E0-190-2008_(8)Chapter_6(Substructure_Method)

That is the first and the second terms of eq11 11 are

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Unformatted text preview: st and the second terms of Eq.(11): (11) are the solutions of the equations below: (12) and (13) The mechanics of Eq.(12) : (12) can be explained by Fig.5: And also, the mechanics of Eq.(13): (13) can be explained by Fig.6. In Eq.(12): (12) Eq.(12-2) is: (12-2) and the displacement vector {XSf} is obtained as: (14) Substituting Eq.(14) into Eq.(12-1) leads to: (15) Because {XFf} is the displacement vector and {F} is the force vector in Eq.(15): (15) the term in the parenthesis in the left hand side refers to the stiffness matrix. Putting: (16) Then, Eq.(15) can be expressed by: (17) The matrix [KF] in Eq.(17): (17) indicates the dynamic stiffness matrix of the soil with the void which is evaluated at the interface F. The mechanics of Eq.(17) is illustrated by the figure: The matrix [KF] is called "Dynamic Impedance matrix of soil at the interface F". Because Eq.(11-1) in Eq.(11): (11) is: (18) the interaction force vector {F} of Eq.(17) : (17) can be expressed by: (19) Substituting Eq.(19): (19) into Eq...
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