30 March 2009 Spectral element formulation for analysis of high-frequency dynamic responses induced by surface-bonded piezoelectric transducers
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Abstract
This paper presents spectral element formulation which simulates high frequency dynamic responses generated by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is developed to represent fundamental Lamb wave modes induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin- Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motion transformed into frequency domain. Detailed spectral element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through a numerical example.
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Hyun Woo Park, Ki Lyong Lim, Eun Jin Kim, Hoon Sohn, "Spectral element formulation for analysis of high-frequency dynamic responses induced by surface-bonded piezoelectric transducers", Proc. SPIE 7292, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2009, 72920N (30 March 2009); doi: 10.1117/12.816088; https://doi.org/10.1117/12.816088
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