Vibrationdata

1. Dynamic Concepts, Inc. Huntsville, Alabama Vibrationdata THE NASA ENGINEERING & SAFETY CENTER (NESC) SHOCK & VIBRATION TRAINING PROGRAM By Tom Irvine

2. Dr. Curtis Larsen Dr. Curtis E. Larsen is the NASA Technical Fellow for Loads and Dynamics  He is the head of the the NASA Engineering & Safety Center (NESC) Loads & Dynamics Technical Disciplines Team (TDT) Thank you to Dr. Larsen for supporting this webinars!

3. NASA ENGINEERING & SAFETY CENTER (NESC) • NESC is an independently funded program with a dedicated team of technical experts • NESC was Formed in 2003 in response to the Space Shuttle Columbia Accident Investigation • NESC’s fundamental purpose is provide to objective engineering and safety assessments of critical, high-risk NASA projects to ensure safety and mission success • The National Aeronautics and Space Act of 1958 • NESC is expanding its services to benefit United States: • Military • Government Agencies Commercial Space

4. NESC Services

5. Preliminary Instructions • You may ask questions during the presentation • Otherwise set your phones to mute • These presentations including your questions and comments are being recorded for redistribution • If you are not already on my distribution list, please send and Email to: tom@vibrationdata.com • You may also contact me via Email for off-line questions • Please visit: http://vibrationdata.wordpress.com/

6. Unit 1A Natural Frequencies: Calculation, Measurement, and Excitation

7. Measuring Frequency

8. Basic Definitions • Natural Frequency The natural frequency is the frequency at which a mass will vibrate if it is given an initial displacement and then released so that it may vibrate freely. This free vibration is also called "simple harmonic motion, " assuming no damping. An object has both mass and stiffness. The spring stiffness will try to snap the object back to its rest position if the object is given an initial displacement. The inertial effect of the mass, however, will not allow the object to stop immediately at the rest position. Thus, the object “overshoots” its mark. The mass and stiffness forces balance out to provide the natural frequency.

9. Basic Definitions (continued) • Damping Consider a mass that is vibrating freely. The mass will eventually return to its rest position. This decay is referred to as "damping.“ Damping may be due to viscous sources dry friction aerodynamic drag acoustic radiation air pumping at joints boundary damping

10. Basic Definitions (continued) • Single-degree-of-freedom System (SDOF) A single-degree-of-freedom system is a system which only has one natural frequency. Engineers often idealize complex systems as single-degree-of-freedom systems. • Multi-degree-of-freedom System (MDOF) A multi-degree-of-freedom system is a system which has more than one natural frequency.

11. Earth EARTH'S NATURAL FREQUENCY The Earth experiences seismic vibration. The fundamental natural frequency of the Earth is 309.286 micro Hertz. This is equivalent to a period of 3233.25 seconds, or approximately 54 minutes. Reference: T. Lay and T. Wallace, Modern Global Seismology, Academic Press, New York, 1995.

12. Golden Gate Bridge Steel Suspension Bridge Total Length = 8980 ft

13. Golden Gate Bridge • In addition to traffic loading, the Golden Gate Bridge must withstand the following environments: 1. Earthquakes, primarily originating on the San Andreas and Hayward faults 2. Winds of up to 70 miles per hour 3. Strong ocean currents • The Golden Gate Bridge has performed well in all earthquakes to date, including the 1989 Loma Prieta Earthquake. Several phases of seismic retrofitting have been performed since the initial construction. • Note that current Caltrans standards require bridges to withstand an equivalent static earthquake force (EQ) of 2.0 G.

14. Golden Gate Bridge Natural Frequencies

15. SDOF System Examples - Pendulum The natural frequency for a pendulum is The natural frequency has dimensions of radians/time. The typical unit is radians/second.

16. X m c k SDOF System Spring-Mass System The natural frequency for a spring-mass system is m = mass k = spring stiffness c = damping coefficient X = displacement

17. L SDOF System Examples Cantilever Beam with End Mass  is the beam mass per length m is the end mass E is the modulus of elasticity I is the area moment of inertia L is the length

18. Circuit Board Natural Frequencies Circuit Boards are often Modeled as Single-degree-of-freedom Systems Average = 328 Hz Std Dev = 203 Hz Range = 65 Hz to 600 Hz

19. More Formulas The variable is the natural frequency in cycles/time. The typical unit is cycles/second, which is called Hertz. The unit Hertz is abbreviated as Hz. Note that the period T is the period is the time required for one complete cycle of oscillation

20. Recommended Text Dave S. Steinberg

21. SDOF System M = 0.71 kg K= 350 N/mm fn = 111.7 Hz

22. SDOF Animation. File: sdof_fna.avi(click on image) fn = 111.7 Hz

23. Two DOF System M2 = 0.71 kg K2 = 175 N/mm M1 = 0.71 kg K1 = 350 N/mm

24. Two DOF System Animation Files: tdofm1.avi & tdofm2.avi(click on images) Mode 1 f1 = 60.4 Hz Mode 2f2 = 146 Hz

25. Astronaut Spring-loaded chair device for measuring astronaut's mass The chair oscillates at a natural frequency which is dependent on the astronaut's mass.

26. Resonance • Resonance occurs when the applied force or base excitation frequency coincides with the system's natural frequency. • As an example, a bulkhead natural frequency might be excited by a motor pressure oscillation. • During resonant vibration, the response displacement may increase until the structure experiences buckling, yielding, fatigue, or some other failure mechanism. • The Tacoma Narrows Bridge failure is often cited as an example of resonant vibration. In reality, it was a case of self-excited vibration.

27. Excitation Methods There are four methods by which a structure's natural frequency may be excited: 1. Applied Pressure or Force Hammer strikes mass Modal TestBat hits baseball, exciting bat’s natural frequencies Airflow or wind excites structure such as an aircraft wing Ocean waves excite offshore structure Rotating mass imbalance in motor Pressure oscillation in rocket motor 2. Base Excitation Vehicle traveling down washboard road Earthquake excites building A machine tool or optical microscope is excited by floor excitation Shaker Table Test

28. Excitation Methods (Continued) 3. Self-excited Instability Airfoil or Bridge Flutter 4. Initial Displacement or Velocity Plucking guitar string Pegasus drop transient Accidental drop of object onto floor

29. Base Excitation Courtesy of UCSB and R. Kruback

30. 1989 Loma Prieta Earthquake

31. LOMA PRIETA EARTHQUAKE (continued) The earthquake caused the Cypress Viaduct to collapse, resulting in 42 deaths. The Viaduct was a raised freeway which was part of the Nimitz freeway in Oakland, which is Interstate 880. The Viaduct had two traffic decks. Resonant vibration caused 50 of the 124 spans of the Viaduct to collapse. The reinforced concrete frames of those spans were mounted on weak soil. As a result, the natural frequency of those spans coincided with the forcing frequency of the earthquake ground motion. The Viaduct structure thus amplified the ground motion. The spans suffered increasing vertical motion. Cracks formed in the support frames. Finally, the upper roadway collapsed, slamming down on the lower road. The remaining spans which were mounted on firm soil withstood the earthquake.

32. Pegasus Vehicle

33. Pegasus Drop Video (click on image)

34. Pegasus

35. Pegasus Drop Transient Fundamental Bending Mode

36. Boeing 747 Wind Tunnel Test Boeing 747 – Flutter_747.avi Flutter – combined bending and torsional motion. (Courtesy of Smithsonian Air & Space. Used with permission.) (click on image)

37. More Flutter Videos (Courtesy of Smithsonian Air & Space. Used with permission.)

38. TacomaNarrows Bridge Torsional Mode at 0.2 Hz - Aerodynamic Self-excitation Wind Speed = 42 miles per hour. Amplitude = 28 feet (336 inch)

39. Tacoma Narrows Bridge Failure November 7, 1940

40. Helicopter Ground Resonance A new design undergoing testing may encounter severe vibration while it is on the ground, preparing for takeoff. As the rotor accelerates to its full operating speed, a structural natural frequency of the helicopter may be excited. This condition is called resonant excitation.

41. TH-55 Osage, Military Version of the Hughes 269A

42. Guidance Systems • Consider a rocket vehicle with a closed-loop guidance system. • The autopilot has an internal navigation system which uses accelerometers and gyroscopes to determine the vehicle's attitude and direction. • The navigation system then sends commands to actuators which rotate the exhaust nozzle to steer the vehicle during its powered flight. • Feedback sensors measure the position of the nozzle. The data is sent back to the navigation computer. • Unfortunately, the feedback sensors, accelerometers, and gyroscopes could be affected by the vehicle's vibration. Specifically, instability could result if the vibration frequency coincides with the control frequency.

43. SHOCK PULSE

44. Response Spectra Concept Soft Hard Natural Frequencies (Hz): 0.063 0.125 0.25 0.50 1.0 2.0 4.0

45. Unit 1A Exercise 1 • A particular circuit board can be modeled as a single-degree-of-freedom system. • Its weight is 0.1 pounds. • Its stiffness is 400 pounds per inch. • Calculate the natural frequency using Python script: vibrationdata > miscellaneous functions > Structural Dynamics > SDOF System Natural Frequency Script is posted at: http://vibrationdata.wordpress.com/2014/04/02/python-signal-analysis-package-gui/

46. Unit 1A Exercise 2 • A rocket vehicle is carried underneath an aircraft. It experiences an initial displacement because gravity causes it to bow downward while it is attached to the aircraft. It is suddenly released and allowed to vibrate freely as it falls. It continues falling for about 5 seconds prior to its motor ignition, as a safety precaution. • An acceleration time history of the drop is given in file: drop.txt. • Plot using script: vibrationdata > Statistics • Determine the natural frequency by counting the peaks and dividing the sum by time. • Estimate damping using script: vibrationdata > Sine & Damping Curve-fit

47. Unit 1A Exercise 3 A flagpole is made from steel pipe. The height is 180 inches. The pipe O.D. is 3 inches. The wall thickness is 0.25 inches. The boundary conditions are fixed-free. Determine the fundamental lateral frequency. Use script: vibrationdata > Miscellaneous functions > Structural Dynamics > Beam Bending

48. First Three Modes of Flagpole Mode 2 Mode 1 Mode 3

49. Unit 1A Exercise 4 Tuning Fork Determine the natural frequency of the tuning fork. The file is: tuning_fork.txt