E0-190-2008_(4)Chapter_3

# 5yeit are caused an equation of the motion for this

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Unformatted text preview: yeiωt are caused, an equation of the motion for this spring system can be expressed by: (3-7) Calculating the ratio of the left to the right hand side of Eq.(3-7), we obtain the relation as: (3-8) The real part K of the dynamic spring constant for the Voigt Model is constant and independent of the excitation frequencies ω, while the imaginary part ω C increases in proportion to the excitation frequencies ω. You can understand the physical meaning of the complex number, which expresses D.I.F. However, D.I.F exhibits more inherent variation with changing of frequencies as shown in the figure. The real parts K(R) of D.I.F in the lower frequencies up to the first natural frequency 1.25Hz of the surface stratum decrease monotonously with increase of frequencies. This tendency can be approximated by: (3-9) Ko is the real part at the frequency zero and denotes a static stiffness. Ma corresponds to a mass of soil portion which is vibrating in same phase of the foundation vibration. The imaginary parts of the horizontal D.I.F for both the raft and the pile foundation are nearly constant in lower frequencies up to 1.25Hz and they increase rapidly in higher frequencies. This tendency of the imaginary parts results from the characteristic of the radiation waves. The excitation forces on the foundation in higher frequencies are transmitted by the radiation wave and propagate outward. While, the forces in lower frequencies are hard to transmit outward in the form of the radiation wave and the forces transmit as same as the static loading on the so...
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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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