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are restricted to a homogeneous half space. When the
ground is consists of layered strata, the waves transmitted
from the building are reflected at the layer interfaces and are
returned to the building. Therefore, the radiation damping
becomes normally smaller and the entire phenomenon
becomes more complicated. 1.3 Vibration of the Foundation on Ground
The vibration of the foundation is considered for the case
when the dynamic force is applied to the top of the
foundation on the ground surface.
For simplification, it is
assumed that the
foundation is not
deformed locally and that
there are no shape
changes during the
vibration.
When the sine excitation
is applied in horizontal
direction, the horizontal
displacement UO and the
rotation φ occur at the
foundation bottom. Contact earth pressure resisting this displacement UO and
the rotation φ is generated at the interface between the
bottom surface of the foundation and the ground surface,
and the radiation waves are transmitted to the ground.
When the ground is represented by a spring and a dashpot
to resist the displacement UO and the rotation φ, the
numerical modeling for the foundation can be expressed by:
As this foundation has
two degrees of freedom in
the horizontal
displacement and the
rotation, this model is
called “ Sway Rocking
Model” , abbreviated to
SR model. KH denotes the spring value of the ground resistance
regarding the horizontal displacement UO.
CH denotes the coefficient viscous damping absorbing
energy proportional to the velocity dUO/dt as the energy is
dissipated into the ground by the radiation waves.
KR and CR are the same quantities as mentioned above
regarding the rotation. The figures show the
calculation results for KH, CH,
KR and CR under that the
ground and the bottom of the
foundation are in perfect
contact with each other.
The horizontal spring value KH
and the dashpot coefficient CH
are nearly constant with
increase of the vibration
frequency.
But, KR and CR exhibit
remarkable frequency
dependency.
The KR decreases gradually
with increasing frequency, and
the CR shows opposite
characteristic. The figure shows the
horizontal
displacement Uf at the
top of the rigid
foundation.
The displacements
are normalized by the
exciting force .
γf in the figure
indicates the unit
volumetric weight of
the foundation.
When the γf becomes smaller, that is, when the foundation
becomes lighter, it can be seen that the peak frequencies
(“ Resonance frequencies”) of the resonance curve become
higher, and that the vibration amplitude becomes smaller. Equation of One Degree of
Freedom System &
m&& + cx + kx = Peiω t
x (1) Static (ω=0) Displacement： Xs = P / k (2) Natural Circu...
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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.
 Summer '14
 DrGRD

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