Experimental passive self-tuning behavior of a beam resonator with sliding proof mass

A passively self-tuning resonator configuration is presented in this study. Three different prototype beam–mass systems were built and tested and all successfully displayed passive self-tuning behavior when driven by vibrations at frequencies ranging from 45 to 140 Hz and accelerations ranging from 0.007 to 2g. All three systems were able to achieve tuning within their operating regime when driven at a single frequency, as well as maintain a tuned condition as frequency was stepped up or down, demonstrating a bandwidth between 6 and 40 Hz. One application of such a passively self-tuning system is in vibration energy harvesting, where it is critical for performance that the harvester device resonance frequency matches the input vibration frequency, yet the input frequency may change over time and is not known a priori. The self-tuning resonator demonstrated in this paper can enable the energy harvesting system to adjust to the varying input frequencies and thereby increase the energy harvested over time.     

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.     

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.     

An improved piezoelectric harvester available in scavenging-energy from the operating environment with either weaker or stronger vibration levels

An improved harvester available in scavenging energy from the operating environment with either weaker or stronger vibration levels is studied. To ensure the optimal harvester performance, a Cuk dc-dc converter is employed into the modulating circuit. This paper reports how this harvester scavenges maximal energy from varying-level vibrations and store energy into an electrochemical battery. Dependence of the duty cycle upon the external vibration level is calculated, and it is found that: 1) for weaker vibrations, the charging current into the battery is smaller than the allowable current, and thus all the optimal output power of the harvesting structure can be absorbed by the battery. In this case, the duty cycle should be fixed at 1.86%; 2) for stronger external forcing, the allowable charging current of the battery is smaller than the optimal harvested current. This indicates that just a portion of the scavenged energy can be accepted by the battery. Thus, the duty cycle should be decreased gradually with the increase of the vibration level. Finally the energy transmission process and the roles of each electronic element are analyzed. It is shown that a Cuk converter can greatly raise the efficiency of such a harvester, particularly when subjected to a weaker ambient vibration. Supported by the National Natural Science Foundation of China (Grant No. 10872074) and the National Basic Research Program of China (Grant No. 2009CB724205)     

Enhanced vibration energy harvesting using dual-mass systems

A type of dual-mass vibration energy harvester, where two masses are connected in series with the energy transducer and spring, is proposed and analyzed in this paper. The dual-mass vibration energy harvester is proved to be able to harvest more energy than the traditional single degree-of-freedom (dof) one when subjected to harmonic force or base displacement excitations. The optimal parameters for maximizing the power output in both the traditional and the new configurations are discussed in analytical form while taking the parasitic mechanical damping of the system into account. Consistent of the previous literature, we find that the optimal condition for maximum power output of the single dof vibration energy harvester is when the excitation frequency equals to the natural frequency of the mechanical system and the electrical damping due to the energy harvesting circuit is the same as the mechanical damping. However, the optimal conditions are quite different for the dual-mass vibration energy harvester. It is found that two local optimums exist, where the optimal excitation frequency and electrical damping are analytically obtained. The local maximum power of the dual-mass vibration energy harvester is larger than the global maximum power of single dof one. Moreover, at certain frequency range between the two natural frequencies of the dual-mass system, the harvesting power always increases with the electrical damping ratio. This suggests that we can obtain higher energy harvesting rate using dual-mass harvester. The sensitivity of the power to parameters, such as mass ratio and tuning ratio, is also investigated.     

Extending the dynamic range of an energy harvester using nonlinear damping

This paper introduces the use of nonlinear damping for extending the dynamic range of vibration energy harvesters. A cubic nonlinear damper is initially considered and the average harvested power and the throw are obtained for different sinusoidal base excitation amplitudes and frequencies, both numerically and analytically. It is demonstrated that when excited at resonance, at an amplitude below its maximum operational limit, the harvested power using a nonlinear damper can be significantly larger than that of a linear energy harvester, therefore expanding its dynamic range. A potential approach to implementing cubic nonlinearity using a shunted electromagnetic device is also presented.     

Output response identification in a multistable system for piezoelectric energy harvesting

In this paper we examine in detail the multiple responses of a novel vibrational energy harvester composed of a vertical bistable beam whose complex non-linear behavior is tuned via magnetic interaction. The beam was excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric element. The bistable laminate beam coupled to the piezoelectric transducer showed a variety of complex responses in terms of the beam displacement and harvested power output. The range of vibration patterns in this non-linear system included single-well oscillations and snap-through vibrations of periodic and chaotic character. Harvested power was found to be strongly dependent on the vibration pattern with nonlinearities providing a broadband response for energy harvesting. Wavelet analysis of measured voltage, displacement and velocity time histories indicated the presence of a variety of nonlinear periodic and also chaotic phenomena. To measure the complexity of response time series we applied phase portraits and determine stroboscopic points and multiscale entropy. It is demonstrated that by changing parameters such as the magnetic interaction, the characteristics of the bistable laminate harvester, such as the natural frequency, bandwidth, vibration response and peak power can be readily tailored for harvesting applications.     

Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation

A recently reported design of a hybrid vibration absorber (HVA) which is optimized to suppress resonant vibration of a single degree-of-freedom (SDOF) system is re-optimized for suppressing wide frequency band vibration of the SDOF system under stationary random force excitation. The proposed HVA makes use of the feedback signals from the displacement and velocity of the absorber mass for minimizing the vibration response of the dynamic structure based on the H₂ optimization criterion. The objective of the optimal design is to minimize the mean square vibration amplitude of a dynamic structure under a wideband excitation, i.e., the total area under the vibration response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure and it can provide significant vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square vibration amplitude of the primary system. The proposed HVA are tested on a SDOF system and continuous vibrating structures with comparisons to the traditional passive vibration absorber.     

NON-LINEAR VIBRATION ABSORBER FOR A SYSTEM UNDER SINUSOIDAL AND RANDOM EXCITATION: EXPERIMENTS

A system consisting of a primary structure coupled with a passive tuned vibration absorber is experimentally studied. The primary structure consists of four flexible columns with a mass, while the absorber consists of a beam with a tip-mass. The system, which is a coupled non-linear oscillator, is subjected to sinusoidal and random excitation. The effects of the forcing frequency, forcing amplitude, mass ratios and frequency ratios on the displacement response of the system in the neighborhood of the autoparametric region are studied. Control parameters related to effectiveness of the absorber are determined. The objective of this study is to experimentally define an absorption region for the passive vibration absorber and to determine the parameters that influence the effectiveness of the vibration absorber.     

Two-degree-of-freedom rotational-pendulum vibration absorbers

This paper presents experimental as well as analytic results on a rotational-pendulum vibration absorber. The characteristic frequencies of the absorber can be tuned dynamically by adjusting the rotational speed. The device is coupled to the primary structure through a mechanical spring, thus possessing two natural modes of vibrations in the vertical plane. When the primary structure is excited by a harmonic disturbance of which the frequency matches one of the two natural frequencies, the oscillations will be minimized. Whether the pendulum absorber is operating in a resonant mode can be detected by measuring the phase difference between the motions of the primary structure and the absorber, which provides an efficient way to tune the rotational speed for optimal performance. Experimental results confirm the theoretical developments and also demonstrate the effectiveness of the proposed scheme.     

Three dimensional vibration generators with a single rotational input

This paper presents a novel device capable of generating three-dimensional vibrations with a single-axis of rotation. The device resembles a vibration motor with an eccentric weight, but the weight is allowed to move up and down in parallel to the axis of rotations. While spinning of the eccentric weight causes lateral vibrations, vertical vibrations are excited by superposing a periodic torque on the rotary shaft. The frequency and magnitude of vertical oscillations can be independently regulated. Since the vertical natural frequency is sensitive to rotational speeds, maximum vertical oscillations can be achieved by properly adjusting the rotational speed according to the excitation frequency. Relations between the excitation torque and the vertical shaking force are examined using the frequency response for the linearized system. Numerical simulations on the original nonlinear system are conducted to verify the performance of vertical oscillations.     

一种采用双换能器和摆式结构的宽频振动能量采集器

针对悬臂梁振动能量采集器在大振幅振动下梁容易断裂的缺点,本文提出了一种基于摆式结构的具有宽频和倍频特性的振动能量采集器,该采集器由两个Terfenol-D/PMN-PT/Terfenol-D磁电换能器和嵌有六个磁铁的旋转摆构成.文中建立了摆式结构的摆动方程,分析了采集器的频率响应特性以及谐振时的机-磁-电转换特性,并对采集器输出电压波形进行了频谱分析.理论和实验研究表明:该采集器具有宽频和倍频特性,采集器样机在1 g(1 g=9.8 m/s~2)有效值加速度振动下,向下扫频时的半功率带宽达到4.8 Hz,且能在f=16.9 Hz的振动下获得3.569 mW的负载功率.利用双换能器以及采集器的倍频和宽频特性,能有效地提高低频时采集器的输出功率.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

带碰撞双稳态压电俘能系统的俘能特性研究

双稳态俘能系统的运动常常会陷入单个势能阱中, 导致俘能效率降低. 为了解决这个问题, 本文提出了一类带碰撞的磁斥力双稳态压电振动能量采集系统. 建立了该碰撞双稳态系统的机电耦合方程, 分析了碰撞对双稳态系统动力学特性的影响. 研究了确定性激励和低强度随机激励下碰撞对系统响应特性和俘能效率的影响. 结果表明: 简谐激励下, 碰撞能够使得原双稳态系统的单阱小幅周期运动转变为双阱间的大幅运动, 从而有效地提高输出功率. 得到了低强度随机激励下, 不同碰撞间隙对系统动力响应特性和输出功率的影响规律. 对一个给定的随机激励, 存在一个最优的碰撞间隙, 此时碰撞能够将原双稳态系统单阱内的随机运动转化为频繁的双阱跳跃, 出现大幅值运动, 从而大幅提高了系统的俘能效率.     

Forced transverse vibrations of an elastically connected complex simply supported double-beam system

The present paper is devoted to analyzing undamped forced transverse vibrations of an elastically connected complex double-beam system. The problem is formulated and solved in the case of simply supported beams. The classical modal expansion method is applied to ascertain dynamic responses of beams due to arbitrarily distributed continuous loads. Several cases of particularly interesting excitation loadings are investigated. The action of stationary harmonic loads and moving forces is considered. In discussing vibrations caused by exciting harmonic forces, conditions of resonance and dynamic vibration absorption are determined. The beam-type dynamic absorber is a new concept of a continuous dynamic vibration absorber (CDVA), which can be applied to suppress excessive vibrations of corresponding beam systems. A numerical example is presented to illustrate the theoretical analysis.     

随机激励下双稳态压电俘能系统的相干共振及实验验证

随着压电晶体材料的迅速发展, 基于压电效应的能量采集系统是俘获环境中的宽带随机振动能量的一种有效途径. 研究了有限宽带随机激励作用下, 磁斥力双稳态压电俘能系统的相干共振俘能机理, 并进行了实验验证. 运用Euler-Maruyama方法求解了随机非线性压电振动耦合方程, 比较分析了相干共振发生前后系统的动力学特性和俘能效率, 然后基于Kramers逃逸速率解释了相干共振. 最后的随机振动实验结果验证了双稳态压电俘能系统的相干共振俘能机理. 并且观察到: 当相干共振发生时, 系统会在两个势能阱之间剧烈运动, 此时宽带随机振动能量会被转化为大幅值窄带低频振动响应, 从而极大地提高了宽带随机振动能量的俘获效率.     

Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling

An important issue in resonant vibration energy harvesters is that the best performance of the device is limited to a very narrow bandwidth around the fundamental resonance frequency. If the excitation frequency deviates slightly from the resonance condition, the power out is drastically reduced. In order to overcome this issue of the conventional resonant cantilever configuration, a non-resonant piezomagnetoelastic energy harvester has been introduced by the authors. This paper presents theoretical and experimental investigations of high-energy orbits in the piezomagnetoelastic energy harvester over a range of excitation frequencies. Lumped-parameter nonlinear equations (electromechanical form of the bistable Duffing oscillator with piezoelectric coupling) can successfully describe the large-amplitude broadband voltage response of the piezomagnetoelastic configuration. Following the comparison of the electromechanical trajectories obtained from the theory, it is experimentally verified that the piezomagnetoelastic configuration can generate an order of magnitude larger power compared to the commonly employed piezoelastic counterpart at several frequencies. Chaotic response of the piezomagnetoelastic configuration is also compared against the periodic response of the piezoelastic configuration theoretically and experimentally. Overcoming the bias caused by the gravity in vertical excitation of the piezomagnetoelastic energy harvester is discussed and utilization of high-energy orbits in the bistable structural configuration for electrostatic, electromagnetic and magnetostrictive transduction mechanisms is summarized.     

Broad band metamaterial absorber based on wheel resonators with lumped elements for microwave energy harvesting

A new metamaterial absorber structure is designed and characterized both numerically and experimentally for microwave energy harvesting applications. The proposed structure includes four wheel resonators with different dimensions, from which the overall response of the structure can then be obtained by summing all the overlapping frequency responses corresponding to each dimension. The essential operation frequency range of the wheels is selected in such a way that the energy used in wireless communications and found within the environment that we live is absorbed. The dimensions are obtained using parametric study and genetic algorithm to realize wideband absorption response. When the simulation and measurement results are taken into account, it is observed that the metamaterial absorber based harvester has potential to absorb and convert microwave energy with an absorption ratio lying within the range of 80 and 99% for the frequency band of 3–5.9 and 7.3–8 GHz. The conversion efficiency of the structure as a harvester is found to be greater than 0.8 in the interval of 2–5 GHz. Furthermore, the incident angle and polarization dependence of the wheel resonator based metamaterial absorber and harvester is also investigated and it is observed that the structure has both polarization and incident angle independent frequency response with good absorption characteristics in the entire working frequency band. Hence, the suggested design having good absorption, polarization and angle independent characteristics with wide bandwidth is a potential candidate for future energy harvester using wireless communication frequency band.     

The effective damping approach to design a dynamic vibration absorber using Coriolis force

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of the DVA. The closed forms obtained show that the natural frequency of the absorber should be tuned to twice that of the pendulum. The closed forms of optimal parameters are verified by numerical optimization. The modified forms of optimal parameters are proposed to be used in case of general excitation. Base on this modified form, the design procedure is demonstrated by the numerical calculation of the free vibration and wind-induced vibration of a ropeway gondola.     

Vibration confinement and energy harvesting in flexible structures using collocated absorbers and piezoelectric devices

We propose an optimal design for supplementing flexible structures with a set of absorbers and piezoelectric devices for vibration confinement and energy harvesting. We assume that the original structure is sensitive to vibrations and that the absorbers are the elements where the vibration energy is confined and then harvested by means of piezoelectric devices. The design of the additional mechanical and electrical components is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers and capacitances, load resistances, and electromechanical coupling coefficients are optimized to minimize the total energy of the structure. We use the Galerkin procedure to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers and harvesting devices. We develop a numerical code that determines the unknown parameters of a pre-specified set of absorbers and harvesting components. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To illustrate the proposed design, we consider a simply supported beam with harmonic external excitations. Here, we consider two possible configurations for each of the additional piezoelectric devices, either embedded between the structure and the absorbers or between the ground and absorbers. We present simulations of the harvested power and associated voltage for each pair of collocated absorber and piezoelectric device. The simulated responses of the beam show that its energy is confined and harvested simultaneously.