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The present work examines the influence of time delay introduced in the piezoelectric circuit of an excited Duffing harvester device with hardening stiffness on the vibration and voltage amplitudes. Specifically, we seek to exploit a delayed electrical circuit of the harvester to enhance its performance. We consider the case of a monostable system and we use a perturbation technique to approximate the periodic response and the corresponding voltage amplitude near the principal resonance. It is shown that for appropriate values of delay amplitude, the energy harvesting performance is improved over a certain range of coupling parameters and excitation frequencies. Numerical simulation is conducted to support the analytical predictions.

In the present work, we report on energy harvesting in a delayed Rayleigh oscillator coupled to a piezoelectric harvester device. Analytical investigation using the multiple scales method is performed to obtain approximation of the periodic and QP amplitude response. The influence of different parameters of the harvesting system on the output power coupling to periodic and QP vibrations is examined. Results show that for appropriate values of the delay parameters, QP vibrations can also be exploited to harvest energy with good performence.

We explore quasi-periodic (QP) vibration-based energy harvesting (EH) in a forced nonlinear oscillator under time delay. The energy harvesting system consists in a delayed Duffing oscillator subject to harmonic excitation coupled to an electric circuit through an electromechanical coupling mechanism.We consider the case of primary resonance for which the frequency of the excitation is near the natural frequency of the oscillator. Application of the double-step perturbation method enables the approximation of the amplitude of the QP vibrations used to extract the average powers from the harvester device. Results shown that for a small value of delay amplitude, the periodic vibration-based EH can be extracted in a narrow range near the resonance, while QP vibration-based EH can be extracted over broad ranges of excitation. For relatively increasing value of the delay amplitude, only QP vibration-based EH can be extracted.

This paper presents the application of delayed feedback velocity for optimizing the harvested power in cubic nonlinear damper system. We consider a harvester consisting of a nonlinear single degree of freedom system (spring-masse-damper) subjected to a base excitation near the primary resonance. Analytical investigation using the multiple scales method is performed to obtain approximation of the amplitude response. This amplitude can be used to extract the average power. Results show that for appropriate values of the feedback gain, energy harvesting is more efficient at resonance compared to the cubic nonlinear damper system without time delay.

We study the control of bistability in non-contact mode AFM using time delay with modulated feedback gain. We consider that the tip-sample interaction force is described by Lennard-Jones potential and the equation of motion is modeled by single degree of freedom system. Perturbation analysis is performed to obtain the modulation equations of the slow dynamic. The influence of the modulated time delay on the nonlinear characteristic of the frequency response is analyzed and the evolution of the bistability region in the modulated time delay parameter plan is examined. Results show that modulation of the feedback gain can be used to reduce the amplitude of the microcanteliver response and to suppress the bistability regime in large region of the modulated delay parameter space. The analytical predictions are compared to numerical simulations for validation.

This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.

This paper investigates the influence of combined fast external excitation and fast parametric damp-ing on the amplitude and the onset of galloping of a tower submitted to steady and unsteady wind flow. A lumped single degree of freedom model is considered and the cases where the turbulent wind activates either external ex-citation, parametric one or both are studied. The methods of direct partition of motion and the multiple scales are used to drive a slow dynamic near primary resonance. The influence of the combined excitations on the galloping is examined showing the beneficial effect on the amplitude and the onset of galloping when the excitations are introduced together.

We report on the dynamic behavior of a rotary lip seal by considering the interaction between lip, film and shaft roughness assumed to have a periodic form. The nonlinearities of stiffness and viscosity of the film are taken into account in a mass-spring-dumper model. Using the harmonic balance method, analytical prediction of the lip displacement is obtained, the frequency response is provided and the effect of the shaft undulation on the amplitude jumps of the lip displacement and on the film thickness fluctuations are discussed. The results have direct applications in reducing leakage that may occur between a smooth lip seal and a rough shaft.

The aim of the present paper is to examine the effect of the vertical quasiperiodic oscillations on the stability of the free surface of an ideal horizontal liquid layer. The quasiperiodic motion considered here is characterized by two incommensurate frequencies ω1 and ω2. The governing system of equations is reduced to a quasiperiodic Mathieu equation. In this situation, using the harmonic balance method developed by Rand et al. [10, 11] and Hill’s determinants, we determine the marginal stability curves. We show that the quasiperiodic excitation produces a stabilizing or a estabilizing effect and is strongly depending on the ratio of the frequencies.

Vibroimpact dynamics of a forced single-sided Hertzian contact oscillator are typically initiated by jumps phenomena near resonances. It was shown that high-frequency excitations can be used to shift the threshold of such vibroimpacts toward higher or lower frequencies of the basic excitation depending on the type of the high-frequency excitation. These excitations not only produce a shift, but also soften the system behavior. The present paper investigates the effect of time delay state feedback on the threshold of vibroimpact dynamics of a forced Hertzian contact oscillator near the primary resonance. It is shown that for certain combinations of the gain parameters of delay state feedback, the jumps disappear leading the system to be maintained in contact when the excitation frequency sweeps through the resonance.

In this paper, vibrations of a self-excited tower under turbulent wind flow, in the presence of a fast frequency excitation, are investigated and the corresponding equations of motion are derived. The nonlinear terms in the governing equation due to the simultaneous presence of the self, parametric and external excitation, are considered and the galloping phenomena of the tall cantilever structure is studied. It is demonstrated that fast excitations may shift the frequency response and delays Hopf bifurcation of the tower. For validation of analytical results, comparisons with numerical simulations are given for different kinds of excitations.

In this paper the frequency response shift and hysteresis suppression of contact-mode atomic force microscopy is investigated using parametric modulation of the contact stiffness. Based on the Hertzian contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics contact-mode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the contact stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies.