Wave Travel and Attenuation and Machine Foundations Richard P.
Ray, Ph.D., P.E. Civil and Environmental Engineering University of
South Carolina
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Topics for Today Waves in Elastic Media Waves in the Earth
Surface Excitations Machine Foundations
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Waves Rayleigh, R Surface (2-D) Shear,S Secondary (1-D)
Compression, P Primary (1-D)
http://paws.kettering.edu/~drussell/demos.html
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Resonant Column - MOC - Wavelets Discrete Properties
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Resonant Column - MOC - Wavelets Rock Motion Soil 1: G 1, 1, 1
Soil j: G j, j, j Soil m: G m, m, m............................
Surface Block Mass Horizontal Polarization Vertical Propagation
Computational Reaches Nodes z n-1 z 1 z i i,Vii,Vi A B P
t=0......1.......2......3
Resonant Column - MOC - Wavelets S time P B A B2 A2 CC2C3 B3 A3
C + C - t z R time R space S space Nonlinear Interpolation
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Resonant Column - MOC - Wavelets zz 30 31
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Resonant Column - MOC - Wavelets
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Cumulative Hysteretic Energy Time (sec) Reach Number Strain
400Hyst 400
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A1A1 A2A2 A3A3 A4A4 Wavelets
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Resonant Column - MOC - Wavelets
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Profile View
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MEMS Accelerometer
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Data Acquisition
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Resonant Column - MOC - Wavelets Wavelets
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Resonant Column - MOC - Wavelets Wavelets
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Resonant Column - MOC - Wavelets By varying the wavelet scale s
and translating along the localized time index n, one can construct
a picture showing both the amplitude of any features versus the
scale and how this amplitude varies with time. Wavelet Scale
Localized Time Index Fourier Transform Wavelet via Fourier
Transform
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Resonant Column - MOC - Wavelets
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Wavelets
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r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal
component Shear window Rayleigh wave Relative amplitude + + + + - -
+ + Wave TypePercentage of Total Energy Rayleigh67 Shear26
Compression7 Waves
Fundamentals-Modeling-Properties-Performance
Karlstrom and Bostrom 2007 Trench Isolation
Fundamentals-Modeling-Properties-Performance
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Chehab and Nagger 2003
Fundamentals-Modeling-Properties-Performance
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Celibi et al (in press)
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ATST Telescope and FE Model
Fundamentals-Modeling-Properties-Performance
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Summary and Conclusions (Cho, 2005) 1.High fidelity FE models
were created 2.Relative mirror motions from zenith to horizon
pointing: about 400 m in translation and 60 rad in rotation.
3.Natural frequency changes by 2 Hz as height changes by 10m.
4.Wind buffeting effects caused by dynamic portion (fluctuation) of
wind 5.Modal responses sensitive to stiffness of bearings and drive
disks 6.Soil characteristics were the dominant influences in modal
(dynamic) behavior of the telescopes. 7.Fundamental Frequency (for
a lowest soil stiffness): OSS=20.5hz; OSS+base=9.9hz;
SS+base+Coude+soil=6.3hz 8.A seismic analysis was made with a
sample PSD 9.ATST structure assembly is adequately designed: 1.
Capable of supporting the OSS 2. Dynamically stiff enough to hold
the optics stable 3. Not significantly vulnerable to wind loadings
Fundamentals-Modeling-Properties-Performance
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Foundation Movement X Z Y
Fundamentals-Modeling-Properties-Performance
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Design Questions (1/4) How Does It Fail? Static Settlement
Dynamic Motion Too Large (0.02 mm) Settlements Caused By Dynamic
Motion Liquefaction What Are Maximum Values of Failure?
(Acceleration, Velocity, Displacement)
Fundamentals-Modeling-Properties-Design-Performance
Design Questions (2/4) What Are Relations Between Loads And
Failure Quantities? Loads -Harmonic, Periodic, Random Load
Structure Foundation Soil Neighboring Structures Model:
Deterministic or Probabilistic
Fundamentals-Modeling-Properties-Performance
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Design Questions (3/4) How Do We Measure What Is Necessary?
Full Scale Tests Prototype Tests Small Scale Tests (Centrifuge)
Laboratory Tests (Specific Parameters) Computer Model
Fundamentals-Modeling-Properties-Performance
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Design Questions (4/4) What Factor of Safety Do We Use? Does
FOS Have Meaning What Happens After There Is Failure Loss of Life
Loss of Property Loss of Production Purpose of Project, Design
Life, Value Fundamentals-Modeling-Properties-Performance
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r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal
component Shear window Rayleigh wave Relative amplitude + + + + - -
+ + Wave TypePercentage of Total Energy Rayleigh67 Shear26
Compression7 Waves
Fundamentals-Modeling-Properties-Performance
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r -2 r -0.5 r -1 r Shear wave Vertical component Horizontal
component Shear window Rayleigh wave Relative amplitude + + + + - -
+ + Wave TypePercentage of Total Energy Rayleigh67 Shear26
Compression7 Waves
Fundamentals-Modeling-Properties-Performance
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Modeling Foundations Lumped Parameter (m,c,k) Block System
Parameters Constant, Layers, Special Impedance Functions Function
of Frequency (), Layers Boundary Elements (BEM) Infinite Boundary,
Interactions, Layers Finite Element/Hybrid (FEM, FEM-BEM) Complex
Geometry, Non-linear Soil
Fundamentals-Modeling-Properties-Performance
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Lumped Parameter m G k m c r
Fundamentals-Modeling-Properties-Performance