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

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image (215)

σrz=2μεrz=μ{22Φrz+r(1r(rH)r)2H2z} (216)

image (216)

6.5.5.4 Calculation of Stresses in Terms of the Unknowns A1,A2,B1,B2

Recall the identities of Eq. (90), i.e.,

(λ+2μ)ξ2+λζP2=μ(ξ2+ζS22ζP2)λξ2+(λ+2μ)ζP2=μ(ζS2ξ2) (217)

image (217)

Substitution of Eqs. (201) and (208)(211) into Eq. (197) and use of Eq. (217) yields

σrr=λΔ+2μεrr=λ(ξ2+ζP2)fJ02μ(ξf+h)(ξJ0J1r)=λ(ξ2+ζP2)fJ02μξf(ξJ0J1r)2μh(ξJ0J1r)=λ(ξ2+ζP2)fJ02μξfξJ0+2μξfJ1

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