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

2. Vibrationdata Dr. Curtis Larsen 2 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. Vibrationdata NASA ENGINEERING & SAFETY CENTER (NESC) 3 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. Vibrationdata NESC Services 4 NESC Engineers Provide a Second Pair of Eyes Design and Analysis Reviews Test Support Flight Accelerometer Data Analysis Tutorial Papers Perform Research as Needed NESC Academy, Educational Outreach http://www.nasa.gov/offices/nesc/academy/

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

7. Vibrationdata 7 Measuring Frequency

8. Vibrationdata 8 Basic Definitions n 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. Vibrationdata 9 Basic Definitions (continued) n 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. Vibrationdata 10 Basic Definitions (continued) n 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. n Multi-degree-of-freedom System (MDOF) A multi-degree-of-freedom system is a system which has more than one natural frequency.

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

13. Vibrationdata 13 Golden Gate Bridge n 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 n 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. n Note that current Caltrans standards require bridges to withstand an equivalent static earthquake force (EQ) of 2.0 G.

14. Vibrationdata 14 Golden Gate Bridge Natural Frequencies

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

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

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

18. Vibrationdata 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. Vibrationdata 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. Vibrationdata Recommended Text Dave S. Steinberg 20

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

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

23. Vibrationdata 23 Two DOF System M 2 = 0.71 kg M 1 = 0.71 kg K 2 = 175 N/mm K 1 = 350 N/mm

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

25. Vibrationdata 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. Vibrationdata 26 Resonance n Resonance occurs when the applied force or base excitation frequency coincides with the system's natural frequency. n As an example, a bulkhead natural frequency might be excited by a motor pressure oscillation. n During resonant vibration, the response displacement may increase until the structure experiences buckling, yielding, fatigue, or some other failure mechanism. n 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. Vibrationdata 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 Test Bat 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. Vibrationdata 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