Energy harvesting using semi-active control

This paper presents the application of semi-active control for optimising the power harvested by an electro-mechanical energy harvester. A time-periodic damper, defined by a Fourier series, is introduced for energy harvesting in order to increase the performance of the device. An analytical solution for the transmissibility and the average absorbed power is derived based on the method of harmonic balance. The coefficients of the semi-active model are optimised to maximise the harvested power. The harvested power from the optimum periodic time-varying damper at a particular frequency is compared and is shown to be greater than that from an optimum passive damper and a semi-active on–off damper not only at that particular frequency but also at other frequencies. In addition, the performance of the optimised periodic time-varying damper is also compared with an arbitrary semi-active time-periodic damper, which has the same transmissibility at resonance. An optimisation is carried out to maximise the power in a frequency range and the optimum damper is derived as a function of the excitation frequency. The numerical results are validated with the analytical approach.     

Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters

We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered wing has a low-aspect ratio and hence three dimensional aerodynamic effects cannot be neglected. To this end, the three dimensional unsteady vortex lattice method for the prediction of the unsteady aerodynamic loads is developed. A strong coupling scheme that is based on Hamming's fourth-order predictor–corrector method and accounts for the interaction between the aerodynamic loads and the motion of the wing is employed. The effects of the electrical load resistance, nonlinear torsional spring and eccentricity between the elastic axis and the gravity axis on the level of the harvested power, pitch and plunge amplitudes are investigated for a range of operating wind speeds. The results show that there is a specific wind speed beyond which the pitch motion does not pick any further energy from the incident flow. As such, the displacement in the plunge direction grows significantly and causes enhanced energy harvesting. The results also show that the nonlinear torsional spring plays an important role in enhancing the level of the harvested power. Furthermore, the harvested power can be increased by an order of magnitude by properly choosing the eccentricity and the load resistance. This analysis is helpful in designing piezoaeroelastic energy harvesters that can operate optimally at specific wind speeds.     

Performance analysis of nonlinear vibration isolator with magneto-rheological damper

A nonlinear vibration isolator is considered to study effectiveness of isolation against harmonic force and displacement excitations. Nonlinearity in the magneto-rheological (MR) fluid based damper as well as in the elastic member is taken into account. The MR-damper has been modeled including Bouc–Wen hysteretic element and the spring is taken to have cubic nonlinearity. Analytical expression for the energy dissipation characteristics of the damper has been derived. Near resonant response of the isolated mass is obtained by a modified averaging technique suitable for hysteretic type nonlinearity present in the system. The performance of the isolators is estimated for various nonlinear stiffness values, both hardening and softening types. Different performance measures are also proposed to judge the performance of the nonlinear isolator.     

Piezoelectric diaphragm for vibration energy harvesting

This paper presents a technique of electric energy generation using a mechanically excited unimorph piezoelectric membrane transducer. The electrical characteristics of the piezoelectric power generator are investigated under dynamic conditions. The electromechanical model of the generator is presented and used to predict its electrical performances. The experiments was performed with a piezoelectric actuator (shaker) moving a macroscopic 25 mm diameter piezoelectric membrane. A power of 0.65 mW was generated at the resonance frequency (1.71 kHz) across a 5.6 kOmega optimal resistor and for a 80 N force. A special electronic circuit has been conceived in order to increase the power harvested by the piezoelectric transducer. This electrical converter applies the SSHI (synchronized switch harvesting on inductor) technique, and leads to remarkable results: under the same actuation conditions the generated power reaches 1.7 mW, which is sufficient to supply a large range of low consumption sensors.     

Analysis of energy dissipation in an elastic moving string with a viscous damper at one end

In this paper transverse vibration of an axially moving viscoelastic string with a viscous damper at one end is investigated analytically. The string is assumed to be travelling with constant velocity and the length of string is constant or time varying. The linear and nonlinear mathematical models are derived using the Lagrangian function and implemented using a finite element method. The method considers a time varying state space function applied to the linear model, the Newmark-Beta method is used to solve the response for the nonlinear problem numerically. The case of energy dissipated by a viscoelastic damper at one end of the string for different axial string velocities is considered. When a disturbance arrives at the boundary an exact value for the damper which provides maximum energy dissipation is investigated. Finally, numerical simulations are presented to establish the feasibility of the method.     

Active vibration control in Duffing mechanical systems using dynamic vibration absorbers

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass–spring–damper dynamic vibration absorbers. An active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform reference position trajectory tracking tasks planned for the nonlinear primary system. A differential flatness-based disturbance estimation scheme is also described to estimate the unknown multiple time-varying frequency disturbance signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. Some numerical simulation results are provided to show the efficient performance of the proposed active vibration absorption scheme and the fast estimation of the vibration disturbance signal.     

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of-freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20–40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.     

立方非线性Schr?dinger方程的动力学行为分析

本文采用辛算法，研究了立方非线性Schr?dinger方程在不同的空间离散下的动力学行为，并讨论了其在不同的非线性参数下的动力学性质。 我们指出，系统的守恒量在长时间的演化下保持不变，但对于强非线性，不同的空间离散精度，将导致不同的动力学行为。     

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibration absorber is thus employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions. The values of the spring stiffness and mass of the vibration absorber are significantly lower than their counterpart of the forced nonlinear oscillator. Vibrational energy of the forced nonlinear oscillator is transferred to the attached light mass through linked spring and damper. As a result, the nonlinear vibrations of the forced oscillator are greatly reduced and the vibrations of the absorber are significant. The method of multiple scales is used to obtain the averaged equations that determine the amplitude and phases of the first-order approximate solutions to primary resonance vibrations of the forced nonlinear oscillator. Illustrative examples are given to show the effectiveness of the dynamic vibration absorber for suppressing primary resonance vibrations. The effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibrations are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.     

Rotor drop and following thermal growth simulations using detailed auxiliary bearing and damper models

Catcher bearings (CBs) or auxiliary bearings provide mechanical backup protection in the events of magnetic bearing failure. This paper presents numerical analysis for a rotor drop on CBs and following thermal growths due to their mechanical rub using detailed CB and damper models. The detailed CB model is determined based on its material, geometry, speed and preload using the nonlinear Hertzian load–deflection formula, and the thermal growths of bearing components during the rotor drop are estimated using a 1D thermal model. A finite-element squeeze film damper provides the pressure profile of an annular oil film and the resulting viscous damping force. Numerical simulations of an energy storage flywheel with magnetic suspensions failed reveal that an optimal CB design using the detailed simulation models stabilizes the rotor drop dynamics and lowers the thermal growths while preventing the high-speed backward whirl. Furthermore, CB design guides based on the simulation results are presented.     

起落架磁流变减摆器模糊PID控制算法的研究

为了减小飞机机轮的摆振,提高飞机乘坐的舒适性和驾驶的安全性,将磁流变控制技术应用于飞机起落架减摆器,实现减摆器阻尼力的实时智能控制。针对磁流变减摆器,建立了飞机起落架摆振的半主动控制非线性动力学模型,设计了模糊PID控制算法,并使用Matlab/Simulink建立了半主动控制仿真模型。通过调节流过磁感线圈的电流大小改变磁流变减摆器的阻尼力,从而减小机轮摆动实现半主动控制。通过动力学仿真,在给定速度下分别对比未安装减摆器、被动控制下以及半主动控制下机轮摆角、侧向位移、侧滑角随时间变化的曲线,结果表明了模糊PID控制算法的正确性和可行性,该控制策略可以较好的抑制机轮的摆振,同时也表明模糊PID控制算法具有良好的可控性,减摆效果也明显优于传统的被动控制。     

Isolation effect of a dynamic damper and a trench on ground vibration caused by a construction machine

In this study, a simple isolation method of ground vibration is proposed by using a dynamic damper and a trench, which is feasible for temporary use during a construction period. The ground is modeled as a two-dimensional plane model. Periodic impulsive excitation acts at one point on the ground surface, and the vibrations are measured at several evaluation points on the ground surface. A simple dynamic damper composed of a weight and a restoring element is set up at the ground surface or in the shallow trench, and the vibration isolation effect is examined. The simulation shows that the ground vibration can be isolated when the dynamic damper is set near the excitation point on the ground surface, and setting the dynamic damper in a shallow trench has almost the same isolation effect as that in a deep trench. The results indicate that the proposed isolation method is feasible for actual application.     

Nonlinear optimization of acoustic energy harvesting using piezoelectric devices

In the first part of the paper, a single degree-of-freedom model of a vibrating membrane with piezoelectric inserts is introduced and is initially applied to the case when a plane wave is incident with frequency close to one of the resonance frequencies. The model is a prototype of a device which converts ambient acoustical energy to electrical energy with the use of piezoelectric devices. The paper then proposes an enhancement of the energy harvesting process using a nonlinear processing of the output voltage of piezoelectric actuators, and suggests that this improves the energy conversion and reduces the sensitivity to frequency drifts. A theoretical discussion is given for the electrical power that can be expected making use of various models. This and supporting experimental results suggest that a nonlinear optimization approach allows a gain of up to 10 in harvested energy and a doubling of the bandwidth. A model is introduced in the latter part of the paper for predicting the behavior of the energy-harvesting device with changes in acoustic frequency, this model taking into account the damping effect and the frequency changes introduced by the nonlinear processes in the device.     

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time-frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.     

Transverse emittance blow-up from beam injection errors in synchrotrons with nonlinear feedback systems

The problem of transverse emittance blow-up from beam injection errors in synchrotrons with nonlinear feedback systems is considered. The relative emittance growth is calculated for linear and nonlinear feedback transfer functions. Effects of an increase of the damping decrement of the beam coherent oscillations and of a decrease of the coherent transverse amplitude spread of different bunches in case of the damper with a positive cubic term in the feedback transfer function are discussed. The text was submitted by the author in English.     

Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.     

立方非线性Schr?dinger方程的动力学性质研究及其解模式的漂移

采用辛算法数值求解一维立方非线性Schr?dinger方程，研究了随着非线性参数的变化立方非线性Schr?dinger方程的动力学性质和解的模式的漂移.数值结果表明，随着非线性参数的增加解模式的漂移速度越来越快. 关键词： 动力学性质 相轨线 解模式的漂移 辛算法     

High-Q microwave photonic filter with self-phase modulation spectrum broadening and third-order dispersion compensation

We propose and experimentally demonstrate a scheme of high-Q microwave photonic filter （MPF） using the techniques of self-phase modulation （SPM） spectrum broadening and third-order dispersion （TOD） compensation. The optical pulses from a mode-locking laser are spectrally broadened by the SPM in the highly nonlinear fiber. A wideband optical frequency comb with 365 spectral lines within 10-dB power variation from the highest spectral power is obtained. By applying a cubic phase modulation via a waveshaper, the effect of TOD which broadens the MPF passband is eliminated. The final implemented MPF has a Q-value as high as 296 and a tuning range of 700 MHz.