117 Fundamentals of Vibration for Design Applications

Applications  Random vibration is important in most engineering applications where the product is exposed to vibration and shock during transport and 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 design engineers, test engineers and project managers. 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. 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 is the initial course in TTi’s Mechanical Design Specialist Diploma program. It 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 three days. While mathematics is kept to a minimum, it is necessary to cover a sufficient amount so that the concepts of vibration can be understood. The use and application of decibels (dB) is described, then the theory of dynamics is covered including the relationships between displacement, velocity and acceleration. Damping theory and its effect on transmissibility ratio and resonance stacking and on product design is addressed.

Random vibration theory, including power spectral density theory, is discussed and video demonstrations show the effects of sinusoidal and random vibration. Various types of vibration exciters or shakers are discussed and the concept of test fixture design for vibration testing is covered.

The course proceeds to present some basic theory of electronic filters and vibration measurement systems to provide a background for understanding data acquisition and analysis topics of Spectral Analysis. Various types of vibration testing using sinusoidal and random vibration tests is discussed and the theory of material fatigue and the correct use of S-N curves for designing product life testing and developing accelerated product development testing procedures is covered. An introduction to model analysis and testing theory and application is addressed and its use for product design. Mechanical shock applications are addressed, including a brief description of the effects of seismic events and a review of designing to withstand vibration and shock.

The various standards and specifications which are applicable in product design to meet various environmental conditions are discussed and the differences and possible conversion between design procedures and various documents is covered. A discussion of methods for tailoring requirements completes the course presentation. Classroom and nightly review problems measure progress. (Bring an electronic calculator to class).

Related Courses  Course 116, Fundamentals of Vibration for Test Applications, covers some of the same topics as course 117, but places less emphasis on design and more emphasis on testing, including issues such as random vibration, instrumentation, power amplifiers, shakers and test control techniques. Course 116/117, Fundamentals of Vibration for Test and Design Applications combines courses 116 and 117. Course 310 contains design theory but omits 117’s testing content, adding advanced examples and applications.

Diploma Programs  This course is required for TTi’s Mechanical Design Specialist Diploma Program and may be used as an optional course for an of TTi’s other Specialist Diploma Programs.

Prerequisites  There are no definite prerequisites. Supervisors are invited to telephone or write to TTi on prospective attendees' backgrounds and needs.

Text  Each student will receive access to the on-line electronic course workbook, including most of the slides used in the course presentation. An initial subscription is included in the price of the course and renewals 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 Most chapters of course 117 are available as OnDemand Internet Short Topics. See below for details and ordering.

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
    • 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 - Random Vibration and Spectral Analysis

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OnDemand Short Topics$25.00
  • Sinusoidal vs Complex vs Random Vibration
    • "Single Sweep" Time History
  • Demonstration of the Effects of Random Vibration
  • Special Definitions for Random Vibration
  • Why use frequency domain?
    • Phase of Frequency Domain Components
    • Time and Frequency Domain
  • Spectral Analysis
  • Power Spectral Density
    • Shaker Power Spectral Density Response
    • Equalization to Correct PSD
    • Calculating the RMS From the PSD
    • Developing Total RMS from Spectral Plot
    • RMS Calculation
  • Transmissibility Derived From Random Vibration
  • The Fourier Transform
    • Discrete Fourier Analysis
    • Fast Fourier Transform
  • Spectrum Analyzers

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
    • Electrodynamic Shaker— Armature
    • Force Rating and Available Acceleration
    • Displacement and Velocity Limits of Electrodynamic Shaker
  • Shaker Ratings Example
  • Shaker Technologies—Stroke vs. Frequency Range
  • Extending Table Diameter
    • Table (Head) Expander
    • Horizontal Accessory - Oil-Slip Tables
    • Vibration Testing on a Slip Plate
  • Combined Environmental Reliability Testing (CERT)
  • Electrodynamic Shakers System Maintenance
  • Electric Vibration Actuators

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 - Vibration Measurement

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OnDemand Short Topics$200.00
  • Characteristics of an Ideal Transducer
  • Velocity Sensing
  • Measuring Vibration Displacement or Velocity
    • Displacement Readout: Integration
    • Acceleration Readout: Differentiation
  • Accelerometers
    • Wire Strain Gage Accelerometer

Chapter 9 - Vibration Testing

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OnDemand Short Topics$100.00
  • Types of Vibration Testing
    • Development Testing
    • Qualification Testing
    • Acceptance Testing
    • Screening Tests (or Procedures)
    • Reliability Tests
    • Durability and Functional Tests
    • Functional Tests
    • Accelerated Testing
  • The Applied Environment ... Philosophy
  • Vibration Testing -- Control
    • Control System Function
    • Exciter Programming
  • Multiple Degrees Of Freedom Testing
  • Sine Vibration Testing
    • Closed Loop Control
    • Sine Sweep Rates
  • Vibration Nomographs
  • Random Vibration Testing
    • Random Vibration Structural Analysis—Example
    • Random Vibration Test Spectrum

Chapter 10 - Fatigue

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OnDemand Short Topics$250.00
  • Fatigue-Crack-Growth Rate
  • How Materials Behave: The S-N Curve
  • Factors Influencing Fatigue Behavior
  • Stress Concentration
  • Photoelasticity
  • Fracture Mechanics
    • Fracture Toughness of Some Common Materials
    • Crack Propagation
    • Crack Growth Rate
    • Example of a Fracture Surface
    • Fracture Surfaces
  • 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
  • Fatigue Damage Model Based Upon S-N Curve - Number of Cycles to Failure
    • Idealized S-N Curve for Structural Materials
  • 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 11 - Modal Testing

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OnDemand Short Topics$100.00
  • 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
  • Mounting of Sensors--for Modal Testing

Chapter 12 - Accelerated Testing

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OnDemand Short Topics$50.00
  • 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 13 - 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 14 - Design to Withstand Shock

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OnDemand Short Topics$50.00
  • 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 15 - 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 of Terms and Acronyms

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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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OnDemand Short Topics$25.00

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

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Appendix C5 - Calculating RMS from PSD (Chapter 5 reference)

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OnDemand Short Topics$25.00

Appendix C7 - Swept Sine Resonance Search—Fixture Evaluation Example (Chapter 7 reference)

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Final Review

Award of Certificates for Successful Completion

Click for a printable course outline (pdf).