Planar electromechanical coupling

Fig. .5-33 (PbTi03)j (Pb(Sci/2Nbi/2)03)i 3 (ceramic), fcp versus x. is the planar electromechanical coupling factor...

The planar effective electromechanical coupling factor kp is decreased with the increasing in overtone mode order also, as shown in Fig.8, it also can be fit with second order polynomial ... 

The series resonant and pjarallel resonant frequencies of fundamental radial vibration modes are increased with the decreasing of electrode size, but the planar effective electromechanical coupling factor is decreased with the decreasing of electrode size, as shown in Fig.lO. 

The relation between series resonant frequency (fs) and planar effective electromechanical coupling factor (kp) with electrode size (De) is second order pwlynomial and can be expressed as ... 

For piezoelectric ceramic thin disk with larger (diameter/thick) ratio, in the lower frequency range, the major vibration mode is radial vibration mode. In the radial vibration mode, besides the fundamental mode, there are some overtone modes with inharmonic frequency separation. The planar effective electromechanical coupling factor kp is decreased with the increasing in overtone mode order. The relation between planar effective electromechanical coupling factor and overtone mode order can be fit with second order polynomial. 

By virtue of the assumptions of unidirectional electrostatic fields and planar mechanical stress, the electromechanically coupled constitutive relations have been modified significantly. In example, the formulation on the left-hand side of Eq. (4.10a) reduces to Eq. (4.28) or (4.30). A transformation of coordinates on the considered plane may be performed as a rotation around the axis normal to this plane. In the case of Eq. (4.30), the base vector C2 represents the axis of rotation and thus this planar rotation may be formulated as follows ... 

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