116 Fundamentals of Vibration for Test Applications

Applications Random vibration and shock are important in most engineering applications where the product is ex­posed to transportation and to possible vibration and shock during service. An understanding of vibration and shock is crucial to improving the reliability of today’s products, wher­ever electronic components appear.

 For Whom Intended Many engineers need specialized edu­cation to properly measure, quantify, and analyze this generally unfamiliar environment and to reproduce it in environmental test laboratories. This course is for test laboratory managers, engineers and technicians. It also helps quality and reliability specialists and acquisition personnel in gov­ernment and military activities and their contractors. It is designed to serve the needs of person­nel in a wide range of industries where equipment problems may be encountered during the shipment and use of their product.

Electrohydraulic ShakerBrief Course Description This course covers a wide range of topics associated with vibration and shock applica­tions in order to enable the course participants to acquire a basic understanding of the complex field of vibration and shock. Each of the subject areas covered in this course have expanded coverage in their own three day courses for those individuals who need a more thorough understanding for their application.

Lectures and videotaped physical demonstrations show for exam­ple: how structures behave when mechanically excited, how to use pickups to sense input and response forces and motions, how to read out and evaluate the resulting electrical signals.

The course commences with an introduction to vibration and its ef­fects and then proceeds to cover the basic theory needed to under­stand the material covered during the course. Mathe­matics are kept to the minimum necessary for the concepts of vibration to be under­stood. The  theory of dynamics is covered, including the relation­ships between displacement, velocity and acceleration. Electronic filters are covered, and then random vibration theory. Test equipment is discussed next, including the var­ious types of vibration exciters, along with test fixtures and power amplifiers.

The course next presents some basic theory of measurement systems before addressing vibration measurement and data acquisition. Spectral analysis and transforms are discussed before covering sine and random vibration testing, mech­anical shock applications and environmental specification and standards.

Diploma Programs  This course is required for TTi’s Environmental Engineering Specialist (EES) and Dynamic Test Specialist (DTS) Diploma Programs and may be used as an optional course for any other TTi Diploma Program.

Related Courses Course 116-117 includes content from this course and Course 117, Fundamentals of Vibration for Design Applications. These courses (or any TTi course) may be presented onsite at your organization, for a group.

Prerequisites  There are no definite prerequisites. Super­vis­ors are in­vited to tele­phone or e-mail TTi on prospective atten­dees’ back­grounds and needs.

Text  Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks are available for an additional fee.

OnDemand Internet Complete Course 116 features over fourteen hours of video as well as more in-depth reading material. All chapters of course 116 are also available as OnDemand Internet Short Topics. See the course outline below for details.

Course  Hours, Certificate and CEUs  On-site cour­ses can vary from 14–35 hours over 2–5 days as re­ques­ted by our clients. Upon suc­cessful course completion, each partici­pant re­ceives a certificate of completion and one Con­tinu­ing Edu­ca­tion Unit (CEU) for every ten class hours.

Click for a printable course outline (pdf).

Course Outline

Chapter 1 - Introduction to Vibration

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OnDemand Short Topics$100.00
  • Design and Testing for Vibration and Shock
  • Rotational Unbalance Example—Automobile Engine
  • Natural Frequency
  • Forcing Frequency and Resonance
  • Prolonged Excitation of Natural Frequency
  • Tacoma Narrows Bridge: A Example of Resonance

Chapter 2 - Decibels (dB), Logarithmic vs. Linear Scaling, Frequency Spectra, Octaves

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OnDemand Short Topics$50.00
  • Decibels
    • Decibels for Power and Voltage Ratios
    • dB Ratio Conversions
  • Logarithmic vs. Linear Scaling
    • Logarithmic vs. Linear Scaling in PSD Plots
  • Introduction to Frequency, Octaves and Sound
    • Sound Perception
    • Sound, Vibration and Music
    • Diatonic Musical Scale
  • Octaves
    • Acoustic Analysis
    • 1/3 Octave Bandwidth Definitions
    • Center Frequency Examples

Chapter 3 - Dynamic Force and Motion

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OnDemand Short Topics$250.00
  • Laws of Motion
    • Weight vs. Mass
    • System of Units
    • Units of Force and Mass; Example
    • Mass, Weight, Common Units of Mass
    • Gravity
    • Weight, Specific Weight and Density
    • Relative Density or Specific Gravity
    • Work, Power, Energy
  • Some Fundamentals of Dynamics
    • A Simple Dynamic System
    • Degrees of Freedom
    • Examples of Various Degrees of Freedom
    • Single-Degree-of-Freedom (SDoF)
    • Undamped Vibrations
    • Sinusoidal Waveform
  • SDoF — Sinusoidal Relationships
    • Relationships Between Displacement, Velocity, and Acceleration
    • Effect of Frequency on Displacement, Velocity, and Acceleration
  • Natural Frequency
    • Decaying Sinusoidal Vibration
    • Forced Vibration for SDoF System
    • Transmissibility
    • Plotting Transmissibility vs. Frequency Ratio
  • Isolation and Damping
    • Determining Damping Ratio Experimentally
    • Effect of Damping
    • Transient Peak Ratio vs. Damping Ratio
    • Effect of Damping on Frequency of Max Response
    • Vibration Isolators
    • Continuous Systems
    • Viscoelastic Damping on Laminated Beam
    • Damped vs Undamped Response
  • Modal Testing & Analysis
  • Vibration Considerations for Design Engineers

Chapter 4 - Introduction to Signal Waveforms and Electronic Filters

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OnDemand Short Topics$50.00
  • Understanding RMS
    • Addition of Sine Waves to Provide Square Wave
  • Capacitors in DC Circuits
    • RC Time Constant
  • Filtering .. What is It?
    • Integrating Circuits       
    • High-Pass Filtering & Differentiating Circuits
    • Low-pass, High-pass, Bandpass and Notch Filters
    • 3 dB Bandwidth and 1/3 Octave Bandwidth
    • Undamped (high Q) vs. Damped (low Q) Filters
    • Filtering a Square Wave
  • Working with Digital Signals
  • Complex Periodic Signals
  • Complex (Pyroshock) Time History
  • Random Signals

Chapter 5 - Introduction to Random Vibration

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OnDemand Short Topics$150.00
  • Demonstrations — Sinusoidal Vibration, Complex Waveform, Random Vibration
    • “Single Sweep” Time History
    • Demonstration of the Effects of Random Vibration
  • Statistics and Random Vibration
    • Probability Distribution
    • Statistical Evaluations
    • Random Data Spectrum
    • Gaussian (Normal) Distribution Curve
    • Continuous Probability Distribution
  • Random Data
    • Random Vibration Spectrum
    • Time-History Properties
  • Spectra
    • Spectrum Calculation ... Comb Filter Analogy
    • The Spectral View
    • Auto Spectral Density or Power Spectral Density
    • Spectral Density
    • ESS Random Vibration Spectrum
    • PSD Graph, Linear vs. Logarithmic Scale
    • Example of Vibration Spectrum
  • Calculating the RMS From the PSD
  • Shaker Power Spectral Density Response
    • Equalization to Correct PSD
  • High-Frequency Noise
  • Deriving Transmissibility from Random Vibration

Chapter 6 - Introduction to Vibration Exciters (Shakers)

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OnDemand Short Topics$150.00
  • Mechanical Shakers
  • Electrohydraulic (EH) Shaker
    • Automotive Applications
  • Electrodynamic Shakers
    • Theory of Electromagnetic Operation
    • Electrodynamic Shaker— Armature
    • Force Rating and Available Acceleration
    • Displacement and Velocity Limits of Electrodynamic Shaker
  • Shaker Ratings Example
  • Shaker Technologies—Stroke vs. Frequency Range
  • Electrodynamic Shakers System Maintenance
  • Extending Table Diameter
    • Table (Head) Expander
    • Horizontal Accessory - Oil-Slip Tables
    • Vibration Testing on a Slip Plate
  • Combined Environmental Reliability Testing (CERT)
  • Electric Vibration Actuators
  • Installing a Vibration Exciter (Shaker)
    • Shaker Isolation
    • Measuring Ambient Vibration
    • Shaker foundation platform design process
    • Characteristics of Pier or Pad

Chapter 7 - Introduction to Test Fixtures

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OnDemand Short Topics$100.00
  • Purpose of a Fixture
  • The “Black Art” of Fixture Design
  • Basic Considerations for Fixtures
  • Fixture Fabrication Methods
    • Typical Machined Fixture
  • Evaluating Fixtures
    • Fixture Weight Relative to Test Item Weight
  • Orthogonal Motion in Sinusoidal System
    • Shaker Crosstalk—Orthogonal Motion

Chapter 8 - Introduction to Power Amplifiers

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OnDemand Short Topics$50.00
  • Harmonic Distortion
  • Non-Linearity Distortion
  • Power Amplifiers—Block Diagram
  • Shaker Armature Electrical Resonance
    • Effect of Mechanical Resonant Loads

Chapter 9 - Vibration Measurement

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OnDemand Short Topics$200.00
  • Characteristics of an Ideal Transducer
  • Velocity Sensing
  • Measuring Displacement
    • Optical Wedge—Estimating Displacement due to Vibration
    • Displacement Sensor
  • Strain Measurement
    • Problems with Strain Gages
    • Wheatstone Bridge
    • Four Sensing Resistors in a Wheatstone Bridge
    • Strain Gage Compensation
  • Silicon Semiconductor Transducers
    • Compound Two-stage Transducer
  • Variable Capacitance Sensors
  • Measuring Vibration Displacement or Velocity
    • Velocity Sensors (Pickups)
  • Accelerometers
    • Wire Strain Gage Accelerometer
    • Piezoresistive (PR) Accelerometers
    • Piezoelectric Transduction
    • Glue Mounting Method
    • Mounting Variations
    • Cable Noise
  • Signal Conditioning Approaches
  • Voltage Measurement: Charge Mode Sensors
    • “Charge” Amplifiers
    • T-Insert Calibration
    • Internal Electronic Systems
    • Calibration
  • Selecting a Measurement System

Chapter 10 - Basics of Spectral Analysis

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OnDemand Short Topics$50.00
  • Why Do We Use the Frequency Domain?
    • Time and Frequency Domain
    • Spectral Analysis ... What? Why?
  • Windowing
    • Forcing Measured Data

Chapter 11 - Vibration Testing

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OnDemand Short Topics$100.00
  • Types of Vibration Tests
    • Development Testing
    • Qualification Testing
    • Acceptance Testing
    • Screening Tests (or Procedures)
    • Reliability Tests
    • Durability and Functional Tests
  • Accelerated Testing
    • Accelerated Vibration Testing
    • “S-N” Curve from Fatigue Testing
    • Idealized “S-N” Curve for Typical Steel Alloy
    • Designing Accelerated Durability Vibration Tests
  • What is the Environment?
    • The Applied Environment … Philosophy
  • Vibration Testing — Control
    • Closed Loop Control
    • Control System Function
    • Function Generators
    • Location of Control Accelerometer
  • Unwanted Table Movement
    • Resonant Distortion of Electrodynamic Shaker Table
    • Axial Resonance of Shaker Slip Tables
    • Shaker Slip Table — High cg Load
  • Shaker Control—Input or Response
    • Notching the Spectrum
    • Strobe Light used with Sinusoidal Vibration Test
  • Multiple Degrees of Freedom Testing
    • What a Multi-Axis System Provides
    • What Is NOT A Multi-Axis System?
    • Simultaneous 3-Axis Testing
    • “Real” Multiple Degree-of-Freedom Systems
    • “Tri-Axial Quasi-Random” Systems
    • Two-Shaker, Two DOF Systems
    • Three-Degree-of-Freedom Systems
      • Army Research Lab (ARL) 3-DOF Machine
      • Team Mantis
      • Team Cube
      • Hydraulic Test System—6 Degrees of Control, the CUBE™

Chapter 12 - Sine Vibration Testing

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OnDemand Short Topics$50.00
  • Sine Vibration System
    • Closed Loop Control
  • Sine Sweep
    • Slow Sweep
    • Fast Sweep
    • Effect of Sweep Speed
    • Minimum Sweep Rates for Full Resonance Response
  • Crossover Frequency
  • Control of Vibration Systems

Chapter 13 - Random Vibration Testing

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OnDemand Short Topics$25.00
  • Calculating the RMS From the PSD
  • Gaussian Random Signal
    • Standard Deviation
    • Statistical Degrees of Freedom
    • Accuracy/Confidence vs. DOF
  • Time and Frequency Domain Terminology
  • Transfer Functions
    • Actuator System Transfer Function
    • The Transfer Function - Gain Relationship
    • Determining the Transfer Function
    • The “Tickle Test”
  • Specialized Tests
    • Sine on Random (SoR) Tests
    • Random on Random (RoR) Tests
  • Overtest Protection
    • Vibration Protection
  • Random Vibration Structural Analysis—Example
    • Random Vibration Test Spectrum
  • “Walkthrough” of an Imaginary Test

Chapter 14 - Introduction to Mechanical Shock

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OnDemand Short Topics$100.00
  • Shock Theory
    • What is Shock?
    • Causes of Shock
    • Effects and Remedies of Shock
  • Transient or Shock Tests
    • Effective Transient Duration
    • Half-Sine Shock Pulse
    • Trapezoidal Shock Pulse
    • Sawtooth Shock Pulse
    • Pulse Type Transient Testing
    • Transient Shock Testing on Electrodynamic Shakers
  • Shock Test Machines
    • Pendulum Type Shock Machine
    • Pneumatic Drop Test Shock Machine
    • Free-Fall Shock Machine
    • Drop Testing Machine
    • Free Fall Drop Test Machine
  • Drop Test Procedures
    • Free Fall Edge Drop Test
    • Table-Top Drop Shock Test
    • Sequence of Tests
  • MIPS Table
  • Shock Response Spectrum
    • Transient Test...Definition
    • Transient Test Types
    • Transient Tests: Analysis Options
    • PSD of 0.01 Second Sine Pulse
    • Shock Response Spectrum (SRS)
    • SRS Mechanical Analog
    • Element Dynamic Response
    • SRS Analysis Element
    • Assembly of Filter Elements
    • SRS Analysis Procedure
    • Shock Analysis Example
    • SRS vs. Fourier Analysis

Chapter 15 - Standards, Specifications and Procedures

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OnDemand Short Topics$50.00
  • Standards vs. Specifications
  • Why are Standards Needed?
  • Why are Specifications Needed?
  • Prominent Standards
  • Procedures

Appendix A - Glossary and Definitions

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OnDemand Short Topics$25.00

Appendix B - Index of Equations

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OnDemand Short Topics$25.00

Appendix C-2 - Understanding Decibels and Octaves (Chapter 2 reference)

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OnDemand Short Topics$25.00
  • Decibels—Power Ratio
  • Decibel—Voltage Ratio
  • Application of dB notation

Appendix C-3 - Dynamic Force and Motion (Chapter 3 reference)

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OnDemand Short Topics$25.00
  • Weight, Specific Weight and Density
    • Relative Density or Specific Gravity
  • Common Units of Force
  • SDoF-Sinusoidal Relationships
    • Calculating Peak X, V and A
  • Undamped Vibrations — Single Degree of Freedom Systems
    • Calculating Natural Frequency
    • Calculating Stiffness
    • Example—Damped Resonant System

Appendix C-5 - Calculating RMS from PSD (Chapter 5 reference)

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OnDemand Short Topics$25.00

Appendix C-7 - Fixture Design (Chapter 7 reference)

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OnDemand Short Topics$25.00

Appendix C-10 - Fourier Transforms, Aliasing (Chapter 10 reference)

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OnDemand Short Topics$25.00
  • The Fourier Transform
    • Discrete Fourier Analysis
    • Fast Fourier Transform (FFT)
    • Phase of Frequency Domain Components
  • Spectrum Analyzers
    • Quick Look vs. Detailed Analysis
    • Power Spectral Density .. Physical Meaning
    • Transfer Functions
  • Data Acquisition
    • Sampling Theory.. Digitizing "Rules"
    • How Often to Sample?
    • Shannon's Theorem
    • The Nyquist Frequency
    • Aliasing Example
    • The Spectral View
    • Aliasing.. Viewed as Folding
    • Alias Protection with Filters

Appendix C-12 - Sine Vibration Testing — Crossover Frequency Example (Chapter 12 reference)

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OnDemand Short Topics$25.00

Appendix C-13 - Random Vibration Testing (Chapter 13 reference)

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OnDemand Short Topics$25.00
  • Determining the Transfer Function
    • The "Tickle Test"
  • Random Vibration Structural Analysis—Example


Final Review

Award of certificates for successful completion

Click for a printable course outline (pdf).

Revised 2/18/2019