Transcript future of vibration research

Vibration from
Underground Trains
*
Pipe-in-Pipe Software
Hugh Hunt
Cambridge University Engineering Department
www.hughhunt.co.uk
“Common sense will carry one a long way
but no ordinary mortal is endowed with
an inborn instinct for vibrations”.
“Vibrations are too rapid for our sense of sight …
common sense applied to these
phenomena is too common to be other
than a source of danger”.
Professor C E Inglis, FRS,
James Forrest Lecture, 1944
The basis for “common sense”
• Stiffness
Frequency =
• Mass
k
m
m
• Damping ?
• Continuous media ?
k
c
The mkc model
Vibration from Railways
… where is the “mass-on-spring”?
… how do I use my “intuition”?
Source: Talbot
Vibration isolation of rail track in tunnels
Floating Slab Track
Source: Tiflex Ltd
Undersleeper pads
Source: Edilon
Novel designs for vibration control
Source: Pandrol Ltd
Insertion Gain
for
Floating Slab Track
Isolation
frequency
6.3Hz
Insertion gain
(dB)
20
10
0
-10
-20
-30
-40
-50
Floating Slab Track 2
4
5
10
12.5
25
50
100
125
Source: GERB
200
What is Insertion Gain?
response
T2
m
m
T1
k
k
kadditional
before “insertion”
frequency
after “insertion”
Insertion Gain
T2
T1
0 dB
Amplification at
new resonance
typically 10dB
Benefit, typically
10 to 20 dB
frequency
The Pipe-in-Pipe model
(a)
(b)
z
eq
y
er
x
q
h
z
ez
r
q
R2
a
q
Tunnel:
thin-walled cylinder
• radius R
• wall thickness t
• infinite length
R1
Coupling
Discrete Fourier transform
around q
Continuous Fourier transform
along z
Soil:
thick-walled cylinder
• inner radius R
• outer radius 
• infinite length
vertical vibration
virtual free surface
isolation
dB ref mm
(rms)
Insertion Gain
isolation
Acknowledgements: Dr James Forrest
Dr Mohammed Hussein
rms insertion
gain (dB)
When downloading the software you
will need to enter a username and
password. These are available on
request. This is a requirement of
Mathworks (ie MATLAB) to permit
use of the MCR-installer which is a
suite of DLLs needed to run PiP as a
pre-compiled MATLAB executable.
This is a demonstration of the Pipe-in-Pipe software.
It is freeware and can be obtained by following the
PiP link at www.hughhunt.co.uk
I am hugely indebted to Dr Mohammed Hussein from
the University of Nottingham for his enormous
contribution to the development of PiP software.
Please be patient when installing and
running PiP for the first time – it may
take a few minutes to get started.
Subsequent uses are quick.
-75
-80
-85
-90
This shows how different – by as
much as 5dB - the vibration
levels can be when the material
properties are changed by only
15%. This begins to put into
question the possibility of
prediction accuracy any better
than ± 10dB.
This shows how an increase in
the bending stiffness of the
slab leads, in this case, to an
increase in vibration.
-75
-80
-85
-90
-70
-75
-80
-85
-90
-95
This shows how an
increase in the mass and
bending stiffness of the
slab plus a reduction in the
natural frequency of the
slab from 40Hz to 25Hz
leads to a reduction in
vibration.
It is convenient to plot
Case2, Case 3 and Case 4 as
“Insertion Gains” measured
relative to Case 1. These
show clearly where the
changes made lead to
reduction in vibration
(ie IG < 0dB)
5
0
-5
- 10
0dB
-70
-75
-80
-85
-90
-95
Here the measurement poin
is shifted from being 20m
directly above the tunnel to
being 20m above and 5m to
one side. Note that the
response is as much as 5dB
different at certain
frequencies. This again put
into question the possibility
of obtaining prediction of
vibration within an accuracy
of better than ±10dB.
-40
-50
-60
-70
-80
5
- 0
- 5
-10
The PiP software also
allows the user to plot
contour plots such as these
which illustrate where the
vibration is greatest at
different frequencies. This
can help guide the location
and distribution of piled
foundations.
The PiP software can also
include the effect of rigid
bedrock and the latest
version of PiP (soon to be
released) includes a free
surface and layered soil.
Validation – PiP vs. coupled FEM-BEM
The PiP software is in
excellent agreement
with other models
Source: Mohammed Hussein / Shashank Gupta / Lars Rikse
Conclusions
• The mass-on-spring model is not good for
predicting Insertion Gain
• The PiP model is a very fast and convenient tool
for computing vibration from railway tunnels
• The use of PiP puts into question the possibility of
obtaining better than ±10dB prediction accuracy
from any model – no matter how detailed.
• PiP is freeware and is easy to use.