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Research Papers

Specified Motion of Piezoelectrically Actuated Structures

[+] Author and Article Information
T. M. Seigler, A. H. Ghasemi

 University of Kentucky, Lexington, KY 40506-0503

J. Vib. Acoust 134(2), 021002 (Jan 13, 2012) (7 pages) doi:10.1115/1.4005018 History: Received May 14, 2010; Accepted July 15, 2011; Published January 13, 2012; Online January 13, 2012

The problem considered is that of solving for the control input that generates partly specified motion of a deformable structure with distributed piezoelectric actuation. The motion constraint, called the program constraint, is specified as a desired relation on the motion of selected material points of the structure. The solution is based on a projection method applicable to a class of finite-dimensional dynamical systems which includes many common vibration models. For a nonlinear model with a nonlinear program constraint, the procedure in general results in a set of differential algebraic equations. It is shown that for linear models with linear periodic program constraints, the system is reduced to a set of algebraic equations. Application examples are presented for a Euler-Bernoulli beam to demonstrate the usefulness of the procedure.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Examples of specified motion problems

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Figure 2

Piezoelectrically actuated cantilever beam: (a) Case 1; (b) Case 2

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Figure 3

Piezoelectric actuation input requirements for Case 1 (x2  = L, a1  = 0.1L, b1  = 0.2L, x2  = 0.3L, a2  = 0.3L, b2  = 0.4L)

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Figure 4

Piezoelectric actuation input requirements for Case 1 (x2  = L, a1  = 0.1L, b1  = 0.2L, x2  = 0.3L, a2  = 0.5L, b2  = 0.65L)

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Figure 6

Piezoelectric actuation input requirements for Case 2 (x2  = 0.5L, xd  = L, a1  = 0.1L, b1  = 0.2L, a2  = 0.3L, b2  = 0.4L)

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Figure 5

Piezoelectric actuation input requirements for Case 2 (x2  = 0.5L, xd  = 0.8L, a1  = 0.1L, b1  = 0.2L, a2  = 0.3L, b2  = 0.4L)

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