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Analysis of a Curved Beam MEMS Piezoelectric Vibration Energy
Harvester
Yong ZHOUa, Yong DONGb, Shi LIc
College of Mechanical Engineering, Hunan Institute of Science and Technology, Yueyang, China
Keywords: MEMS, Curved beam, Piezoelectric, Finite deformation, Coupling vibration
Abstract. An analytical model is derived for obtaining the dynamic performance of a thin curved
composite piezoelectric beam with variable curvatures for the MEMS piezoelectric vibration energy
harvester. The plane curved beam theory with rectangular section is employed to explore the bending
and twisting coupling vibration characteristics. In order to satisfy the most available environmental
frequencies, which are on the order of 1000Hz, the parameters of the spiraled composite beam bonded
with piezoelectric on the surfaces are investigated to provide a method of how to design low
resonance beams while keeping the compacting structural assembly. The results indicate the adoption
of ANSYS®
software to carry out the MEMS piezoelectric vibration energy harvester’s numerical
simulation can improve the accuracy of the harvester designing and manufacturing consumedly. And
the simulation data also provide a theory analysis foundation for the engineering, design and
application of harvester.
Introduction
In the past few years, the applications of wireless networking micro-sensors, micro-electronic devices
and other smart devices have a great growth in the fields of civil, medical, traffic etc. At the same
time, there is a remarkable challenge of supplying power to these devices. In [1], a vibration-based
harvesting micro power generator was used to power the sensor node. The energy generators based on
the piezoelectric materials are of the greatly promising devices because of their significant efficiency.
Converting environmental vibration into electric energy has been actively investigated based on many
kinds of designs with various piezoelectric materials [2-4].
The objective of this paper is to present an analytical model to evaluate the dynamic phenomena of
a thin curved composite piezoelectric beam with variable curvatures for the MEMS piezoelectric
vibration energy harvester. In order to satisfy the most available low environmental frequencies,
which are on the order of 1000Hz, the parameters of the spiraled laminated piezoelectric beam are
investigated to provide guidances of how to design low resonance scavenging generator while
keeping the compacting structural assembly. Results of present research indicate that the interaction
between the geometric quantities and the parametric resonance plays an important role to the
dynamical performance of the cantilevered piezoelectric beam generator.
Structure of the Harvester
Consider an elastic Archimedes’ spiral curved beam given by the polar equation
R αθ= , (1)
where R is the radius of the curved beam, α is the parameter controlling the gap between consecutive
inner and outer arc of the spiral, θ is the polar angle of the curved beam. Then, the arc length, s, is
( )2 211 ln 1
2s α θ θ θ θ = + + + +
. (2)
Advanced Materials Research Vols. 139-141 (2010) pp 1578-1581Online available since 2010/Oct/19 at www.scientific.net© (2010) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.139-141.1578
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 152.14.136.96, NCSU North Carolina State University, Raleigh, United States of America-08/11/13,19:30:21)
Fig. 1 shows the geometry of the general curved laminated beam whose cross section is rectangular
and symmetrical about both the y and z axes. Assume that the cross section is rigid with respect to
in-plane deformation and the shearing deformation of the middle surface of the member is negligible.
Based on the Hamilton theory, the mechanical mode shapes of the beam are [5]
( ) ( ) ( ) ( )sinh cosh sin cosrN N N N Nc x d x e x f xψ λ λ λ λ= + + + , (3)
where the subscript r denotes that it is a mechanical mode shape, N is the mode number, and c, d, e, f
are coefficients determined by the enforcing boundary conditions.
Fig. 1 Geometry of the composite beam
Focusing on the first structure vibration mode of interest, the quantities can be simplified. The
scalar governing equations are [5]
10
f
p
l
Mr Cr Kr v B w
r C v vR
+ + −Θ = −Θ + + =
�� � ��
� �, (4)
where r represents the amplitude of the displacement (w), and v represents the amplitude of the
voltage and the other coefficients are referenced literature.
Parameter Analysis of the Piezoelectric Harvester
The dynamical performances of the spiral piezoelectric harvester with one end fixed were
investigated under different dimensional parameters based on ANSYS®
. The material constants of the
matrix, SU-8, and the bonded layer, piezoelectricity, were referenced to the literature [1]. The initial
width and length of the harvester was 35µm and 3590µm respectively, and the expected thickness
with all layers was 1µm. The meshed model using the solid5 element in the ANSYS®
was listed in
Fig. 2. For the sake of the accuracy, the piezoelectric parts were finely meshed and totally 24860
elements were used for the mode shape calculations of the piezoelectric harvester.
Modal analysis in ANSYS®
will provide information about free vibration. Stiffness and mass
effects are held constant and damping is ignored. No time varying forces, pressures, displacements, or
other externalities are applied. Mode shapes and resonant frequencies are extracted using the internal
Block-Lanczos method.
Advanced Materials Research Vols. 139-141 1579
Fig. 2 Meshed model
Fig. 3 Resonant frequencies vs. thickness
The resonant frequencies up to 2kHz are calculated, with the lowest frequency plotted in Fig. 3.
The figure shows that the relationship between the cantilever length and the thickness is linear. In this
case, the thickness of the piezoelectric layer and matrix layer is equal and the effective length is
l=3590µm. Because of the decreasing of the total thickness, the stiffness of the beam is smaller, which
leads the lower resonant frequency of the piezoelectric harvester.
Fig. 4 shows the relationship between the harvester first resonant frequency and the length with
total 2µm thickness and 35µm width. The overall trends retain their shape from one-dimensional
situation. But there are some details that changed.
The variation of the beam length has definite effect on the relationship between resonant frequency
and length. In the one-dimensional case, the resonant frequency varies with the length according to
the l-3/2
. In this case, the resonant frequency varies with l-k
, where k is approximately 1.29 for the data
collected. One possible reason for the intuition is the difference of the internal moments. The
one-dimensional beam is subject to a pure bending moment, but two-dimensional spiral beams have
both a bending moment and a twisting moment or torsional component. These added moments
complicate any attempts at analytical analysis significantly.
Fig. 4 Resonant frequencies vs. length
Fig. 5 Resonant frequencies vs. width
Resonant frequency for spiral beam is not independent of width. As is the case with a
one-dimensional beam. Fig. 5 shows the variation of the resonant frequency of the harvester with the
width. Increases in width tend to shift the point up in frequency, which is consistent with the situation
of the larger structure having low resonance. As in the Fig. 3, the increasing of the beam width
augments the stiffness of the beam, which leads the larger resonant frequency of the piezoelectric
harvester. At the same time, the increased width raises the internal moments not only the bending
moment but also the twisting component, which also brings the nonlinear relationship between the
resonant frequency and the width.
1580 Manufacturing Engineering and Automation I
(a) Undeformed state (b) First mode of vibration
Fig. 6 Oscillation of the beam
The first mode shape represents the primary deflection of the two-dimensional beam. Every point
in the beam deflects to the same side of the horizontal plane. As a unity, the beam oscillates in the
normal direction of the beam surface. Renderings of the deformed shape are shown in Fig. 6(b). The
first or primary mode of resonance closely resembles deformation under the static load of its own
weight. This primary mode is the most useful for power generation and must be maximized. It should
be the resonance target of incoming environmental vibration.
Summary
Using the MEMS technology, a thin film piezoelectric micro-power harvester device could be
constructed. The PMPH is simply a cantilever structure tuned to resonate at ambient frequencies. At
resonance, sizable strain is induced in a layer of the beam made from the piezoelectric material, PZT,
thereby generating electricity because of the piezoelectric effect. Recent studies have found that the
most available environmental frequencies are on the order of 1k Hz. Current PMPH structures were
designed to operate at 20 kHz. This paper is aimed at understanding how to design low resonance
beams while keeping them compact. Two-dimensional spiral beams were designed and analyzed
using analytical as well as finite element methods. A variety of designs were developed using
ANSYS®
which have resonant frequencies in the target range. The mode shapes were also simulated.
Acknowledgements
The authors gratefully acknowledge the financial support of the Hunan Natural Science Foundation,
Grant No. 08JJ4012.
References
[1] S. Roundy, P. K. Wright and J. Rabaey: Computer Communication, Vol. 26 (2003) No.11,
pp.1131-1144.
[2] Y. C. Shu, I. C. Lien: Smart Materials and Structures, Vol. 15 (2006) No. 6, pp.1499-1512.
[3] G. Ottman, H. Hofmann and A Bhatt et al.: IEEE Transactions on Power Electronics, Vol. 17
(2002) No. 5, pp.669-676.
[4] Y. Jeon, R. Sood and J. Jeong, et al.: Sensors and Actuators, A Vol. 122(2005) No. 1, pp.16-22.
[5] N. E. du Toit: Modeling and design of a MEMS piezoelectric vibration energy harvester (MS.,
Massachusetts Institute of Technology, USA 2005), pp.59-92.
Advanced Materials Research Vols. 139-141 1581
Manufacturing Engineering and Automation I 10.4028/www.scientific.net/AMR.139-141 Analysis of a Curved Beam MEMS Piezoelectric Vibration Energy Harvester 10.4028/www.scientific.net/AMR.139-141.1578
DOI References
[1] S. Roundy, P. K. Wright and J. Rabaey: Computer Communication, Vol. 26 (2003) No.11, p.1131-1144.
doi:10.1016/S0140-3664(02)00248-7 [2] Y. C. Shu, I. C. Lien: Smart Materials and Structures, Vol. 15 (2006) No. 6, pp.1499-1512.
doi:10.1088/0964-1726/15/6/001 [3] G. Ottman, H. Hofmann and A Bhatt et al.: IEEE Transactions on Power Electronics, Vol. 17 2002) No. 5,
pp.669-676.
doi:10.1109/TPEL.2002.802194 [1] S. Roundy, P. K. Wright and J. Rabaey: Computer Communication, Vol. 26 (2003) No.11, pp.1131-1144.
doi:10.1016/S0140-3664(02)00248-7 [3] G. Ottman, H. Hofmann and A Bhatt et al.: IEEE Transactions on Power Electronics, Vol. 17 (2002) No.
5, pp.669-676.
doi:10.1109/TPEL.2002.802194
