Sinusoidal oscillation in the incommensurate fractional Chemical Oscillator. We determine parametric range for which an incommensurate fractional order Chemical system with a specific order can perform as an undamped oscillator. Numerical simulations are presented to confirm the given analytical results.

This paper investigates the nonlinear observer design for mechanical systems, viz. nonlinear pendulum systems, undamped oscillators and Lienard systems. Explicitly, Sundarapandian’s Theorem (2002) for observer design for nonlinear systems is used to solve the problem of local exponential observer design for nonlinear pendulum systems, undamped oscillators and Lienard systems. Numerical examples...

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...