Sec substituting eq34 into eq6 35 36 where wave

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Unformatted text preview: stituting Eq.(34) into Eq.(6): (35) (36) where, :wave number(rad.s/m) (37) The solution of Eq.(36) : is given by: (38) where E and F are arbitrary constants. Substituting Eq.(38) into Eq.(34): the displacement u(z,t) can be expressed by: (39) The first term indicates the wave propagating in the negative z direction, while the second term in the positive z direction. E and F express the amplitude of the waves. Hereafter, the time term eiωt is not written. The shear stress τ(z) is expressed by: (40) The coefficient of this equation is: (41) The expression of the shear stress τ(z) is transformed into: (42) Consider the wave propagation in two layered strata as shown, when the SH wave Eoexp(iκ2t) incidents on the interface between the surface stratum and the engineering bedrock. Surface Stratum Engineering Bedrock The displacement and shear stress in both strata are given by: (1) for the surface stratum: (43) (44) (2) for the engineering bedrock: (45) (46) The subscripts 1 and 2 indicate the surface stratum and the engineering bedrock, respectively. The shear stress a...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.

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