MS layer embedded in asymmetric laminate

If the magnetostrictive layer is placed anywhere else, other than in the middle of the laminate, compressive stresses in MS layer result in moment causing bending in the beam [Figure 31.2 (b)].

Figure 31.2 (b) Force and moment balance in asymmetric laminate

Hence, axial strain in MS layer including the bending effect

(31.14)

is the distance from mid plane in thickness direction.

Mid plane curvature

(31.15)

Moment M on beam due to stresses induced in the MS layer

(31.16)

Here a, b and c are the distances from top where the forces are assumed to be acting. Using Equation (31.1) and (31.3), stresses in MS layer including the bending effect are

(31.17)

Putting this stress value in Equation (31.2), the voltage can be obtained as

(31.18)