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Research Papers

Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters

[+] Author and Article Information
Ravindra Masana

Department of Mechanical Engineering, Nonlinear Vibrations and Energy Harvesting Laboratory (NoVEHL), Clemson University, Clemson, SC 29634

Mohammed F. Daqaq

Department of Mechanical Engineering, Nonlinear Vibrations and Energy Harvesting Laboratory (NoVEHL), Clemson University, Clemson, SC 29634mdaqaq@clemson.edu

J. Vib. Acoust 133(1), 011007 (Dec 17, 2010) (10 pages) doi:10.1115/1.4002786 History: Received January 29, 2010; Revised May 30, 2010; Published December 17, 2010; Online December 17, 2010

To maximize the electromechanical transduction of vibratory energy harvesters, the resonance frequency of the harvesting device is usually tuned to the excitation frequency. To achieve this goal, some concepts call for utilizing an axial static preload to soften or stiffen the structure (Leland and Wright, 2006, “Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload,” Smart Mater. Struct., 15, pp. 1413–1420; Morris, 2008, “A Resonant Frequency Tunable, Extensional Mode Piezoelectric Vibration Harvesting Mechanism,” Smart Mater. Struct., 17, p. 065021). For the most part, however, models used to describe the effect of the axial preload on the harvester’s response are linear lumped-parameter models that can hide some of the essential features of the dynamics and, sometimes, oppose the experimental trends. To resolve this issue, this study aims to develop a comprehensive understanding of energy harvesting using axially loaded beams. Specifically, using nonlinear Euler–Bernoulli beam theory, an electromechanical model of a clamped-clamped energy harvester subjected to transversal excitations and static axial loading is developed and discretized using a Galerkin expansion. Using the method of multiple scales, the general nonlinear physics of the system is investigated by obtaining analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. These theoretical expressions are then validated against experimental data. It is demonstrated that in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in (i) increasing the electric damping in the system, thereby enhancing the energy transfer from the beam to the electric load, (ii) amplifying the effect of the external excitation on the structure, and (iii) enhancing the effective nonlinearity of the device. These factors combined can increase the steady-state response amplitude, output power, and bandwidth of the harvester.

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References

Figures

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Figure 1

Schematic of an axially loaded beam harvester

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Figure 2

Deformation of a beam element

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Figure 3

Variation of the first fundamental frequency with the axial load. Circles represent experimental findings.

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Figure 4

Experimental setup

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Figure 5

Fast Fourier transform of the system at different axial loads

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Figure 6

Variation of the effective damping with the axial load for different values of re

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Figure 7

Amplitude-frequency curves for different values of the axial load and a base acceleration of 10 ms−2

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Figure 8

Schematic of experimental setup and data acquisition

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Figure 9

Open-circuit voltage-frequency curves for different values of the axial load and a base acceleration of 10 ms−2. Circles represent experimental findings.

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Figure 10

Open-circuit voltage-frequency curves for constant axial load of P=19 N and different transversal excitations. Circles represent experimental findings.

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Figure 11

Voltage-frequency curves for different load resistances. Results are obtained using P=26 N and a transversal excitation of 10 ms−2. Circles represent experimental findings.

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Figure 12

Variation of the effective nonlinearity with the axial load

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Figure 13

Variation of the output power with the resistance for different axial loads and base acceleration of 10 ms−2. Circles represent experimental findings.

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Figure 14

Power developed across optimum resistance for different axial loads and base acceleration of 10 ms−2

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