116/117 Fundamentals of Vibration for Test and Design 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. The need to understand the effects of vibration and shock on product reliability is paramount today, where electronic/computer components are part of almost every product.

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, design engineers, project managers 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.

PhotoelasticityThe instructor maintains good balance between theory and practical applications. Instrumentation specialists who will measure transportation, service, and laboratory vibration need this course. Metrologists learn about vibration the use of sensors. Project personnel, structures and packaging engineers learn about developmental testing. Product assurance and acquisition specialists learn to evaluate test facilities and methods, and to interpret specifications.

Brief 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 basic theory needed to understand the rest of the material covered. While mathematics are kept to a minimum, it is necessary to cover a sufficient amount so that the concepts of vibration can be understood. The course presents some basic theory of data acquisition, electronic filters and measurement systems.

Various types of vibration exciters or shakers are discussed next. Random vibration theory, including power spectral density theory, is discussed and video demonstrations show the effects of sinusoidal and random vibration. Some basic theory of spectral analysis, filters and vibration measurement systems provides a background for understanding data acquisition and analysis topics. The course touches on test fixture design for vibration testing.

Different types of sinusoidal and random vibration testing are discussed next. Material fatigue and the correct use of S-N curves for designing product life testing and developing accelerated product development testing procedures are covered. An introduction to modal analysis and testing theory and application is addressed and its use for product design.

Mechanical shock applications, including design to withstand shock, are discussed in some detail. Environmental test standards and specifications are surveyed, along with methods for tailoring of requirements for the test department. Finally, the course addresses reliability topics.

Related Courses  Course 116, Vibration for Test Applications and Course 117, Fundamentals of Vibration for Design Applications, cover some of the same topics as course 116/117, but place differing degrees of emphasis on testing vis-a-vis design. These courses (or any TTi course) may be presented on-site at your facility, for a group.

Diploma Programs  This course is required for TTi’s Mechanical Design Specialist (MDS) Diploma Program. It may be used to satisfy the Course 116 requirement for TTi’s Dynamic Test Specialist (DTS) or Environmental Test Specialist (EES) Diploma Program. It may be used as an optional course for any other Specialist Diploma program.

Prerequisites  There are no formal prerequisites for this course. Supervisors are invited to contact 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.

Course Hours, Certificate and CEUs Class hours/days for 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.

OnDemand Internet Course 116/117 features over nineteen hours of video as well as more in-depth reading material.  All chapters of course 116/117 are also available as OnDemand Internet Short Topics. See the course outline below for details.

Click for a printable course outline (pdf).


Course Outline

chapter 1 - Introduction to Vibration

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  • Design and Testing for Vibration and Shock
  • Rotational Unbalance Examples
    • Automobile Engine
    • Water Turbine Rotor Unbalance
  • 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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  • 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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  • 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
    • Effect of Damping
    • Vibration Isolators
    • Isolation vs. Damping
    • Damping in Laminates, Elastomers, Materials
    • Continuous Systems
    • Viscoelastic Damping on Laminated Beam
    • Damped vs Undamped Response
  • Modal Testing & Analysis
  • Vibration Considerations for Design Engineers
  • Vibration Mount Design Example

chapter 4 - Introduction to Signal Waveforms and Electronic Filters

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  • 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
    • Effects of Filtering
  • Working with Digital Signals
  • Complex Periodic Signals
  • Complex (Pyroshock) Time History
  • Random Signals

Chapter 5 - Introduction to Random Vibration

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  • 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
    • White Noise, Grey Noise, Blue Noise, Violet Noise, Pink Noise, Brown Noise

Chapter 6 - Introduction to Vibration Exciters (Shakers)

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  • Mechanical Shakers
  • Electrohydraulic (EH) Shaker
    • Automotive Applications
  • Electrodynamic Shakers
    • Electrodynamic Shaker— Armature
    • Force Rating and Available Acceleration
    • Displacement and Velocity Limits of Electrodynamic Shaker
  • Shaker Ratings Example
  • 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)
  • Piezoelectric Shakers
  • Shaker Technologies—Stroke vs. Frequency Range
  • 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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  • 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 - Vibration Measurement

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  • 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
    • Increased Sensitivity for Force Sensing 
    • 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
  • Sensor Response 
    • Contamination
    • Mounting Adaptors, Studs, Tape
    • Cable Management
  • Calibration
  • Selecting a Measurement System
  • MEMS Devices
    • Choosing an appropriate technology

Chapter 9 - Basics of Spectral Analysis

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  • Why Use the Frequency Domain?
  • Time and Frequency Domain
  • Spectral Analysis ... What?
  • Fourier Transforms
    • Discrete Fourier Analysis
    • Fast Fourier Transform (FFT)
    • FT Basic Relationships
  • Phase of Frequency Domain Components
  • Spectrum Analyzers
    • Quick Look vs. Detailed Analysis
  • Power Spectral Density
    • PSD, Physical Meaning
  • Transfer Functions
  • Data Acquisition
  • Sampling Theory—Digitizing “Rules”
    • How Often to Sample?
    • Conventional Wisdom
    • Shannon’s Theorem
    • The Nyquist Frequency
  • Aliasing
    • Demo: Digitizing with Different Points/Cycle
    • Aliasing Example: Correctly Sampled Set , Undersampled Set, Comparison of Data Sets
    • The Spectral View
    • Aliasing Viewed as Folding
    • The Insidious Part
    • Alias Protection with Filters
    • Aliasing/Critical Points
  • FFT Distortion
    • Windowing
    • Forcing Measured Data

Chapter 10 - Vibration Testing

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  • 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
    • Exciter Programming
    • 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 11 - Sine Vibration Testing

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  • Sine Vibration System
  • Closed Loop Control
    • Slow Sweep
    • Fast Sweep
    • Effect of Sweep Speed
    • Minimum Sweep Rates for Full Resonance Response
  • Crossover Frequency
    • Reactance Log-Log Graph Paper
    • Vibration Nomographs
  • Control of Vibration Systems

Chapter 12 - Random Vibration Testing

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  • 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
  • Spectrum Splitting 
  • Overtest Protection
    • Vibration Protection
  • Random Vibration Structural Analysis—Example
    • Random Vibration Test Spectrum
  • “Walkthrough” of an Imaginary Test

Chapter 13 - Fatigue

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  • Fatigue-Crack-Growth Rate
  • How Materials Behave: The S-N Curve
  • Factors Influencing Fatigue Behavior
  • Stress Concentration
  • Photoelasticity
  • Fracture Mechanics
    • Fracture Toughness
    • Fracture Toughness of Some Common Materials
  • Crack Propagation
    • Crack Growth Rate
  • Fracture Surfaces
    • Fatigue Crack Growth Prevention
  • Forensics
  • Failure Models
  • Failure Mechanism
  • Time-Dependent Failures
  • First Passage Model (Time to Failure)
  • The Goodman Diagram
  • The Constant Life Diagram
  • Exceeding a Critical Stress During Random Vibration
  • Inverse Power Law Model - Time to Failure
    • Inverse Power Law Model, Example
  • Fatigue Damage Model Based Upon S-N Curve - Number of Cycles to Failure
    • Idealized S-N Curve for Structural Materials
    • Actual Fatigue Data
    • Fatigue Testing with Electromagnetic Shaker
  • Fatigue Damage Model Based on Crack Growth Rate
  • Crack Growth Rate vs. Stress Intensity Factor
  • Stress Intensity Factors
  • Miner's Hypothesis for Fatigue Damage Accumulation
    • Miner's "Rule" Cautions
  • Determination of Effective Excitation
  • Fatigue, Miner’s Rule Example
  • Typical Endurance Limits
  • "S-N" Curve from Fatigue Testing
  • Fatigue Case Study
  • Example: Rating a Printed Circuit Board

Chapter 14 - Modal Testing

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  • Introduction to Modal Testing
  • Applications of Modal Testing
    • Modes of Stretched String
    • Modes of a Rail Car
  • Theoretical Approach
  • Basic Components of Measurement System
  • Exciting a Structure Impulsively (Hammer)
    • Modal Testing Hammer Calibration
  • Structural Dynamic Relationships
  • Interpretation of Modal Test Results
  • Mode Shapes of Square Plate
  • Mounting of Sensors--for Modal Testing
  • Modal Probe (Roving Accelerometer) 
  • Using Mode Shapes in Design
  • Digital Image Correlation 
  • Building Vibrations 

Chapter 15 - Accelerated Testing

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  • Accelerated Tests Are Nothing New
  • Step Stress Tests
  • HALT: Highly Accelerated Life Test
  • HASS / ESS
  • Monitored Ambient Random Vibration Profile
  • Margins
  • Reducing Test Time
  • Assumptions: The Horsepower Behind Accelerated Testing
  • What Does an Accelerated Test Accelerate?
  • Can Accelerated Testing Do What is Expected?
  • Which Environmental Forcing Functions Are Best?
  • What Does Vibration Testing Do?
  • Hidden Vibration Test Assumptions
  • Linear vs. Nonlinear Product Response
  • What to Expect From an Accelerated Test Prediction
  • Coffin-Manson Inverse Power Law
    • Coffin-Manson Model Cautions
  • Critical Aspects of Accelerated Test Models
  • The Basic Principles of Test Time Compression
  • Unrealistic Failure Modes and Mechanisms
  • Synergistic Failure Exaggeration
  • Number of Service Use Cycles and Test Cycles
  • How to Avoid Accelerated Testing Traps and Pitfalls

Chapter 16 - Introduction to Mechanical Shock

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  • Shock Theory
    • What is Shock?
    • Causes of Shock
    • Effects and Remedies of Shock
  • Transient or Shock Tests
    • Impact: The Impact Factor
      • Expressing I.F. in Terms of Velocity 
      • Example: Bending Impact 
    • 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 17 - Design to Withstand Shock

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  • Shock Resistant Design
  • Shock Isolation
    • Shock Isolation vs. Vibration Isolation~
    • Isolators Which Approach the Ideal
    • Shock Isolation Example
  • Protective Packaging
    • Potentially Harmful Environments
    • Drop Height vs. Probability
    • Product Fragility
    • Damage Boundary Theory
    • Step Velocity and Step Acceleration
    • The Step Acceleration Test
    • Damage Boundary Plot

Chapter 18 - Standards, Specifications and Procedures

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  • Standards vs. Specifications
  • Why are Standards Needed?
  • Why are Specifications Needed?
  • Prominent Standards
  • Procedures

Appendix A - Glossary and Definitions

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Appendix B - Index of Equations

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

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  • Decibels—Power Ratio
  • Decibel—Voltage Ratio
  • Application of dB notation

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

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  • 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
    • Determining Damping Ratio Experimentally
      • Transient Peak Ratio vs. Damping Ratio
    • Effect of Damping on Frequency of Max Response
    • Example—Damped Resonant System

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

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Appendix C-7 - Test Fixture Evaluation Example (Chapter 7 reference)

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  • Swept Sine Resonant Search—Fixture Evaluation Example

Appendix C-11 - Sine Vibration Testing — Crossover Frequency Example (Chapter 11 reference)

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Appendix C-12 - Random Vibration Testing (Chapter 12 reference)

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  • Determining the Transfer Function
    • The Tickle Test 
  • Random Vibration Structural Analysis—Example

Summary, Final Review

Award of certificates for successful completion

Click for a printable course outline (pdf).

Revised 8/7/2018