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Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition by Victor Giurgiutiu

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image (254)

The coefficients A1,B2image are given by Eq. (241). Substitution of Eq. (241) into Eqs. (253), (254) yields

urA=[ξ(2ξζSsinζSd)sinζPz+((ξ2ζS2)sinζPd)(ζSsinζSz)]J1uzA=[2ξζSsinζSdζPcosζPz+ξ((ξ2ζS2)sinζPd)cosζSz]J0 (255)

image (255)

σzzA=μ{(ξ2ζS2)(2ξζSsinζSd)sinζPz+[2ξ(ξ2ζS2)sinζPd]ζSsinζSz}J0σrzA=μ{2ξ(2ξζSsinζSd)ζPcosζPz+(ξ2ζS2)[(ξ2ζS2)sinζPd]cosζSz}J1 (256)

(256)

Upon expansion and rearrangement, Eqs. (255), (256) become

urA=ζS

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