PIEZOELEC TRIG CR YS TA LS IN TENSOR FORM 85 



Similarly 



. dr} , drj drj 



ox oy dz 



(13) 



i ^' = ^'^dx'^dyy^dz'- 



' Hence subtracting the two lengths, we iind that the increases in separation 

 \ in the three directions are 



5x = .T ^ + V / + S -^ 



I dx dy dz 



I 



' dr] d-q drj ,... 



5v = ^^+>'t-+2^ (14) 



ox dy dz 



dx dy dz 



d^ 

 The net elongation of the line in the x direction is x — and the elongation 



dx 



. d^ . . . 

 per unit length is —^ which is detined as the linear strain in the x direction. 

 dx 



We have therefore that the linear strains in the x. y and s directions are 



5, = |f; S.^p; 53 = ^f. (15) 



dx dy dz 



The remaining strain coefficients are usually defined as 



oy dz dz dx dx dy 



and the rotation coefficients by the equations 



_ d^ dtf _ d^ d^ _ drj d^ 



dy dz dz dx dx dy 



Hence the relative displacement of any two j.oints can be expressed as 

 h = xS, + y [-~^) + z [-^) 



(17) 



(18) 



