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13 u1 z t e11 and eq16 into eq20 we obtain 22

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Unformatted text preview: g Eq.(13): u1( z, t ) = E1(ς1) and Eq.(16) : into Eq.(20): We obtain: (22) Similarly, putting Eq.(14): and Eq.(17) : into Eq.(21): Then, (23) Defining the impedance ratio α as: (24) then, Eq.(23): leads to: (25) Integrating Eq.(25) gives : (26) Adding Eq.(22): to Eq.(26): then, (27) (28) Substituting Eq.(28) into Eq.(26): then, (29) Define the transmission T and reflection coefficient R as: Transmission coefficient : (30) Reflection coefficient : (31) Using T and R, the transmission wave E1(t+z/V1) and the reflection wave F2(t-z/V2) are given by: (32) (33) ρ1,V1 2 E1(t+z/V1)=T(α) E2(t+z/V2) 1.5 T Medium 1 z E2(t+z/V2) Medium 2 T and R 1 0.5 R 0 F2(t-z/V2) =T(α) E2(t+z/V2) -0.5 ρ2,V2 α=ρ1V1/ρ2V2 0 1 α α 2 (4) Amplification of a surface stratum on the engineering bedrock We consider the SH wave propagation in a surface stratum on the engineering bedrock, when the SH wave EO(t) incidents. The equation of the motion is given by Eq.(6): (6) Putting: (34) in which ω denotes circular frequency(rad./sec). Sub...
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