By Jiashi Yang
A continuation of the author’s prior ebook “An advent to the speculation of Piezoelectricity” (Springer, long island, 2005) at the 3-dimensional thought of piezoelectricity, this quantity covers decrease dimensional theories for numerous piezoelectric constructions and gadget functions. the improvement of two-, one- and zero-dimensional theories for top frequency vibrations of piezoelectric plates, shells, beams, jewelry curved bars and parallelepipeds is systematically offered. as well as linear piezoelectricity, convinced nonlinear results also are thought of and examples for machine functions are supplied. the fabric emphasizes dynamic theories and excessive frequency motions in addition to machine functions as there are fairly few books on piezoelectric buildings, in particular for top frequency theories. the quantity is destined to be some of the most systematic and accomplished books on piezoelectric buildings
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Additional info for The Mechanics of Piezoelectric Structures
A ceramic plate with in-plane poling. 37). For example, c33 is always the stiffness in the poling direction. 45) do not.
However, we are not interested in accurately describing the field variation along the plate thickness. Our main goal is to develop plate theories than can predict the frequencies and dispersion relations of these modes accurately. For this purpose, following Mindlin, we use a linear function x3u^\xux2,t), a= 1, 2, to approximately describe the fundamental thicken-shear motion. The main advantage of using a linear function is its simplicity. The error due to the approximation in resonant frequencies can be reduced or removed by introducing some correction factors.
2 4) +l) l)53/" . (2) ^ > = I4J> + 2II[2>, r,(2) _ S^ug+^J. 9) Sf^ag+31^, £,(2)=-$2). £< 2 >=-30 (3) . 5) describe homogeneous deformations of a plate element. 6) represent higher-order deformations of a plate element like curvature and twist, etc. Pictures of zero- and first-order deformed plate elements can be found in . 3 Constitutive relations The plate resultants of various orders are defined by 7j"> = J * / ^ , A(n) = [hDiX"3dx3. 12) D^=^Bmn(eiJkS^+evE^), where h 2h Bmn=\ x»x»dXiJ •>-* /(« + » + lX « + » even, 0.
The Mechanics of Piezoelectric Structures by Jiashi Yang