Axial and Transverse Vibration of a Cantilever Beam Energy Harvester with a Tip Mass with Axial and Transverse Eccentricity

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.

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Study on Modal Shape of the Vibration of an Axially Moving Cantilever Beam with Tip Mass

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.211-212.200 ◽

2011 ◽

Vol 211-212 ◽

pp. 200-204 ◽

Cited By ~ 1

Author(s):

Li Wang ◽

Huai Hai Chen ◽

Xu Dong He

Keyword(s):

Theoretical Result ◽

Cantilever Beam ◽

Transverse Vibration ◽

Experimental Result ◽

Modal Shape ◽

Vibration Equation ◽

The Difference ◽

Axially Moving ◽

Set Up ◽

Tip Mass

The transverse vibration equation of an axially moving cantilever beam with tip mass is given. The instant linearized equations are set up based on Galerkin’s method. The tip mass influences to the first three order modes of the beam are computed. The calculated responses using the modes with tip mass are compared with the results using the modes without tip mass. Modes without tip mass can replace the modes with tip mass while the tip mass is small. The heavier the tip mass is, the bigger the difference of using the replacement is. It is found that the experimental result is fit well with the theoretical result using the modes with tip mass.

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Experimental and Simulation Investigations of the Cantilever Beam Energy Harvester

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.248.249 ◽

2016 ◽

Vol 248 ◽

pp. 249-255

Author(s):

Radosław Nowak ◽

Marek Pietrzakowski

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Cantilever Beam ◽

Beam Energy ◽

Energy Harvester ◽

Mechanical Energy ◽

Element Model ◽

Piezoelectric Energy ◽

Piezoelectric Elements ◽

Analytical Approaches

Machines, cars suspensions, buildings steel constructions etc. usually generate vibrations, which can be the excitement signal for piezoelectric energy harvesters. The piezoelectric patches attached to the vibrating construction have ability to convert mechanical energy of harmful vibrations into electrical energy.The goal of the study was to verify a finite element model of the piezoelectric beam energy harvester by comparing results of numerical simulations with those obtained experimentally. The stand used in the experiment consists of the cantilever beam with piezoelectric elements attached, which is excited by the base harmonic movement. The transverse displacements of the selected beam’s point and the base, and also the frequency of vibrations were observed and measured using an accelerometer and a B&K Pulse platform. A portable data acquisition module was used to quantify the voltage generated by the piezoelectric layers.The finite element model was built in ANSYS software. The beam and piezoelectric layers were modeled by twenty node elements with an additional electric degree of freedom for piezoelectric elements. A full piezoelectric matrix was used in the finite element analysis instead of a one-dimensional piezoelectric effect, which dominates in many analytical approaches. It allowed building a more accurate model of the system. The experimental tests and finite element method simulations were performed and acquired results were compared. The characteristics of voltage amplitude in the time and frequency domain were shown and discussed.

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Evaluation of a cantilever beam energy harvester subjected to impacts

10.20906/cps/cilamce2017-0710 ◽

2017 ◽

Author(s):

Arthur Guilherme Mereles ◽

Marcus Varanis ◽

José M. Balthazar ◽

Angelo M. Tusset ◽

Rodrigo Rocha ◽

...

Keyword(s):

Cantilever Beam ◽

Beam Energy ◽

Energy Harvester

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Nonlinear performances of an autoparametric vibration-based piezoelastic energy harvester

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x16649450 ◽

2016 ◽

Vol 28 (2) ◽

pp. 254-271 ◽

Cited By ~ 20

Author(s):

Zhimiao Yan ◽

Muhammad R Hajj

Keyword(s):

Cantilever Beam ◽

Energy Harvester ◽

Multiple Scales ◽

Damping Ratio ◽

Load Resistance ◽

Governing Equations ◽

Near Resonance ◽

Base Displacement ◽

Tip Mass ◽

Analytical Expressions

Nonlinear characterizations of an autoparametric vibration-based energy harvester are investigated. The harvester consists of a base structure subjected to an external excitation and a cantilever beam with a tip mass. Two piezoelectric sheets bounded to both sides of the cantilever beam are used to harvest the energy. The governing equations accounting for the coupled effects of the base vibration, the response of the cantilever beam and the generated power are derived. Approximate analysis of the simplified governing equations is then performed by the method of multiple scales. The usefulness of this approach is demonstrated by deriving analytical expressions for the global frequency and damping ratio of the cantilever beam. Their dependence on the electrical load resistance is quantified. Analytical expressions for the amplitudes of the base displacement and the displacement of the tip mass are derived. An expression that relates the output power to the load resistance, global damping, and displacement of the tip mass is derived. The effects of the external force and electric load resistance on the nonlinear responses of the system are determined. The results show different responses for different operational electric loads. The broadening of the excitation regime over which energy can be harvested is analyzed. The effects of the load resistance on the types of bifurcations near resonance are determined.

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Auxetic cantilever beam energy harvester

Smart Structures and NDE for Industry 4.0, Smart Cities, and Energy Systems ◽

10.1117/12.2559327 ◽

2020 ◽

Author(s):

Saman Farhangdoust

Keyword(s):

Cantilever Beam ◽

Beam Energy ◽

Energy Harvester

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Horizontally Assembled Trapezoidal Piezoelectric Cantilevers Driven by Magnetic Coupling for Rotational Energy Harvester Applications

Energies ◽

10.3390/en14020498 ◽

2021 ◽

Vol 14 (2) ◽

pp. 498

Author(s):

Yonghyeon Na ◽

Min-Seon Lee ◽

Jung Woo Lee ◽

Young Hun Jeong

Keyword(s):

Cantilever Beam ◽

Lead Zirconate Titanate ◽

Energy Harvester ◽

Magnetic Coupling ◽

Rotational Energy ◽

Resistive Load ◽

Piezoelectric Cantilever ◽

Resistance Torque ◽

Piezoelectric Cantilevers ◽

Tip Mass

Horizontally assembled trapezoidal piezoelectric cantilevers driven by magnetic coupling were fabricated for rotational energy harvester applications. A dodecagonal rigid frame with an attached array of six trapezoidal cantilevers served as a stator for electrical power generation. A rotor disk with six permanent magnets (PMs) interacted magnetically with the counterpart cantilever’s tip-mass PMs of the stator by rotational motion. Each trapezoidal piezoelectric cantilever beam was designed to operate in a transverse mode that utilizes a planar Ag/Pd electrode printed onto lead zirconate titanate (PZT) piezoelectric thick film. The optimized distance between a pair of PMs of the rotor and the stator was evaluated as approximately 10 mm along the same vertical direction to make the piezoelectric cantilever beam most deflectable without the occurrence of cracks. The theoretically calculated resistance torque was maximized at 46 mN·m for the optimized trapezoidal piezoelectric cantilever. The proposed energy harvester was also demonstrated for wind energy harvester applications. Its harvested output power reached a maximum of approximately 22 mW at a wind speed of 10 m/s under a resistive load of 30 kΩ. The output performance of the proposed energy harvester makes it possible to power numerous low-power applications such as smart sensor systems.

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Theoretical and Experimental Studies on MEMS Variable Cross-Section Cantilever Beam Based Piezoelectric Vibration Energy Harvester

Micromachines ◽

10.3390/mi12070772 ◽

2021 ◽

Vol 12 (7) ◽

pp. 772

Author(s):

Xianming He ◽

Dongxiao Li ◽

Hong Zhou ◽

Xindan Hui ◽

Xiaojing Mu

Keyword(s):

Power Density ◽

Cantilever Beam ◽

Cross Section ◽

Energy Harvester ◽

Variable Cross Section ◽

Vibration Energy ◽

Variable Cross ◽

Vibration Energy Harvester ◽

Piezoelectric Vibration Energy Harvester ◽

Piezoelectric Vibration

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.

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