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TECHNICAL PAPERS

3-D Elasticity-Based Modeling of Anisotropic Piezocomposite Transducers for Guided Wave Structural Health Monitoring

[+] Author and Article Information
Ajay Raghavan

Department of Aerospace Engineering,  University of Michigan, Ann Arbor, MI 48109-2140

Carlos E. S. Cesnik1

Department of Aerospace Engineering,  University of Michigan, Ann Arbor, MI 48109-2140cesnik@umich.edu

1

Corresponding author.

J. Vib. Acoust 129(6), 739-751 (Feb 08, 2007) (13 pages) doi:10.1115/1.2748776 History: Received May 16, 2006; Revised February 08, 2007

Anisotropic piezocomposite transducers (APTs), such as macro fiber composites and active fiber composites, have great potential to be used as structurally integrated transducers for guided-wave (GW) structural health monitoring. Their main advantages over conventional monolithic piezoceramic wafer transducers are mechanical flexibility, curved surface conformability, power efficiency, their ability to excite focused GW fields, and their unidirectional sensing capability as a GW sensor. In this paper, models are developed to describe excitation of GW fields by APTs in isotropic structures. The configurations explored are plane Lamb-wave fields in beams with rectangular cross-section, axisymmetric GW fields in cylinders, and 3-D GW fields in plates. The dynamics of the substrate and transducer are assumed uncoupled. The actuator is modeled as causing shear traction at the edges of the actuator’s active area along the fiber direction. The sensor is modeled as sensing the average extensional strain over the active area along the fiber direction. The work is unique in that the formulation is based on 3-D elasticity, and no reduced-order structural assumptions are used. This is crucial to model multimodal GW propagation, especially at high frequencies. A formulation is also proposed to model the behavior of APTs as GW sensors. Finally, results from experimental tests to examine the validity of the models are discussed and the possible sources of error are examined in detail.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) The packaged MFC and (b) the components of a AFC actuator (8)

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Figure 2

(a) Configuration of 3-3 APT surface-bonded on an isotropic beam with rectangular cross-section and (b) modeled representation

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Figure 3

(a) Configuration of 3-3 APT surface-bonded on a hollow cylinder and (b) modeled representation

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Figure 4

Contour integral in the complex ξ -plane to invert the displacement integrals using residue theory

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Figure 5

(a) Configuration of 3-3 APT surface-bonded on an isotropic plate and (b) modeled representation

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Figure 6

Harmonic wave field (u3) by square 3-3 APT (in gray stripes) at 100kHz, A0 mode in a 1-mm thick aluminum plate (the actuators are at the center, on either free surface, of size 0.5×0.5cm2 with the fibers along the vertical direction)

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Figure 7

Harmonic wave field (u3) by 0.5×0.5cm2 square uniformly poled piezo-actuators (in gray, at the center; other plate variables are unchanged from Fig. 6)

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Figure 8

Harmonic wave field (u3) by three-element comb array of 0.5×0.5cm2 square 3-3 APTsa

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Figure 9

Harmonic wave field (u3) by three-element comb array of 0.5×0.5cm2 square uniformly poled piezo-actuators

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Figure 10

Illustration of thin aluminum strip instrumented with MFCs

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Figure 11

Theoretical and experimental normalized sensor response over various frequencies in the beam experiment for (a)S0 mode and (b)A0 mode

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Figure 12

Schematic of aluminum plate experiment

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Figure 13

Theoretical and experimental normalized sensor response over various center frequencies in the plate experiment for (a)S0 mode and (b)A0 mode

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Figure 14

Normalized surface plots showing out-of-plane velocity signals over a quarter section of the plate spanning 20×20cm2. The MFC is at the upper left corner, shown using a striped rectangle, and its fiber direction is along the vertical direction: (a), (b), (c): Experimental plots obtained using laser vibrometry and (d), (e), (f) theoretical plots obtained using the model developed in this work.

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