Abstract:
This paper reports on the modeling and on the experimental verification of electromechanically coupled beams with varying cross-sectional area for piezoelectric energy harvesting. The governing equations are formulated using the Rayleigh-Ritz method and Euler-Bernoulli assumptions. A load resistance is considered in the electrical domain for the estimate of the electric power output of each geometric configuration. The model is first verified against the analytical results for a rectangular bimorph with tip mass reported in the literature. The experimental verification of the model is also reported for a tapered bimorph cantilever with tip mass. The effects of varying cross-sectional area and tip mass on the electromechanical behavior of piezoelectric energy harvesters are also discussed. An issue related to the estimation of the optimal load resistance (that gives the maximum power output) on beam shape optimization problems is also discussed. 1. Introduction The interest in converting vibrations into usable electrical energy has increased over the past years [1–5]. Vibration based energy harvesting is particularly useful for wireless sensor nodes and remotely operated systems with limited energy source. The aim is to provide electrical energy for such systems by using the vibrations available in their environment. Although different transduction mechanisms can be used to convert vibrations into electricity, the recent literature shows that piezoelectric transduction has drawn the most attention [1, 3, 5]. The literature on piezoelectric energy harvesting includes different models to represent the behavior of electromechanically coupled harvesters. Such models range from lumped parameter models [6, 7] to Rayleigh-Ritz type approximate distributed parameter models [7–9] as well as analytical distributed parameter solution attempts [10, 11]. The analytical distributed parameter solutions for unimorph [12] and bimorph [13] piezoelectric energy harvester configurations with closed-form expressions have been presented. The convergence of the Rayleigh-Ritz type electromechanical solution [7, 9] to the analytical solution given by Erturk and Inman [12] was reported by Elvin and Elvin [14] when a sufficient number of admissible functions were used. The investigation into alternative configurations of electromechanical beams has also been reported in the literature. Erturk et al. [15] presented a linear distributed parameter model for predicting the electromechanical behavior of an L-shaped piezoelectric energy harvester configuration. A broadband harvester can

Abstract:
A double-clamped piezoelectric energy harvester subjected to random excitation is presented, for which corresponding analytical model is established to predict its output characteristics. With the presented theoretical natural frequency and equivalent stiffness of vibrator, the closed-form expressions of mean power and voltage acquired from the double-clamped piezoelectric energy harvester under random excitation are derived. Finally theoretical analysis is conducted for the output performance of the double-clamped energy harvester with the change of spectrum density (SD) of acceleration, load resistance, piezoelectric coefficient and natural frequency value, which is found to closely agree with Monte Carlo simulation and experimental results. A double-clamped piezoelectric energy harvester subjected to random excitation is presented, for which corresponding analytical model is established to predict its output characteristics. With the presented theoretical natural frequency and equivalent stiffness of vibrator, the closed-form expressions of mean power and voltage acquired from the double-clamped piezoelectric energy harvester under random excitation are derived. Finally theoretical analysis is conducted for the output performance of the double-clamped energy harvester with the change of spectrum density (SD) of acceleration, load resistance, piezoelectric coefficient and natural frequency value, which is found to closely agree with Monte Carlo simulation and experimental results.

Abstract:
针对微机电系统和传感器等低能耗电子产品的持续供能问题,提出了一种涡激振动式压电俘能器。该俘能器由压电悬臂梁和末端圆柱体组成,结构简单,可在较低水流流速下产生涡激共振,得到较大的能量输出。通过数学建模和实验测试的方法,研究了水流速度和外接电阻对压电俘能器振动和俘能的影响规律。实验结果表明:压电俘能器的振动频率随流速的增大而增大,振动幅值在涡激共振时最大,输出功率受流速和外接电阻两者影响,较小外接电阻适合较高流速,较大电阻适合较低流速,压电俘能器在涡激共振处可获得最大的能量输出,当外接电阻为0.5 MΩ、流速为0.41 m/s时,实验测试得到了8.3 μW的最大输出功率。数值分析结果与实验测试结果吻合较好,验证了数学模型的正确性。 A vortex？？induced piezoelectric energy harvester (PEH) is proposed to meet the requirement of continuous energy supply for low energy？？consumed electronic devices such as MEMS and sensors. The PEH is composed of a piezoelectric cantilever beam and a cylinder and has a simple mechanical structure. The PEH generates vortex？？induced resonance at relatively low water velocities and obtains larger output powers. Effects of both the water velocity and the resistance on hydrodynamic response and energy harvesting ability of the PEH are investigated through mathematical modeling and experimental study. It is found that the vibration frequency increases as the velocity increases and the maximum vibration amplitude is found when the vortex？？induced resonance appears. The Output power depends on both the water velocity and the resistance. More output power can be achieved through configurations of a smaller resistance with a higher velocity or a larger resistance with a lower velocity. The maximum output power is obtained with vortex？？induced resonance. The maximum output power of 8.3 μW is obtained in experimental study with 0.5 MΩ and 0.41 m/s. Furthermore, the results of numerical study are consistent with those of the experimental study well, and the validity of the mathematical model is verified

The study of the experimental investigation
of a disk-type piezoelectric energy harvester presented. The harvester contains
disk bimorph piezoceramic element of the umbrella form and contains two disk
PZT plates. The element is excited at the base point at its center. The element
is supplied by a loading ring mass to decrease its resonance frequency. The
dependences of the vibration displacement along the radii of the bimorph and
the ring mass from the frequency of excitation are presented and the output
voltage frequency response is also presented as well. The idle mode and the
load duty are investigated. The value of the internal resistance of the
harvester is obtained using the load characteristic. The piezoelectric specific
power is estimated experimentally.

Abstract:
为了提高压电振动能量俘获的效率，提出了一种新型的压电悬臂梁俘能器。新的压电俘能器在悬臂梁固定端安装一个新型动力放大器系统，另一端带有一个有限尺寸的质量块。新型动力放大器由平移及转动约束的弹簧-质量块系统组成。考虑有限尺寸质量块的质量分布效应和平移及转动约束的弹簧刚度等结构参数的影响，利用广义Hamilton原理，针对带有新型动力放大器的压电式悬臂梁俘能器，建立了分布参数型运动微分方程，获得了相应的特征函数，分析了自振频率和能量俘获效果。分析结果表明，考虑质量块偏心距和转动惯量可提高能量俘获效率的预测精度；合理选择动力放大器的平移及转动弹簧刚度可提高能量俘获的效率，降低俘能器的共振频率。 In order to improve the efficiency of piezoelectric vibration energy harvesting,a cantilevered piezoelectric vibration energy harvester is proposed.The new cantilevered piezoelectric energy harvester consists of a new dynamic magnifier (a translation-and rotation-restrained spring-mass system) installed at the restrained end and a tip mass at the free end.Taking into account the translation and rotation-restrained stiffness,and the distribution effect of the tip mass over a finite length,a distributed parameter model of piezoelectric cantilevered energy harvesters is developed by using the generalized Hamilton's principle.The eigen-function and natural frequency formulation of the presented model are obtained.The efficiency of energy harvesting is investigated.The analytical results show that the accuracy of predicting energy harvesting efficiency can be improved by considering the eccentricity of mass and moment of inertia.A reasonable selection of the translational and rotational spring stiffness can improve energy harvesting efficiency,and reduce the resonant frequency of the energy harvesting system.

Abstract:
Piezoelectric energy harvesting technology is used to design battery less microelectronic devices such as wireless sensor nodes. This paper investigates the necessary conditions to enhance the extracted AC electrical power from exciting vibrations energy using piezoelectric materials. The effect of tip masses and their mounting positions are investigated to enhance the system performance. The optimal resistive load is estimated to maximize the power output. Different capacitive loads are tested to store the output energy. The experimental results validated the theoretical analysis and highlighted remarks in the paper.

Abstract:
A novel square canister piezoelectric energy harvester was proposed for harvesting energy from asphalt pavement. The square of the harvester was of great advantage to compose the harvester array for harvesting energy from the asphalt pavement in a large scale. The open circuit voltage of the harvester was obtained by the piezoelectric constant d_{33} of the piezoelectric ceramic. The harvester is different from the cymbal harvester which works by the piezoelectric constant d_{31}. The finite element model of the single harvester was constructed. The open circuit voltage increased with increase of the outer load. The finite element model of the single harvester buried in the asphalt pavement was built. The open circuit voltage, the deformation difference percent and the stress of the ceramic of the harvester were obtained with different buried depth. The open circuit voltage decreased when the buried depth was increased. The proper buried depth of the harvester should be selected as 30 - 50 mm. The effects of structure parameters on the open circuit voltage were gotten. The output voltage about 64.442 V could be obtained from a single harvester buried under 40 mm pavement at the vehicle load of 0.7 MPa. 0.047 mJ electric energy could be gotten in the harvester. The output power was about 0.705 mW at 15 Hz vehicle load frequency.

Abstract:
摘要 基于压电陶瓷的振动能量收集器以其结构简单、清洁环保及易于微型化等诸多优点受到广泛关注。利用压电陶瓷的正压电效应，根据机电理论和结构动力学理论，采用模态法建立了压电悬臂梁的双向耦合分布参数模型，仿真分析了外激励频率和外接负载对压电能量收集器输出电压特性的影响，设计制作了铝制悬臂梁，并进行了地面振动和能量收集试验，试验结果与理论仿真吻合较好，验证了理论建模的正确性。试验结果表明，单个压电片的能量收集电压最大为73 V/N。 Abstract：Piezoelectric ceramic vibration energy harvester has attracted great attention for its simple structure, environment protection, easy miniaturization and other advantages. According to piezoelectric effect, a double-coupled distributed parameter model was established using mode method by combination of electromechanical theory and structural dynamics theory. Simulation analysis of effect of excitation frequency and load on output voltage of piezoelectric energy harvester was performed. Al-cantilever energy harvester was made to perform ground vibration and energy harvesting test. The experimental results are in good agreement with the numerical simulation, which verifies the correctness of theoretical modeling. Experimental results show that the max voltage output of a single piezoelectric patch is 73 V/N.

Vibration energy harvesting is widely
recognized as the useful technology for saving energy. The piezoelectric energy
harvesting device is one of energy harvester and is used to operate certain
types of MEMS devices. Various factors influence the energy regeneration
efficiency of the lead zirconate titanate piezoelectric (PZT) devices in
converting the mechanical vibration energy to the electrical energy. This paper
presents the analytical and experimental evaluation of energy regeneration
efficiency of PZT devices through impedance matching method and drop-weight
experiments to different shape of PZT devices. The results show that the
impedance matching method has increased the energy regeneration efficiency
while triangular shape of PZT device produce a stable efficiency in the energy
regeneration. Besides that, it becomes clear that the power, energy and
subsequently efficiency of the triangular plate are higher than those of the
rectangular plate under the condition of the matching impedance and the same
PZT area.