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

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image (136)

Substitution of A1, B2 from Eq. (120) into Eq. (136) yields

σxxA=μ[(ξ2+ηS22ηP2)2ξηSsinηSdsinηPy2ξηS(ξ2ηS2)sinηPdsinηSy]σyyA=μ[(ξ2ηS2)2ξηSsinηSdsinηPy+2ξηS(ξ2ηS2)sinηPd(sinηSy)]σxyA=iμ[2ξηP2ξηSsinηSdcosηPy+(ξ2ηS2)(ξ2ηS2)sinηPdcosηSy] (137)

image (137)

Upon expansion and rearrangement, Eq. (137) becomes

σxxA=2μξηS[(ξ2+ηS22ηP2)sinηSdsinηPy(ξ2ηS2)sinηPdsinηSy]σyyA=2μξηS(ξ2ηS2)(sinηSdsinηPysinηPdsinηSy)σxyA=iμ[4ξ2ηPηSsinηSdcosηPy+(ξ2ηS2)2sinηPdcosηSy] (138)

(138)

Showing explicitly the x,t dependency through the common factor ...

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