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71.
Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters 总被引:1,自引:0,他引:1
A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed.
The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric,
inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler–Lagrange principle
and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions
for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of
the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested
electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient
to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence
on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that,
for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation. 相似文献
72.
This paper provides a thorough review of the significant work done so far in the area of flight dynamics and control of flapping-wing micro-air-vehicles (MAVs). It provides the background necessary to do research in that area. Furthermore, it raises questions that need to be addressed in the future. The three main blocks constituting the flight dynamic framework of flapping MAVs are reviewed. These blocks are the flapping kinematics, the aerodynamic modeling, and the body dynamics. The design and parametrization of the flapping kinematics necessary to produce high-control authority over the MAV, as well as design of kinematics suitable for different flight conditions, are reviewed. Aerodynamic models used for analysis of flapping flight are discussed. Particular attention is given to the physical aspects captured by these models. The issues and consequences of averaging the dynamics and neglecting the wing inertia are discussed. The dynamic stability analysis of flapping MAVs is usually performed by either averaging, linearization and subsequent analysis or using Floquet theory. Both approaches are discussed. The linear and nonlinear control design techniques for flapping MAVs are also reviewed and discussed. 相似文献
73.
Abdessattar Abdelkefi Rui Vasconcellos Ali H. Nayfeh Muhammad R. Hajj 《Nonlinear dynamics》2013,71(1-2):159-173
We perform an analytical and experimental investigation into the dynamics of an aeroelastic system consisting of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The experimental results show that the onset of flutter takes place at a speed smaller than the one predicted by a quasi-steady aerodynamic approximation. On the other hand, the unsteady representation of the aerodynamic loads accurately predicts the experimental value. The linear analysis details the difference in both formulation and provides an explanation for this difference. Nonlinear analysis is then performed to identify the nonlinear coefficients of the pitch spring. The normal form of the Hopf bifurcation is then derived to characterize the type of instability. It is demonstrated that the instability of the considered aeroelastic system is supercritical as observed in the experiments. 相似文献
74.
We present an analytical model and closed-form expressions describing the response of a tunable MEMS filter made of two electrostatic
resonators coupled by a weak microbeam. The model accounts for the filter geometric and electric nonlinearities as well as
the coupling between them. It is obtained by discretizing the distributed-parameter system to produce a reduced-order model.
We predict the filter deflection and static pull-in voltage by solving a boundary-value problem (BVP). We also solve an eigenvalue
problem (EVP) to determine the filter poles (the natural frequencies delineating the filter bandwidth). We found a good agreement
between the results obtained using our model and published experimental results. We found that, when the input and output
resonators are mismatched, the first mode is localized in the softer resonator whereas the second mode is localized in the
stiffer resonator. We demonstrated that mismatch between the resonators can be countermanded by applying different DC voltages
to the resonators. As the effective nonlinearities of the filter grow, multi-valued responses appear and distort the filter
performance. Once again, we found that the filter can be tuned to operate linearly by choosing a DC voltage that makes the
effective nonlinearities vanish. 相似文献
75.
A.H. Nayfeh 《Journal of sound and vibration》1984,96(3):333-340
The interaction of fundamental parametric resonances with subharmonic resonances of order one-half in a single-degree-of-freedom system with quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to derive two first-order ordinary differential equations that describe the modulation of the amplitude and the phase of the response with the non-linearity and both resonances. These equations are used to determine the steady state solutions and their stability. Conditions are derived for the quenching or enhancement of a parametric resonance by the addition of a subharmonic resonance of order one-half. The degree of quenching or enhancement depends on the relative amplitudes and phases of the excitations. The analytical results are verified by numerically integrating the original governing differential equation. 相似文献
76.
The method of renormalization is used to determine a uniformly valid expansion for the problem of non-linear waves produced in a fluid by spatially non-uniform simple harmonic motion of the surface of a sphere. The effect of dimensionless quantities upon the acoustic shock-formation distance is examined. 相似文献
77.
A.H. Nayfeh 《Journal of sound and vibration》1984,92(3):379-386
The method of multiple scales is used to analyze the response of a single-degree-of-freedom system to either the combination resonance of the additive type or the combination resonance of the difference type , where and are the frequencies of the excitation and ω0 is the linear undamped natural frequency of the system. To the second approximation, the combination resonance of the additive type has three effects on the steady state response. First, it produces terms having the frequencies and at first order and terms having the frequencies 0, , and at second order. Second, it produces a shift in the natural frequency of the system. Third, it produces a virtual primary-resonant excitation having the frequency that makes the component having the frequency be of first rather than second order. Similar effects are produced by a combination resonance of the difference type or a superharmonic resonance of order two. 相似文献
78.
A non-linear analysis is developed for sound propagation in a variable-area duct in which the mean flow approaches choking conditions. A quasi-one-dimensional model is used and the non-linear analysis represents the acoustic disturbance as a sum of interacting harmonics. The numerical procedure is stable for cases of strong interaction and is able to integrate through the throat region without any numerical instability. 相似文献
79.
The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band. 相似文献
80.
Nonlinear modal interactions in the forced vibrations of a thermally loaded pre-buckled annular plate with clamped–clamped immovable boundary conditions are investigated. The mechanism responsible for the interaction is a combination internal resonance involving the natural frequencies of the three lowest axisymmetric modes. The in-plane thermal load acting on the plate is assumed to be axisymmetric and the plate is externally excited by a harmonic force. The nonlinear von Kármán plate equations along with the heat conduction equation are combined to model the behavior of the system. An analytical/numerical approach is used to examine the plate vibrations to a harmonic excitation near primary resonance of one of the modes. 相似文献