By Jiashi Yang
This can be the main systematic, complete and up to date ebook at the theoretical research of piezoelectric units. it's a traditional continuation of the writer s earlier books: An advent to the speculation of Piezoelectricity (Springer, 2005) and The Mechanics of Piezoelectric constructions (World clinical, 2006). in response to the linear, nonlinear, 3-dimensional and lower-dimensional structural theories of electromechanical fabrics, theoretical effects are awarded for units comparable to piezoelectric resonators, acoustic wave sensors, and piezoelectric transducers. The e-book displays the contribution to the sector from Mindlin s college of utilized mechanics researchers because the Nineteen Fifties.
Contents: three-d Theories; Thickness-Shear Modes of Plate Resonators; Slowly various Thickness-Shear Modes; Mass Sensors; Fluid Sensors; Gyroscopes -- Frequency influence; Gyroscopes -- cost impact; Acceleration Sensitivity; strain Sensors; Temperature Sensors; Piezoelectric turbines; Piezoelectric Transformers; strength Transmission via an Elastic Wall; Acoustic Wave Amplifiers.
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Extra info for Analysis of piezoelectric devices
Substituting Eq. 25) into Eq. 27) 7T2 "26 1 + -U2 - A t 2 2h\ p 26 ? 27) shows that piezoelectric coupling raises the frequency. ~2h\ p 1 i T ft This effect is called piezoelectric stiffening. 3. Forced vibration For forced vibration we have A2 = 0 and 0 e26 V 2h -e26V 4 = c66£cos£/? 29) 2c66 ^h cos £/z - 2 -^- sin ^2 f 2/? 30) - = -cr, 2fc£/z-/t226tan#z where ae is the surface free charge per unit area on the electrode at x2 = h. 31) Note the following limits: lim C = ^ L , «26^o 2h E 22 HmC = ^ 2 «-><> 2h 1 ~2h k (1 + 4 ) .
They depend on the initial deformation xJX) and electric potential 0°(X). , K[a^i=T; (DxKNK=-axE Sy, on ST, on SD. 10) alE^dS. dt f T„uadS- [dt f The admissible u and 01 must satisfy du„ I, = 8u„ I, = 0 in V. 11) $6> t0
22 We can add Eqs. 14)12, and also subtract them from each other. The Eqs. 15) 2 - ^ - 4 sin ^ + 2fl,A = F. 2. Free vibration First, consider free vibrations with V= 0. 15) decouples into two sets of equations. For symmetric modes, c66^2£sin£/2 = 0. 18) which determines the following resonant frequencies: ^ ) = «^g7 2hV p „ = o,2,4,6,.... 17) implies that B\ = 0 and Ax modes are u:=cos^(,x--(») 2, 0. 20) 22 where n = 0 represents a rigid-body mode. 21) 2^Axsm%h + 2Bxh = Q. 21) determine the resonant frequencies and modes.
Analysis of piezoelectric devices by Jiashi Yang