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.     

Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam

This study presents a novel resonant fuzzy logic controller (FLC) to minimize structural vibration using collocated piezoelectric actuator/sensor pairs. The proposed fuzzy controller increases the damping of the structures to minimize certain resonant responses. The vibration absorber is first experimentally examined by a cantilever beam test bed for impulse and near-resonant excitation cases. Moreover, the effectiveness of the new fuzzy control design to a state-of-the-art control scheme is compared through the experimental studies. The experimental results indicate the proposed controller is highly promising for this application field. Our results further demonstrate that the fuzzy approach is much better than traditional control methods. In summary, a novel vibration absorption scheme using fuzzy logic has been demonstrated to significantly enhance the performance of a flexible structure with resonant response.     

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

This paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities. The Galerkin method is employed to discretize the governing equations. A high-dimensional model that can take nonlinear model coupling into account is derived, and the incremental harmonic balance (IHB) method is employed to obtain the steady-state response of the curved beam. The cases investigated include softening stiffness, hardening stiffness and modal energy transfer. The stability of the periodic solutions for given parameters is determined by the multi-variable Floquet theory using Hsu's method. Particular attention is paid to the anti-symmetric response with and without excitation, as the excitation frequency is close to the first and third natural frequencies of the system. The results obtained with the IHB method compare very well with those obtained via numerical integration.     

Coupling analysis of a matched piezoelectric sensor and actuator pair for vibration control of a smart beam

This paper presents a theoretical and experimental study of the in-plane and out-of-plane coupling of a matched piezoelectric sensor/actuator pair bonded on a beam. Both the sensor and actuator are triangularly shaped polyvinylidene fluoride (PVDF) transducers and are intended to provide a compact sensor/actuator system for beam vibration control. The measured sensor-actuator frequency response function has shown an unpredicted increase in magnitude with frequency, which was found, to be due to in-plane vibration coupling. An analytical model has been developed to decompose the sensor-actuator response function into an in-plane contribution and an out-of-plane contribution. This in-plane coupling can limit the feedback control gains when a direct velocity feedback control is applied. A method called the j omega s compensation method is proposed to identify the effect of the in-plane vibration coupling at low frequencies. Even after this compensation, however, there was unexpected strong out-of-plane coupling at even modes, which may have been caused by a lack of accuracy in the shaping of the PVDF sensor and actuator. Numerical simulations have confirmed the sensitivity of the matched sensor/actuator pair with shaping errors.     

用动能定理讨论三线摆的扭转振动

建立了摆的动力学方程,导出了动能定理的微分表达式和积分表达式,用MATLAB软件编程画出了转动动能、平动动能与角坐标间的关系曲线,分析了平动动能对振动周期的影响。     

单摆运动的实时测量

对传统单摆装置进行改进,在摆球上安装小金属探针,用软导线做摆线,在单摆下方放置带电水槽,使单摆摆动时探针在水面划动,将振动量转化为电位量,实现了单摆振动的实时测量.     

外周期力驱动的倒摆混沌运动演示仪

设计并制作了受周期外力驱动的倒摆演示实验装置．利用自主开发的软件可自动演示和记录摆球运动状态的时间序列并存储实验数据．通过改变摆长、驱动电压，观察到该系统存在通过倍周期分岔通向混沌的过程．     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

The dynamic characteristics of harvesting energy from mechanical vibration via piezoelectric conversion

As an alternative power solution for low-power devices, harvesting energy from the ambient mechanical vibration has received increasing research interest in recent years. In this paper we study the transient dynamic characteristics of a piezoelectric energy harvesting system including a piezoelectric energy harvester, a bridge rectifier, and a storage capacitor. To accomplish this, this energy harvesting system is modeled, and the charging process of the storage capacitor is investigated by employing the in-phase assumption The results indicate that the charging voltage across the storage capacitor and the gathered power increase gradually as the charging process proceeds, whereas the charging rate slows down over time as the charging voltage approaches to the peak value of the piezoelectric voltage across the piezoelectric materials. In addition, due to the added electrical damping and the change of the system natural frequency when the charging process is initiated, a sudden drop in the vibration amplitude is observed, which in turn affects the charging rate. However, the vibration amplitude begins to increase as the charging process continues, which is caused by the decrease in the electrical damping （i.e., the decrease in the energy removed from the mechanical vibration）. This electromechanical coupling characteristic is also revealed by the variation of the vibration amplitude with the charging voltage.     

窄带随机激励双稳压电悬臂梁响应机制与能量采集研究

具有中心频率的窄带随机振动是一种典型的环境振动,其振动特征与环境的变化密切相关.本文以双稳压电悬臂梁能量采集系统为研究对象,分析系统在不同磁铁间距下的等效线性固有频率特性,以带通滤波器输出一定带宽的窄带随机激励模拟环境振动,研究系统的响应和能量采集特征.研究表明,对于一定带宽的窄带随机激励,一方面系统始终存在一个固定的磁铁间距使其输出达到峰值,另一方面当激励中心频率在一定范围内变化时,系统还分别存在另外两个或一个不同磁铁间距也能使系统输出达到峰值,而且该峰值特性是系统在其等效线性固有频率处诱导双稳或单稳“共振”形成的.研究结果可为具有窄带随机激励特征的振动能量采集提供一定的理论和技术支持.     

Non-linear free vibration of a simply-supported beam by programming techniques

An account is given of a study of free vibrations of a simply-supported beam with non-linear material properties. The material is of the Ramberg-Osgood type. Non-linear programming technique was used to find the response of the system. The variation of frequency with amplitude has been obtained for different values of material properties. The results indicate that the beam behaves like a soft spring for the type of non-linearity introduced by the material. This method can be used for all modes directly without reference to the lower modes.     

Monoharmonic approximation in the vibration analysis of a sandwich beam containing piezoelectric layers under mechanical or electrical loading

The formulation for the coupled electromechanical problem of forced vibration of a simply supported inelastic sandwich beam with piezoelectric layers is developed. An approximate formulation for the problem in terms of the amplitudes of the main electromechanical field variables is produced by applying the monoharmonic (single-frequency) approach along with the concept of complex moduli to characterize the cyclic properties of the material. Accuracy of the developed monoharmonic approach is estimated. It is achieved through the comparison of the results computed for the transient response of the beam using the complete model with those found using the approximate model. Limitations on the approximate monoharmonic method application are specified. The effect of physically nonlinear behaviour of the passive layer on the beam response is investigated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is also discussed.     

弹性支撑双稳压电悬臂梁振动响应及能量采集研究

在分析了常规刚性支撑非线性能量采集系统的研究基础上,提出外部磁铁弹性支撑的结构设想,保证系统在低强度激励条件下也能处于双稳态振荡,提高机电能量转换效率.研究表明,对于强度变化的随机激励历程,弹性支撑非线性能量采集系统不需要实时调整磁铁间距,能够更好地迎合强度时刻变化的随机激励源,实现高效的机电能量转换.     

利用强迫振动扭摆方法测灵敏电流计临界外电阻

把灵敏电流计的张丝及线圈作为扭摆,用正弦讯号发生器作驱动源,扭摆在驱动电流的作用下做受迫振动．利用扭摆作稳态受迫振动的共振频率公式以及电流计全临界电阻与电流计结构参量的关系推导出测量灵敏电流计临界外电阻的公式．     

Non-linear free vibration of a beam with time-dependent material properties

An account is given of a study of free vibrations of a simply supported beam with a central mass and undergoing creep deformation for the two cases (i) creep deformation is completely recoverable (without hysteresis) and (ii) creep deformation is partly recoverable (with hysteresis). The material is of the Ramberg-Osgood type. Numerical techniques were used to find the response of the system. The results indicate that the beam behaves like a soft spring and that amplitude and frequency decrease with time.     

The vibration characteristics of a beam with an axial force

Equations of motion are found for a non-uniform damped Timoshenko beam with a distributed axial force. Principal modes may be extracted by numerical means when the boundary conditions are specified, and the appropriate orthogonality conditions are given. The theory of linear forced vibration can thus be derived. It is an implicit requirement that all axial forces are conservative. That is to say, tangential, follower and partial follower axial forces (whether applied at an extremity or distributed along the beam) are excluded.