In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on Melnikov method, necessary critical conditions for in system obtained, chaos threshold curve is obtained by calculation numerical simulation. The accuracy analytical result proved some typical simulation results, including local d...

Parametrically excited oscillators are used in several domains, particular to improve the dynamical behaviour of systems like case parametric amplification or energy harvesting. Although dry friction is often omitted during system modelling due complexity its nonsmooth nature, it sometimes necessary account for this kind damping adequately represent motion. In paper, proposed investigate effect...

The paper contains technical details and proofs of recent results developed by the author, regarding the design of LPV controllers directly from experimental data. A numerical example is also presented, about control of the Duffing oscillator.

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

Nonlinear beam resting on linear elastic foundation and subjected to harmonic excitation is investigated. The beam is simply supported at both ends. Both linear and nonlinear analyses are carried out. Hamilton’s principle is utilized in deriv ing the governing equations. Well known forced duffing oscillator equation is obtained. The equation is analyzed numerically using Runk-Kutta technique. T...

The excitation-induced stability (EIS) phenomenon in a harmonically excited bistable Duffing oscillator is studied in this paper. Criteria to predict system and excitation conditions necessary to maintain EIS are derived through a combination of the method of harmonic balance, perturbation theory, and stability theory for Mathieu’s equation. Accuracy of the criteria is verified by analytical an...

Four fractal nonlinear oscillators (The Duffing oscillator, attachment Toda and a oscillator) are successfully established by He’s derivative in space, their variational principles obtained semi-inverse transform method. The approximate frequency of the four found simple formula. results show formula is powerful tool to class oscillators.

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequencyamplitude modulat...

We investigate the dynamics of the vertically forced Duffing oscillator with suspended tuned mass absorber. Three different types of tuned mass absorbers are taken into consideration, i.e., classical single pendulum, dual pendulum and pendulum-spring. We numerically adjust parameters of absorbers to obtain the best damping properties with the lowest mass of attached system. The modification of ...