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 SN 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 online 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 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 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

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
 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  Random Vibration and Spectral Analysis

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)

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

Shaker Technologies—Stroke vs. Frequency Range

Extending Table Diameter

Table (Head) Expander

Horizontal Accessory  OilSlip 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

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 Vibration Displacement or Velocity

Displacement Readout: Integration

Acceleration Readout: Differentiation

Accelerometers

Wire Strain Gage Accelerometer
Chapter 9  Vibration Testing

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

FatigueCrackGrowth Rate

How Materials Behave: The SN 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

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

Fatigue Damage Model Based Upon SN Curve  Number of Cycles to Failure

Idealized SN Curve for Structural Materials

Fatigue Damage Model Based on Crack Growth Rate

Crack Growth Rate vs. Stress Intensity Factor

Miner's Hypothesis for Fatigue Damage Accumulation

Miner's "Rule" Cautions

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 11  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

Mounting of Sensorsfor Modal Testing
Chapter 12  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 13  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 14  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 15  Standards, Specifications and Procedures

Standards vs. Specifications

Why are Standards Needed?

Why are Specifications Needed?

Prominent Standards

Procedures
Appendix A  Glossary of Terms and Acronyms
Appendix B  Index of Equations
Appendix C2  Understanding Decibels and Octaves (Chapter 2 reference)
Appendix C3  Dynamic Force and Motion (Chapter 3 reference)
Appendix C5  Calculating RMS from PSD (Chapter 5 reference)
Appendix C7  Swept Sine Resonance Searchâ€”Fixture Evaluation Example (Chapter 7 reference)
Final Review
Award of Certificates for Successful Completion
Click for a printable course outline (pdf).