Math Papers

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Equivalent loads for two-dimensional distributed anisotropic piezoelectric transducers with arbitrary shapes attached to thin plate structuress
joint work with Arnaud Deraemaeker and Gilles Tondreau,
Journal of the Acoustical Society of America 129 (2011) no 2, 681-690.

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When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.

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This paper appeared in the Journal of the Acoustical Society of America.

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