Exact dynamic solutions to piezoelectric smart beams including peel stresses I: Theory and application |
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Institution: | 1. Department of Mechanical Engineering, Yasouj University, Yasouj 75914-353, Iran;2. Department of Mechanical Engineering, Persian Gulf University, Bushehr 7516913798, Iran;1. Johannes Kepler University Linz, Institute of Technical Mechanics, Altenberger Strasse 69, A-4040 Linz, Austria;2. Johannes Kepler University Linz, Institute of Biomedical Mechatronics, Altenberger Strasse 69, A-4040 Linz, Austria |
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Abstract: | This work presents exact dynamic solutions to piezoelectric (PZT) smart beams including peel stresses. The governing equations of partial differential forms are firstly derived for a PZT smart beam made of the identical adherends, and then general solutions of the governing equations are studied. The analytical solutions are applied to a cantilever beam with a partially bonded PZT patch to the fixed end. For the given boundary conditions, exact solutions of the steady state motions are obtained. Based on the exact solutions, frequency spectra, natural frequencies, normal mode shapes, harmonic responses of the shear and peel stresses are discussed for the PZT actuator. The details of the numerical results and sensing electric charges will be presented in Part II of this work. The exact dynamic solutions can be directly applied to a PZT bimorph bender. To compare with the classic shear lag model whose numerical demonstrations will be given in Part II, the related equations are also derived for the shear lag rod model and shear lag beam model. |
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