E0-190-2008_(10)1D_Shear_Propagation(SHAKE)

That is 7 substituting eq7 into eq4 4 we obtain

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Unformatted text preview: ency ω . That is, (7) Substituting Eq.(7) into Eq.(4) : (4) we obtain the equation below: (8) Introducing the notation: (9) Then, the complex elastic shear modulus can be expressed by: (10) ζ is complex number. We adopt ζ of which both real and imaginary part are positive real numbers. That is, (11) In the left hand side of Eq.(8): (8) Expressing the coefficient of the second term by: (12) Then, Eq.(8): (8) is transformed into Eq.(13): (13) The solution of Eq.(13) is given by: (14) The shear stress(amplitude) Τ, which corresponds to the displacement(amplitude) U, is expressed by : (15) (3) Application to Multi-Layered Strata On the multi-layered strata shown in the figure, we consider the wave propagation due to the incident earthquake wave EOeiωt , which propagates upward in the deepest stratum (Engineering Bedrock). eiωt EO indicates the displacement of the incident wave with the amplitude EO and the angular frequency ω. Interface No. Stratum No. (1) E1 F1 (2) (2) (1) E2 F2 (3) ρ1, V1, h1 ρ2, V2, h...
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