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Natural frequencies of laminated piezoelectric plates with internal electrodes
Author(s) -
Lim C.W.,
Cheng Z.Q.,
Reddy J.N.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310254
Subject(s) - piezoelectricity , vibration , transfer matrix , bimorph , piezoelectric sensor , actuator , natural frequency , mathematical analysis , matrix (chemical analysis) , mathematics , materials science , mechanics , physics , acoustics , composite material , engineering , computer science , computer vision , electrical engineering
Natural vibrations of laminated piezoelectric plates with internal electrodes are analyzed using the transfer matrix method and the asymptotic expansion method. The steady‐state equations of three‐dimensional linear piezoelectricity reduce to a hierarchy of two‐dimensional equations of the same homogeneous operator. The leading‐order equations are easily solvable, whereas the higher‐order equations may contain secular terms and are not straightforward to find their solutions. The solvability condition is established to calculate higher‐order frequency parameters. The present theoretical formulation is used to provide new results by calculating fundamental frequencies of a rectangular laminated plate with two surface‐affixed piezoelectric actuators, a parallel bimorph, a four‐layered multimorph and a functionally graded plate attached with an actuator.