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In this paper, the nonlinear dynamics of a piezoelectric beam under simultaneous parametric and external excitation is studied. The energy sensor considered is composed of a substrate and a piezoelectric layer used as a vibratory sensor located in the middle of the beam. The model thus constituted takes into account the electromechanical nonlinearities. Based on the Galerkin's method, a strongly coupled nonlinear system is obtained. The multiple scales method is used to determine the analytical expressions of the deflection of the beam, the output voltage generated by the piezoelectric patch and the power harvested around the resonant frequency of the structure. The nonlinear characteristics of the energy harvester are explored under parametric and direct excitations. Analytical formulations of the deflection and the output voltage have been provided leading to investigate new insights into the effects of certain parameters such as the electromechanical coupling coefficient, the thickness and width of the elastic beam and the piezoelectric patch. In particular the position of the piezoelectric patch on the performance of the energy harvester is studied. The results show that for large values of the damping coefficient and thickness, the frequency-amplitude response curves of the energy harvester decrease. On the other hand, the frequency response curves of the displacement and voltage increase for large values of the excitation width and amplitude. We also note the fact that the length ratio influences not only the vibration amplitudes but also the output voltage. The deflection amplitudes and the output voltage obtained by the elaborated second-order multiple scale method are higher than those obtained by the first order, these results show the importance of nonlinearities in the dynamic study of vibrational energy harvesting systems by piezoelectric materials. [ABSTRACT FROM AUTHOR]

Interaction between parametric excitation and self-excited vibration has been subjected to numerous investigations in continuous systems. The ability of parametric excitation to quench self-excited vibrations in such systems has also been well documented. But such effects in discontinuous systems do not seem to have received comparable attention. In this article, we investigate the interaction between parametric excitation and self-excited vibration in a four degree of freedom discontinuous mechanical system. Unlike majority of studies in which oscillatory nature of stiffness accounts for parametric excitation, we consider a much more practical case in which parametric excitation is provided by a massless rotor of rectangular cross section with a cylinder-like mass concentrated at the center. The rotor arrangement is placed on a friction-induced self-excited support in the form of a frame placed on a belt moving with constant velocity. This frame is connected to a supplementary mass. A Stribeck friction model is considered for the mass in contact with the belt. The frictional force between the mass and the belt is oscillatory in nature because of the variation of normal force due to parametric excitation from the rotor. Our investigations reveal mutual synchronization of parametric excitation and self-excited vibration in the system for specific parameter values. The existence of a stable limit cycle with constant synchronized fundamental frequency, for a range of parametric excitation frequencies, is established numerically. Investigation based on frequency spectra and Lissajous curves reveals complex synchronization patterns owing to the presence of higher harmonics. The system is also shown to exhibit Neimark–Sacker bifurcations under the variation of belt velocity. Furthermore, variation in belt velocity and coupling stiffness is seen to cause a breakup of quasi-periodic torus with small-amplitude oscillations to form large amplitude chaotic orbits. This points toward the possibility of vibration suppression in the system by tuning the parameters for stabilizing the small-amplitude quasi-periodic response. An example of co-existence of different attractors in the system is also presented. [ABSTRACT FROM AUTHOR]

Phononic crystals composed of delicately designed periodic units are used to control spatial and spectral properties of acoustic or elastic waves. The ability to manipulate transmitting waves in a real-time dynamic manner provides a new concept in programable phononic crystals and metamaterials. In this study, the mechanical waves and bandgaps in a two-dimensional spring-mass array loaded by high-frequency parametric excitation have been investigated by both analytical and numerical methods. It is found that the high-frequency parametric excitation provides an equivalent additional stiffness which leads to low-frequency bandgaps. By tuning the parametric excitation, the versatility of such a dynamic modulating technique has been presented. The waveguide structure has also been designed and studied by non-uniformly distributed parametric excitations. [ABSTRACT FROM AUTHOR]

The marine risers are often subjected to parametric excitations from the fluctuation top tension. The top tension on the riser may fluctuate with multiple frequencies caused by irregular waves. In this paper, the influence between different frequency components in the top tension on the riser system is theoretically simulated and analyzed. With the Euler-Bernoulli beam theory, a dynamic model for the vibrations of the riser is established. The top tension is set as fluctuating with time and it has two different frequencies. The influences from the fluctuation amplitudes, circular frequencies and phase angles of these frequency components on the riser system are analyzed in detail. When these two frequencies are fluctuating in the stable regions, the riser system may become unstable because ?1+?22On. The fluctuation amplitudes of these frequencies have little effect on the components of the vibration frequencies of the riser. For different phase angles, the stability and dynamic behaviors of the riser would be different. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water.

Zhang, J., and Tang, Y., 2015. Fatigue analysis of deep-water risers under vortex-induced vibration considering parametric excitations. This paper presents vortex-induced vibration (VIV) and fatigue analysis of deep-water risers in shear flow considering parametric excitations due to the heave of floating platform. As a first step, the governing equation of transverse motion of the riser is established; the dynamic response of the riser is calculated numerically by the finite difference method based on Van der Pol wake-oscillator model. Then the fatigue damage of the riser is obtained by applying Miner cumulative damage theory and S-N curve. The results show that the VIV response of the riser, especially in the flow with low speed, is much larger due to the parametric excitation. The bending stress and the fatigue damage at the bottom of the riser are significantly increased under parametric excitations. [ABSTRACT FROM AUTHOR]

The aim of this contribution is to present a survey of the main research results dealing with the phenomenon "parametric anti-resonance" and to stimulate the interests of designers for its application in engineering practice especially in machinery and for devices where vibrations are undesirable for the safe run. It is interesting that this phenomenon can be used for vibrations suppressing for all kind of excitations, i.e. not only externally, but also for self-excitation and undesirable parametric resonance. [ABSTRACT FROM AUTHOR]

The excitation of the plasma wake waves by an electron bunch in the presence of an intense electromagnetic radiation with circular polarization has been studied in parametric unstable regimes. In the unperturbed state (in the absence of an electron bunch), the interaction between a pump wave and a plasma is described by the Maxwell's equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by an electron bunch is investigated against a cold plasma background. It is shown that, in a certain range of the parameters of the bunch, pump wave, and plasma, the excitation is resonant in character and the amplitude of the excited plasma wake waves increases with distance from the electron bunch. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water. [ABSTRACT FROM AUTHOR]