scholarly journals An Improved Lumped Parameter Model for a Piezoelectric Energy Harvester in Transverse Vibration

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Guang-qing Wang ◽  
Yue-ming Lu
Keyword(s):  
Correction Factor ◽  
Transverse Vibration ◽  
Energy Harvester ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Tip Mass

An improved lumped parameter model (ILPM) is proposed which predicts the output characteristics of a piezoelectric vibration energy harvester (PVEH). A correction factor is derived for improving the precisions of lumped parameter models for transverse vibration, by considering the dynamic mode shape and the strain distribution of the PVEH. For a tip mass, variations of the correction factor with PVEH length are presented with curve fitting from numerical solutions. The improved governing motion equations and exact analytical solution of the PVEH excited by persistent base motions are developed. Steady-state electrical and mechanical response expressions are derived for arbitrary frequency excitations. Effects of the structural parameters on the electromechanical outputs of the PVEH and important characteristics of the PVEH, such as short-circuit and open-circuit behaviors, are analyzed numerically in detail. Accuracy of the output performances of the ILPM is identified from the available lumped parameter models and the coupled distributed parameter model. Good agreement is found between the analytical results of the ILPM and the coupled distributed parameter model. The results demonstrate the feasibility of the ILPM as a simple and effective means for enhancing the predictions of the PVEH.

An asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester: modeling and experimental investigation

2021 ◽  
Author(s):  
Huirong Zhang ◽  
Wentao Sui ◽  
Chongqiu Yang ◽  
Leian Zhang ◽  
Rujun Song ◽  
...  
Keyword(s):  
Energy Harvester ◽  
Average Power ◽  
Harmonic Excitation ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Piezoelectric Beam ◽  
Lumped Parameter ◽  
Torsion Energy

Abstract This paper presents a detailed investigation on an asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester based on harmonic excitation. There is an eccentricity between the shape center of moving magnets and the axis of the piezoelectric beam, which results in the bending and torsion simultaneously in working condition. The distributed mathematical model is derived from the energy method to describe the dynamic characteristics of the harvester, and the correctness of the model is verified by experiments. To further demonstrate the improvement performance of the proposed energy harvester, the bending-torsion energy harvester (i.e. magnetic-coupled was not configured) is experimented and compared. The theoretical and experimental results indicate that the average power increases about 300% but the resonance frequency decreases approximately 2 Hz comparing to the harvester without magnetic-coupled. According to the characteristic of distributed parameter model, the magnetic force and the size of the piezoelectric beam are investigated respectively. And the lumped-parameter model is introduced to analyze the steady-state characteristic. Accordingly, this paper provides a feasible method to improve performance for piezoelectric energy harvester.

Comparison of Modelling Methods for Hydraulic Valve Gear

1987 ◽  
Author(s):  
H. Shang ◽  
G. K. Matthew ◽  
W. Luo
Keyword(s):  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Comparison Results ◽  
Hydraulic Valve ◽  
Modelling Methods ◽  
Measured Response ◽  
Valve Gear

Abstract A combined lumped/distributed parameter model for the follower system of a hydraulically operated valve is compared to a lumped parameter model of the same system. Since previous results show excellent correspondence between the lumped/distributed parameter model and measured response, it is natural to attempt to simplify the model and to again perform a comparison. Results of several examples are shown.

scholarly journals The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment

2015 ◽  
Vol 47 (4) ◽  
pp. 305-320 ◽  
Author(s):  
Andrzej Wałęga ◽  
Leszek Książek
Keyword(s):  
Hydrological Model ◽  
Model Performance ◽  
Rainfall Data ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Model Structure ◽  
Related Data ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Starting Point

Abstract The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment. The aim of this paper was to determine the influence of a hydrological model structure and rainfall- -related data on flood parameters obtained from a simulation. The study included an upland river Stobnica, right tributary of the Wisłok. The following assumptions were investigated: (i) the greater number of rainfall stations, the more accurate a flood description, i.e. the resulting hydrograph much better describes the actual flood, (ii) a distributed parameter model provides a more precise description of a catchment response to rainfall than a lumped parameter model. All calculations were performed using HEC-HMS 3.4 software. The analyses showed that increasing the number of rainfall stations slightly improved the model performance (by on average 4.1%). Furthermore, it was showed that in the catchment characterized by low topographical variability and stable land use, more reliable flood simulation results were obtained in the lumped parameter model than in the distributed parameter model. Considering the calibration process slightly improved the model performance, irrespective of its structure and the number of rainfall stations. Multivariate analysis of variance (MANOVA) revealed that the resulting differences in the model efficiency for individual variants were not significant. Considering limited empirical evidence on rainfall-runoff episodes, uncertainty of these results is probably high and thus they should be treated as a starting point for further studies.

Modeling of Oscillations in Partially Penetrated Weld Pools

1990 ◽  
Vol 112 (3) ◽  
pp. 469-474 ◽  
Author(s):  
C. D. Sorensen ◽  
T. W. Eagar
Keyword(s):  
Surface Tension ◽  
Weld Pool ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Gas Tungsten Arc ◽  
Geometric Conditions ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Weld Pool Geometry ◽  
Weld Pools

Several investigators have proposed controlling the size and shape of the weld pool based on the weld pool oscillations. This paper proposes two models that could be used to predict the weld pool geometry based on the natural frequency of the pool. The models, one a lumped parameter model and the other a distributed parameter model, included effects of liquid metal density and surface tension along with weld pool geometry. Weld pool oscillations were measured through signal processing of arc voltage and current for stationary gas-tungsten arc (GTA) welds. Welds were performed at different weld voltages and currents on different materials in order to vary width, depth, density, and surface tension. The models developed here were shown to have reasonable agreeement with experimentally measured weld pool resonant frequencies. Also, with geometric conditions similar to those commonly found in GTA weld pools, the different models tend to agree well with one another.

Magnetic Coupled Cantilever Piezoelectric Energy Harvester

2012 ◽  
Author(s):  
Lihua Tang ◽  
Yaowen Yang ◽  
Liya Zhao
Keyword(s):  
Energy Harvester ◽  
Magnetic Interaction ◽  
Experimental Tests ◽  
Governing Equations ◽  
Vibration Energy Harvester ◽  
Single Degree Of Freedom ◽  
Piezoelectric Energy ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Operating Bandwidth

A conventional vibration energy harvester is usually designed as a linear single-degree-of-freedom (1DOF) resonator. The efforts to improve its efficiency involve two aspects, i.e., enlarging the magnitude of output and widening the operating bandwidth. In this paper, we propose a magnetic coupled cantilever piezoelectric energy harvester (PEH) to achieve the above two goals. Different from other reported magnetic coupled PEHs, the magnetic interaction in the proposed design is introduced by a magnetic oscillator. Firstly, the lumped parameter models are established for the conventional linear PEH, the nonlinear PEH with a fixed magnet and the proposed PEH with a magnetic oscillator. The governing equations of the three systems are then provided in the state space form and their dynamics can be simulated by numerical integration. Subsequently, experimental tests are performed to validate the models. Both experiment and simulation show that the dynamics of the magnetic oscillator is able to not only broaden the operating bandwidth but also enhance the maximum power output of the PEH. Based on the validated model, parametric study is conducted to optimize the system performance.

Modeling of Piezoelectric Energy Harvesting from an L-shaped Beam-mass Structure with an Application to UAVs

2008 ◽  
Vol 20 (5) ◽  
pp. 529-544 ◽  
Author(s):  
Alper Erturk ◽  
Jamil M. Renno ◽  
Daniel J. Inman
Keyword(s):  
Energy Harvesting ◽  
Energy Harvester ◽  
Electrical Power ◽  
Distributed Parameter ◽  
Voltage Response ◽  
Shaped Beam ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model

Cantilevered piezoelectric energy harvesters have been extensively investigated in the literature of energy harvesting. As an alternative to conventional cantilevered beams, this article presents the L-shaped beam-mass structure as a new piezoelectric energy harvester configuration. This structure can be tuned to have the first two natural frequencies relatively close to each other, resulting in the possibility of a broader band energy harvesting system. This article describes the important features of the L-shaped piezoelectric energy harvester configuration and develops a linear distributed parameter model for predicting the electromechanically coupled voltage response and displacement response of the harvester structure. After deriving the coupled distributed parameter model, a case study is presented to investigate the electrical power generation performance of the L-shaped energy harvester. A direct application of the L-shaped piezoelectric energy harvester configuration is proposed for use as landing gears in unmanned air vehicle applications and a case study is presented where the results of the L-shaped — energy harvester — landing gear are favorably compared against the published experimental results of a curved beam configuration used for the same purpose.

Modeling and parametric study of a force-amplified compressive-mode piezoelectric energy harvester

2016 ◽  
Vol 28 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Zhengbao Yang ◽  
Jean Zu ◽  
Jun Luo ◽  
Yan Peng
Keyword(s):  
Power Generation ◽  
Energy Harvester ◽  
Low Frequency ◽  
Lumped Parameter Model ◽  
Small Scale ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Compressive Mode

Piezoelectric energy harvesters have great potential for achieving inexhaustible power supply for small-scale electronic devices. However, the insufficient power-generation capability and the narrow working bandwidth of traditional energy harvesters have significantly hindered their adoption. To address these issues, we propose a nonlinear compressive-mode piezoelectric energy harvester. We embedded a multi-stage force amplification mechanism into the energy harvester, which greatly improved its power-generation capability. In this article, we describe how we first established an analytical model to study the force amplification effect. A lumped-parameter model was then built to simulate the strong nonlinear responses of the proposed energy harvester. A prototype was fabricated which demonstrated a superior power output of 30 mW under an excitation of 0.3 g ([Formula: see text] m/s2). We discuss at the end the effect of geometric parameters that are influential to the performance. The proposed energy harvester is suitable to be used in low-frequency weak-excitation environments for powering wireless sensors.

Dynamic Model of a Rotating Channel Used in the Steel Industry and Implementation of a Controller

2004 ◽  
Vol 10 (3) ◽  
pp. 423-445 ◽  
Author(s):  
Alessandro Gasparetto ◽  
Stefano Miani
Keyword(s):  
Dynamic Model ◽  
Coming Out ◽  
Steel Industry ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Control Scheme ◽  
Steel Bars ◽  
Rotating Channel

In the steel industry, the steel bars coming out from the last stand of the rolling train must be conveyed to the cooling bed. For this purpose, various types of devices are used in the different steel factories. In this paper, the rotating channel used in a single steel company is described and investigated. The problem of deriving an adequate dynamic model for the rotating channel is tackled; the model is then exploited to design a controller which can be employed in the real application of the rotating channel. A lumped parameter model of the rotating channel has been designed and used in this work. Moreover, a distributed parameter model has also been implemented, so as to be able to compare the two models and to evaluate the error made by using the lumped parameter model instead of the distributed parameter model. The lumped parameter model has then been used as a basis for the implementation of a time-varying control scheme, which is also presented in the paper. The control has then been successfully tested on an accurate simulator of the plant. The results obtained from the tests have been very encouraging.

scholarly journals A Lumped-Parameter Model of Multiscale Dynamics in Steam Supply Systems

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Hikaru Hoshino ◽  
Yoshihiko Susuki ◽  
Takashi Hikihara
Keyword(s):  
Power Systems ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Short Term ◽  
Distributed Parameter Model ◽  
Multiscale Dynamics ◽  
Lumped Parameter ◽  
Normally Hyperbolic Invariant Manifold ◽  
Supply Systems

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model for slow internal dynamics of boilers. We derive a lumped-parameter model for the dynamics through physically relevant approximations. The derived model is then analyzed theoretically and numerically in terms of existence of normally hyperbolic invariant manifold in the phase space of the model. The existence of the manifold is a dynamical evidence that the derived model preserves the slow–fast dynamics, and suggests a separation principle of short-term and long-term operations of steam supply systems, which is analog to electric power systems. We also quantitatively verify the correctness of the derived model by comparison with brute-force simulation of the original model.

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