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.
The 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 SN 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 visavis design. These courses (or any TTi course) may be presented onsite 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 online electronic course workbook. Renewals and printed textbooks are available for an additional fee.
Course Hours, Certificate and CEUs Class hours/days for onsite courses can vary from 1435 hours over 25 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 indepth 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
 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
 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
 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
 SingleDegreeofFreedom (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
 Understanding RMS
 Addition of Sine Waves to Provide Square Wave
 Capacitors in DC Circuits
 Filtering .. What is It?
 Integrating Circuits
 HighPass Filtering & Differentiating Circuits
 Lowpass, Highpass, 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
 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
 TimeHistory 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
 HighFrequency Noise
 White Noise, Grey Noise, Blue Noise, Violet Noise, Pink Noise, Brown Noise
Chapter 6  Introduction to Vibration Exciters (Shakers)

Mechanical Shakers

Electrohydraulic (EH) Shaker

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  OilSlip 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
 Purpose of a Fixture
 The “Black Art” of Fixture Design
 Basic Considerations for Fixtures
 Fixture Fabrication Methods
 Evaluating Fixtures
 Fixture Weight Relative to Test Item Weight
 Orthogonal Motion in Sinusoidal System
 Shaker Crosstalk—Orthogonal Motion
Chapter 8  Vibration Measurement
 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 Twostage 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
 TInsert 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
 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
 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
 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
 “SN” Curve from Fatigue Testing
 Idealized “SN” 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 MultiAxis System Provides
 What Is NOT A MultiAxis System?
 Simultaneous 3Axis Testing
 “Real” Multiple DegreeofFreedom Systems
 “TriAxial QuasiRandom” Systems
 TwoShaker, Two DOF Systems
 ThreeDegreeofFreedom Systems
 Army Research Lab (ARL) 3DOF Machine
 Team Mantis
 Team Cube
 Hydraulic Test System—6 Degrees of Control, the CUBE™
Chapter 11  Sine Vibration Testing
 Sine Vibration System
 Closed Loop Control
 Slow Sweep
 Fast Sweep
 Effect of Sweep Speed
 Minimum Sweep Rates for Full Resonance Response
 Crossover Frequency
 Reactance LogLog Graph Paper
 Vibration Nomographs
 Control of Vibration Systems
Chapter 12  Random Vibration Testing
 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
 Random Vibration Structural Analysis—Example
 Random Vibration Test Spectrum
 “Walkthrough” of an Imaginary Test
Chapter 13  Fatigue
 FatigueCrackGrowth Rate
 How Materials Behave: The SN Curve
 Factors Influencing Fatigue Behavior
 Stress Concentration
 Photoelasticity
 Fracture Mechanics
 Fracture Toughness
 Fracture Toughness of Some Common Materials
 Crack Propagation
 Fracture Surfaces
 Fatigue Crack Growth Prevention
 Forensics
 Failure Models
 Failure Mechanism
 TimeDependent 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 SN Curve  Number of Cycles to Failure
 Idealized SN 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
 Determination of Effective Excitation
 Fatigue, Miner’s Rule Example
 Typical Endurance Limits
 "SN" Curve from Fatigue Testing
 Fatigue Case Study
 Example: Rating a Printed Circuit Board
Chapter 14  Modal Testing
 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 Sensorsfor Modal Testing
 Modal Probe (Roving Accelerometer)
 Using Mode Shapes in Design
 Digital Image Correlation
 Building Vibrations
Chapter 15  Accelerated Testing
 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
 CoffinManson Inverse Power Law
 CoffinManson 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
 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
 HalfSine 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
 FreeFall Shock Machine
 Drop Testing Machine
 Free Fall Drop Test Machine
 Drop Test Procedures
 Free Fall Edge Drop Test
 TableTop 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
 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
 Standards vs. Specifications
 Why are Standards Needed?
 Why are Specifications Needed?
 Prominent Standards
 Procedures
Appendix A  Glossary and Definitions
Appendix B  Index of Equations
Appendix C2  Understanding Decibels and Octaves (Chapter 2 reference)

Decibels—Power Ratio

Decibel—Voltage Ratio

Application of dB notation
Appendix C3  Dynamic Force and Motion (Chapter 3 reference)

Weight, Specific Weight and Density

Relative Density or Specific Gravity

Common Units of Force

SDoFSinusoidal Relationships

Calculating Peak X, V and A

Undamped Vibrations — Single Degree of Freedom Systems

Calculating Natural Frequency

Calculating Stiffness

Determining Damping Ratio Experimentally

Effect of Damping on Frequency of Max Response

Example—Damped Resonant System
Appendix C5  Calculating RMS from PSD (Chapter 5 reference)
Appendix C7  Test Fixture Evaluation Example (Chapter 7 reference)

Swept Sine Resonant Search—Fixture Evaluation Example
Appendix C11  Sine Vibration Testing — Crossover Frequency Example (Chapter 11 reference)
Appendix C12  Random Vibration Testing (Chapter 12 reference)
 Determining the Transfer Function
 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