Vibrationdata

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

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NESC Services
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/
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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_at_vibrationdata.com
• You may also contact me via Email for off-line
  questions
• Please visit http//vibrationdata.wordpress.
  com/

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Unit 1A

• Natural Frequencies
• Calculation, Measurement, and Excitation

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Measuring Frequency
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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.

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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

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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.

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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.

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Golden Gate Bridge

• Steel Suspension Bridge
• Total Length 8980 ft

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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.

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Golden Gate Bridge Natural Frequencies

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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.
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SDOF System Spring-Mass System

• The natural frequency for a spring-mass system is

m mass k spring stiffness c damping
coefficient X displacement
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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
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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

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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

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Recommended Text

• Dave S. Steinberg

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SDOF System
M 0.71 kg
K 350 N/mm
fn 111.7 Hz
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SDOF Animation. File sdof_fna.avi(click on
image)
fn 111.7 Hz
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Two DOF System
M2 0.71 kg
K2 175 N/mm
M1 0.71 kg
K1 350 N/mm
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Two DOF System Animation Files tdofm1.avi
tdofm2.avi(click on images)
Mode 1 f1 60.4 Hz
Mode 2f2 146 Hz
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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.

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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.

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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 bats
  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

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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

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Base Excitation
Courtesy
of UCSB and R. Kruback
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1989 Loma Prieta Earthquake
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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.

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Pegasus Vehicle
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Pegasus Drop Video
(click on image)
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Pegasus
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Pegasus Drop Transient

• Fundamental Bending Mode

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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)
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More Flutter Videos
(Courtesy of Smithsonian Air Space. Used with
permission.)
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TacomaNarrows Bridge

• Torsional Mode at 0.2 Hz - Aerodynamic
  Self-excitation
• Wind Speed 42 miles per hour. Amplitude 28
  feet

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Tacoma Narrows Bridge Failure

• November 7, 1940

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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.

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

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SHOCK PULSE
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Response Spectra Concept
Soft
Hard
Natural Frequencies (Hz) 0.063 0.125
0.25 0.50 1.0 2.0
4.0
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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 Matlab
  script
• vibrationdata gt miscellaneous
  functions gt Structural Dynamics gt
• SDOF System Natural Frequency
• Script is posted at
• http//vibrationdata.wordpress.com/2013/05/29/vibr
  ationdata-matlab-signal-analysis-package/

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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 gt Statistics
• Determine the natural frequency by counting the
  peaks and dividing the sum by time.
• Estimate damping using script sinefdam.m
• http//vibrationdata.wordpress.com/2013/04/26/curv
  e-fitting-one-or-more-sine-functions/

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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 gt miscellaneous functions gt
Structural Dynamics gt
Beam Natural Frequency Base Excitation
Response
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First Three Modes of Flagpole
Mode 2
Mode 1
Mode 3
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Unit 1A Exercise 4 Tuning Fork

• Determine the natural frequency of the tuning
  fork.
• The file is tuning_fork.txt