This preview shows page 1. Sign up to view the full content.
Unformatted text preview: yeiωt are
caused, an equation of the
motion for this spring system can
be expressed by:
(37)
Calculating the ratio of the left to the right hand side of
Eq.(37), we obtain the relation as:
(38)
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:
(39) 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...
View
Full
Document
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.
 Summer '14
 DrGRD

Click to edit the document details