This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with specific attention to phase resonance and its relation amplitude resonance. To this end, different families resonances, namely primary (1:1), superharmonic (k:1), subharmonic (1:ν) ultra-subharmonic (k:ν) resonances are carefully studied using first higher-order averaging. When lag is calculated between k...

In the present effort, a data-driven modeling approach is undertaken to forecast aperiodic responses of non-autonomous systems. As representative system, harmonically forced Duffing oscillator considered. Along with it, an experimental prototype studied. Data corresponding chaotic motions are obtained through simulations oscillators hardening and softening characteristics experiments bistable o...

Due to great noise interference and strong signal attenuation in low voltage power line, two Duffing oscillator methods is proposed to detect QPSK carrier signal. At the same time, after analyzing the law of system solution of Duffing Oscillator, the algorithm of difference distribution of system solution is proposed to identify phase transition, which can greatly decrease calculation. The expe...

Container motion along a planar circular trajectory at constant angular velocity, i.e. orbital shaking, is of interest in several industrial applications, e.g. for fermentation processes or cultivation stem cells, where good mixing and efficient gas exchange are the main targets. Under these external forcing conditions, free surface typically exhibits primary steady-state through single-crest d...

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of fractional variable order Riemann–Liouville type. issues stability and convergence are considered. Test examples given to substantiate theoretical results. Using Runge rule, results compared explicit scheme. Phase trajectories oscillograms oscillator type constructed, chaotic modes detected ...

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...

This work is focused on the numerical determination of Shannon probabilistic entropy for MEMS devices exhibiting some uncertainty in their structural response. a universal measure statistical or stochastic disorder static deformation dynamic vibrations engineering systems and available both continuous discrete distributions functions parameters. An interval algorithm using Monte Carlo simulatio...

Nonlinear oscillators with hardening and softening cubic Duffing nonlinearity are considered. Such classical conservative oscillators are known to have an amplitude-dependent period. In this work, we design oscillators with the Duffing-type restoring force but an amplitude-independent period. We present their Lagrangians, equations of motion, conservation laws, as well as solutions for motion.