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Wave Travel and Attenuation and Machine Foundations

Wave Travel and Attenuation and Machine Foundations. Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering University of South Carolina. Waves in Elastic Media Waves in the Earth Surface Excitations Machine Foundations. Topics for Today. Waves . Compression, P Primary (1-D).

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Wave Travel and Attenuation and Machine Foundations

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  1. Wave Travel and Attenuation and Machine Foundations Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering University of South Carolina

  2. Waves in Elastic Media Waves in the Earth Surface Excitations Machine Foundations Topics for Today

  3. Waves Compression, P Primary (1-D) Shear,SSecondary (1-D) Rayleigh, R Surface (2-D) http://paws.kettering.edu/~drussell/demos.html

  4. Discrete Properties Resonant Column - MOC - Wavelets

  5. Surface Block Mass Computational Reaches Nodes Δz1 Soil 1: G1,ρ1,μ1 . . . . . . . Δzi Soil j: Gj,ρj,μj τi,Vi Vertical Propagation . . . . . . . A P Soil m: Gm,ρm,μm B Horizontal Polarization Δzn-1 Rock Motion t=0......1.......2......3 Resonant Column - MOC - Wavelets

  6. D z1 D D D z3 z4 z2 D t C+ characteristic: C1 A1 P1 C+ C- A2 C2 P2 B2 C+ = shearing stress; V = particle velocity. S= phase (shear wave) velocity; = mass density; t = time; C- A3 B3 C3 P3 C+ C- A4 C- characteristic: C4 B4 P4 C+ C- B5 P5 C5 Resonant Column - MOC - Wavelets

  7. A3 A2 A Rtime + Rspace C C3 C2 C P D z Sspace - C Stime D t B3 B2 B Nonlinear Interpolation Resonant Column - MOC - Wavelets

  8. 30 Δz 31 Resonant Column - MOC - Wavelets

  9. Resonant Column - MOC - Wavelets

  10. Resonant Column - MOC - Wavelets

  11. Resonant Column - MOC - Wavelets

  12. Cumulative Hysteretic Energy Reach Number Time (sec) Strain 400 Hyst 400 Resonant Column - MOC - Wavelets

  13. Wavelets A1 A2 A3 A4

  14. Resonant Column - MOC - Wavelets

  15. Profile View

  16. MEMS Accelerometer

  17. Data Acquisition

  18. Wavelets Resonant Column - MOC - Wavelets

  19. Wavelets Resonant Column - MOC - Wavelets

  20. Wavelet Scale Localized Time Index Fourier Transform Wavelet via Fourier Transform 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. Resonant Column - MOC - Wavelets

  21. Resonant Column - MOC - Wavelets

  22. Wavelets Resonant Column - MOC - Wavelets

  23. r -2 r -2 r -0.5 + Rayleigh wave + Vertical component Horizontal component Relative amplitude Shear wave + + - - r -1 + Compression wave + r r -1 Shear window Waves Fundamentals-Modeling-Properties-Performance

  24. Free-Field Analytical Solutions ur uz Fundamentals-Modeling-Properties-Performance

  25. Free-Field Analytical Solutions ur uz Fundamentals-Modeling-Properties-Performance

  26. Fundamentals-Modeling-Properties-Performance

  27. Fundamentals-Modeling-Properties-Performance

  28. Fundamentals-Modeling-Properties-Performance

  29. Fundamentals-Modeling-Properties-Performance

  30. Fundamentals-Modeling-Properties-Performance

  31. Trench Isolation Karlstrom and Bostrom 2007 Fundamentals-Modeling-Properties-Performance

  32. Chehab and Nagger 2003 Fundamentals-Modeling-Properties-Performance

  33. Celibi et al (in press)

  34. ATST Telescope and FE Model Fundamentals-Modeling-Properties-Performance

  35. Summary and Conclusions (Cho, 2005) • High fidelity FE models were created • Relative mirror motions from zenith to horizon pointing: about 400 mm in translation and 60 mrad in rotation. • Natural frequency changes by 2 Hz as height changes by 10m. • Wind buffeting effects caused by dynamic portion (fluctuation) of wind • Modal responses sensitive to stiffness of bearings and drive disks • Soil characteristics were the dominant influences in modal (dynamic) behavior of the telescopes. • Fundamental Frequency (for a lowest soil stiffness): OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz • A seismic analysis was made with a sample PSD • ATST structure assembly is adequately designed: • Capable of supporting the OSS • Dynamically stiff enough to hold the optics stable • Not significantly vulnerable to wind loadings Fundamentals-Modeling-Properties-Performance

  36. Foundation Movement Z Y θ φ X ψ Fundamentals-Modeling-Properties-Performance

  37. 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) Design Questions (1/4) Fundamentals-Modeling-Properties-Design-Performance

  38. Velocity Requirements 0,40 Massarch (2004) "Mitigation of Traffic-Induced Ground Vibrations" Fundamentals-Modeling-Properties-Performance

  39. 300 800 Fundamentals-Modeling-Properties-Performance

  40. What Are Relations Between Loads And Failure Quantities? Loads -Harmonic, Periodic, Random Load→ Structure → Foundation → Soil → Neighboring Structures Model: Deterministic or Probabilistic Design Questions (2/4) Fundamentals-Modeling-Properties-Performance

  41. 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

  42. 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

  43. r -2 r -2 r -0.5 + Rayleigh wave + Vertical component Horizontal component Relative amplitude Shear wave + + - - r -1 + Compression wave + r r -1 Shear window Waves Fundamentals-Modeling-Properties-Performance

  44. r -2 r -2 r -0.5 + Rayleigh wave + Vertical component Horizontal component Relative amplitude Shear wave + + - - r -1 + Compression wave + r r -1 Shear window Waves Fundamentals-Modeling-Properties-Performance

  45. Modeling Foundations • Lumped Parameter (m,c,k) Block System • Parameters Constant, Layers, Special • Impedance Functions • Function of Frequency (ω), Layers • Boundary Elements (BEM) • Infinite Boundary, Interactions, Layers • Finite Element/Hybrid (FEM, FEM-BEM) • Complex Geometry, Non-linear Soil Fundamentals-Modeling-Properties-Performance

  46. Lumped Parameter r m m k c ρ ν G Fundamentals-Modeling-Properties-Performance

  47. m k c z Single Degree of Freedom

  48. Single Degree of Freedom c=0…Undamped c=2mω…Critically Damped c<2mω…Underdamped

  49. z(0) t Single Degree of Freedom

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