502 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



Now since the ceramic is plated, the major sui-face is an equipotential 

 surface and hence E. does not vary with r oi' 6. Hence integrating over 

 the surface of the ceramic, we have for the open circuit field 



E, / rdrdd=-2 Qii5,„ / J\,r dr d9 



Jo Jo Jo Jo 



+ Qu5,, [ f (7V. + Tee)rdrdd 

 Jo Jo 



Introducing the values of T^^ , Trr and Tee from Equation (29) and per- 

 forming the integrations we find 



EA = 2 [Qn8,,F + Qi253o (1 + 2a)F] (32) 



where A is the cross-sectional area of the ceramic. The first term agrees 

 with that for a uniform stress, but the second term shows that we have 

 a correction due to the radial and tangential stresses generated by the 

 application of the force at a point. 



The amount of correction can be calculated by putting in the values 

 of Qu and o- the Poisson ratio. Recent measurements of the thickness 

 resonance and the resonance of a torsional ceramic have shown that the 

 best values of the Lame elastic constants are 



X = 5.8 X 10'' dynes/cm'; m = ^ X lO" dynes/cm' (33) 



With these values, Poisson 's ratio becomes 



X 5.8 



2(X + m) 19.6 



= 0.29G (34) 



For 4 per cent lead titanate barium titanate ceramic, introducing the 

 values given above, the voltage generated by a force applied at a point 

 is about 0.4 of that for a force apphed uniformly, giving 



,. 0.575 X lO"' Fit ,, .^.s 



V z = — volts (3o) 



This value corresponds reasonably well with the data of Fig. 4. 



When the remanent polarization is applied along the Y axis and the 

 voltage measured along the Z axis. Equation (24) shows that the open 

 circuit voltage will be 



E,= -2 (Qr, - Qv^d,J, (36) 



where Ti = Y^ is the stress in the direction of polarization (F) applied 

 to the surface of the ceramic. Since the single stress Ti is involved, the 



