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.
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 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 116117 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 email 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.
OnDemand Internet Complete Course 116 features over fourteen hours of video as well as more indepth 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 Onsite 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

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
 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
 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

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

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
 Deriving Transmissibility from Random Vibration
Chapter 6  Introduction to Vibration Exciters (Shakers)

Mechanical Shakers

Electrohydraulic (EH) Shaker

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  OilSlip 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
 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  Introduction to Power Amplifiers

Harmonic Distortion

NonLinearity Distortion

Power Amplifiers—Block Diagram

Shaker Armature Electrical Resonance

Effect of Mechanical Resonant Loads
Chapter 9  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
 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
 Calibration
 Selecting a Measurement System
Chapter 10  Basics of Spectral Analysis
 Why Do We Use the Frequency Domain?
 Time and Frequency Domain
 Spectral Analysis ... What? Why?
 Windowing
Chapter 11  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
 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 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 12  Sine Vibration Testing
 Sine Vibration System
 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

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

Random Vibration Structural Analysis—Example

Random Vibration Test Spectrum

“Walkthrough” of an Imaginary Test
Chapter 14  Introduction to Mechanical Shock

Shock Theory

What is Shock?

Causes of Shock

Effects and Remedies of Shock

Transient or Shock Tests

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 15  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

Example—Damped Resonant System
Appendix C5  Calculating RMS from PSD (Chapter 5 reference)
Appendix C7  Fixture Design (Chapter 7 reference)
Appendix C10  Fourier Transforms, Aliasing (Chapter 10 reference)
 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 C12  Sine Vibration Testing — Crossover Frequency Example (Chapter 12 reference)
Appendix C13  Random Vibration Testing (Chapter 13 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 2/18/2019