Download VIBRATION ANALYSIS FOR ELECTRONIC EQUIPMENT PDF

TitleVIBRATION ANALYSIS FOR ELECTRONIC EQUIPMENT
File Size16.1 MB
Total Pages432
Table of Contents
                            cover.jpg
7685X_fm.pdf
	Front Matter
	Preface
	List of Symbols
	Table of Contents
	Bibliography
	Index
7685X_pref.pdf
	Front Matter
	Preface
	Table of Contents
	Bibliography
	Index
7685X_symb.pdf
	Front Matter
	List of Symbols
	Table of Contents
	Bibliography
	Index
7685X_toc.pdf
	Front Matter
	Preface
	List of Symbols
	Table of Contents
	1. Introduction
		1.1 Vibration Sources
		1.2 Definitions
		1.3 Vibration Representation
		1.4 Degrees of Freedom
		1.5 Vibration Modes
		1.6 Vibration Nodes
		1.7 Coupled Modes
		1.8 Fasteners
		1.9 Electronic Equipment for Airplanes and Missiles
		1.10 Electronic Equipment for Ships and Submarines
		1.11 Electronic Equipment for Automobiles, Trucks, and Trains
		1.12 Electronics for Oil Drilling Equipment
		1.13 Electronics for Computers, Communication, and Entertainment
	2. Vibrations of Simple Electronic Systems
		2.1 Single Spring-Mass System without Damping
			2.1.1 Sample Problem - Natural Frequency of a Cantilever Beam
		2.2 Single-Degree-of-Freedom Torsional Systems
			2.2.1 Sample Problem - Natural Frequency of a Torsion System
		2.3 Springs in Series and Parallel
			2.3.1 Sample Problem - Resonant Frequency of a Spring System
		2.4 Relation of Frequency and Acceleration to Displacement
			2.4.1 Sample Problem - Natural Frequency and Stress in a Beam
		2.5 Forced Vibrations with Viscous Damping
		2.6 Transmissibility As a Function of Frequency
			2.6.1 Sample Problem - Relating the Resonant Frequency to the Dynamic Displacement
		2.7 Multiple Spring - Mass Systems without Damping
			2.7.1 Sample Problem - Resonant Frequency of a System
	3. Component Lead Wire and Solder Joint Vibration Fatigue Life
		3.1 Introduction
		3.2 Vibration Problems with Components Mounted High above the PCB
			3.2.1 Sample Problem - Vibration Fatigue Life in the Wires of a TO-5 Transistor
		3.3 Vibration Fatigue Life in Solder Joints of a TO-5 Transistor
		3.4 Recommendations to Fix the Wire Vibration Problem
		3.5 Dynamic Forces Developed in Transformer Wires during Vibration
			3.5.1 Sample Problem - Dynamic Forces and Fatigue Life in Transformer Lead Wires
		3.6 Relative Displacements between PCB and Component Produce Lead Wire Strain
			3.6.1 Sample Problem - Effects of PCB Displacement on Hybrid Reliability
	4. Beam Structures for Electronic Subassemblies
		4.1 Natural Frequency of a Uniform Beam
			4.1.1 Sample Problem - Natural Frequencies of Beams
		4.2 Nonuniform Cross Sections
			4.2.1 Sample Problem - Natural Frequency of a Box with Nonuniform Sections
		4.3 Composite Beams
	5. Component Lead Wires As Bents, Frames, and Arcs
		5.1 Electronic Components Mounted on Circuit Boards
		5.2 Bent with a Lateral Load - Hinged Ends
		5.3 Strain Energy - Bent with Hinged Ends
		5.4 Strain Energy - Bent with Fixed Ends
		5.5 Strain Energy - Circular Arc with Hinged Ends
		5.6 Strain Energy - Circular Arc with Fixed Ends
		5.7 Strain Energy - Circular Arcs for Lead Wire Strain Relief
			5.7.1 Sample Problem - Adding an Offset in a Wire to Increase the Fatigue Life
	6. Printed Circuit Boards and Flat Plates
		6.1 Various Types of Printed Circuit Boards
		6.2 Changes in Circuit Board Edge Conditions
		6.3 Estimating the Transmissibility of a Printed Circuit Board
		6.4 Natural Frequency Using a Trigonometric Series
		6.5 Natural Frequency Using a Polynomial Series
			6.5.1 Sample Problem - Resonant Frequency of a PCB
		6.6 Natural Frequency Equations Derived Using the Rayleigh Method
		6.7 Dynamic Stresses in the Circuit Board
			6.7.1 Sample Problem - Vibration Stresses in a PCB
		6.8 Ribs on Printed Circuit Boards
		6.9 Ribs Fastened to Circuit Boards with Screws
		6.10 Printed Circuit Boards with Ribs in Two Directions
		6.11 Proper Use of Ribs to Stiffen Plates and Circuit Boards
		6.12 Quick Way to Estimate the Required Rib Spacing for Circuit Boards
		6.13 Natural Frequencies for Different PCB Shapes with Different Supports
			6.13.1 Sample Problem - Natural Frequency of a Triangular PCB with Three Point Supports
	7. Octave Rule, Snubbing, and Damping to Increase the PCB Fatigue Life
		7.1 Dynamic Coupling between the PCBs and Their Support Structures
		7.2 Effects of Loose Edge Guides on Plug-In Type PCBs
		7.3 Description of Dynamic Computer Study for the Octave Rule
		7.4 The Forward Octave Rule Always Works
		7.5 The Reverse Octave Rule Must Have Lightweight PCBs
			7.5.1 Sample Problem - Vibration Problems with Relays Mounted on PCBs
		7.6 Proposed Corrective Action for Relays
		7.7 Using Snubbers to Reduce PCB Displacements and Stresses
			7.7.1 Sample Problem - Adding Snubbers to Improve PCB Reliability
		7.8 Controlling the PCB Transmissibility with Damping
		7.9 Properties of Material Damping
		7.10 Constrained Layer Damping with Viscoelastic Materials
		7.11 Why Stiffening Ribs on PCBs are Often Better Than Damping
		7.12 Problems with PCB Viscoelastic Dampers
	8. Preventing Sinusoidal Vibration Failures in Electronic Equipment
		8.1 Introduction
		8.2 Estimating the Vibration Fatigue Life
			8.2.1 Sample Problem - Qualification Test for an Electronic System
		8.3 Electronic Component Lead Wire Strain Relief
		8.4 Designing PCBs for Sinusoidal Vibration Environments
			8.4.1 Sample Problem - Determining Desired PCB Resonant Frequency
		8.5 How Location and Orientation of Component on PCB Affect Life
		8.6 How Wedge Clamps Affect the PCB Resonant Frequency
			8.6.1 Sample Problem - Resonant Frequency of PCB with Side Wedge Clamps
		8.7 Effects of Loose PCB Side Edge Guides
			8.7.1 Sample Problem - Resonant Frequency of PCB with Loose Edge Guides
		8.8 Sine Sweep through a Resonance
			8.8.1 Sample Problem - Fatigue Cycles Accumulated during a Sine Sweep
	9. Designing Electronics for Random Vibration
		9.1 Introduction
		9.2 Basic Failure Modes in Random Vibration
		9.3 Characteristics of Random Vibration
		9.4 Differences between Sinusoidal and Random Vibrations
		9.5 Random Vibration Input Curves
			9.5.1 Sample Problem - Determining the Input RMS Acceleration Level
		9.6 Random Vibration Units
		9.7 Shaped Random Vibration Input Curves
			9.7.1 Sample Problem - Input RMS Accelerations for Sloped PSD Curves
		9.8 Relation between Decibels and Slope
		9.9 Integration Method for Obtaining the Area under a PSD Curve
		9.10 Finding Points on the PSD Curve
			9.10.1 Sample Problem - Finding PSD Values
		9.11 Using Basic Logarithms to Find Points on the PSD Curve
		9.12 Probability Distribution Functions
		9.13 Gaussian or Normal Distribution Curve
		9.14 Correlating Random Vibration Failures Using the Three-Band Technique
		9.15 Rayleigh Distribution Function
		9.16 Response of a Single-Degree-of-Freedom System to Random Vibration
			9.16.1 Sample Problem - Estimating the Random Vibration Fatigue Life
		9.17 How PCBs Respond to Random Vibration
		9.18 Designing PCBs for Random Vibration Environments
			9.18.1 Sample Problem - Finding the Desired PCB Resonant Frequency
		9.19 Effects of Relative Motion on Component Fatigue Life
			9.19.1 Sample Problem - Component Fatigue Life
		9.20 It's the Input PSD That Counts, Not the Input RMS Acceleration
		9.21 Connector Wear and Surface Fretting Corrosion
			9.21.1 Sample Problem - Determining Approximate Connector Fatigue Life
		9.22 Multiple-Degree-of-Freedom Systems
		9.23 Octave Rule for Random Vibration
			9.23.1 Sample Problem - Response of Chassis and PCB to Random Vibration
			9.23.2 Sample Problem - Dynamic Analysis of an Electronic Chassis
		9.24 Determining the Number of Positive Zero Crossings
			9.24.1 Sample Problem - Determining the Number of Positive Zero Crossings
	10. Acoustic Noise Effects on Electronics
		10.1 Introduction
			10.1.1 Sample Problem - Determining the Sound Pressure Level
		10.2 Microphonic Effects in Electronic Equipment
		10.3 Methods for Generating Acoustic Noise Tests
		10.4 One-Third Octave Bandwidth
		10.5 Determining the Sound Pressure Spectral Density
		10.6 Sound Pressure Response to Acoustic Noise Excitation
			10.6.1 Sample Problem - Fatigue Life of a Sheet-Metal Panel Exposed to Acoustic Noise
		10.7 Determining the Sound Acceleration Spectral Density
			10.7.1 Sample Problem - Alternate Method of Acoustic Noise Analysis
	11. Designing Electronics for Shock Environments
		11.1 Introduction
		11.2 Specifying the Shock Environment
		11.3 Pulse Shock
		11.4 Half-Sine Shock Pulse for Zero Rebound and Full Rebound
			11.4.1 Sample Problem - Half-Sine Shock-Pulse Drop Test
		11.5 Response of Electronic Structures to Shock Pulses
		11.6 Response of a Simple System to Various Shock Pulses
		11.7 How PCBs Respond to Shock Pulses
		11.8 Determining the Desired PCB Resonant Frequency for Shock
			11.8.1 Sample Problem - Response of a PCB to a Half-Sine Shock Pulse
		11.9 Response of PCB to Other Shock Pulses
			11.9.1 Sample Problem - Shock Response of a Transformer Mounting Bracket
		11.10 Equivalent Shock Pulse
			11.10.1 Sample Problem - Shipping Crate for an Electronic Box
		11.11 Low Values of the Frequency Ratio R
			11.11.1 Sample Problem - Shock Amplification for Low Frequency Ratio R
		11.12 Shock Isolators
			11.12.1 Sample Problem - Heat Developed in an Isolator
		11.13 Information Required for Shock Isolators
			11.13.1 Sample Problem - Selecting a Set of Shock Isolators
		11.14 Ringing Effects in Systems with Light Damping
		11.15 How Two-Degree-of-Freedom Systems Respond to Shock
		11.16 The Octave Rule for Shock
		11.17 Velocity Shock
			11.17.1 Sample Problem - Designing a Cabinet for Velocity Shock
		11.18 Nonlinear Velocity Shock
			11.18.1 Sample Problem - Cushioning Material for a Sensitive Electronic Box
		11.19 Shock Response Spectrum
		11.20 How Chassis and PCBs Respond to Shock
			11.20.1 Sample Problem - Shock Response Spectrum Analysis for Chassis and PCB
		11.21 How Pyrotechnic Shock Can Affect Electronic Components
			11.21.1 Sample Problem - Resonant Frequency of a Hybrid Die Bond Wire
	12. Design and Analysis of Electronic Boxes
		12.1 Introduction
		12.2 Different Types of Mounts
		12.3 Preliminary Dynamic Analysis
		12.4 Bolted Covers
		12.5 Coupled Modes
		12.6 Dynamic Loads in a Chassis
		12.7 Bending Stresses in the Chassis
		12.8 Buckling Stress Ratio for Bending
		12.9 Torsional Stresses in the Chassis
		12.10 Buckling Stress Ratio for Shear
		12.11 Margin of Safety for Buckling
		12.12 Center-of-Gravity Mount
		12.13 Simpler Method for Obtaining Dynamic Forces and Stresses on a Chassis
	13. Effects of Manufacturing Methods on the Reliability of Electronics
		13.1 Introduction
		13.2 Typical Tolerances in Electronic Components and Lead Wires
			13.2.1 Sample Problem - Effects of PCB Tolerances on Frequency and Fatigue Life
		13.3 Problems Associated with Tolerances on PCB Thickness
		13.4 Effects of Poor Bonding Methods on Structural Stiffness
		13.5 Soldering Small Axial Leaded Components on Through-Hole PCBs
		13.6 Areas Where Poor Manufacturing Methods Have Been Known to Cause Problems
		13.7 Avionic Integrity Program and Automotive Integrity Program (AVIP)
		13.8 The Basic Philosophy for Performing an AVIP Analysis
		13.9 Different Perspectives of Reliability
	14. Vibration Fixtures and Vibration Testing
		14.1 Vibration Simulation Equipment
		14.2 Mounting the Vibration Machine
		14.3 Vibration Test Fixtures
		14.4 Basic Fixture Design Considerations
		14.5 Effective Spring Rates for Bolts
		14.6 Bolt Preload Torque
			14.6.1 Sample Problem - Determining Desired Bolt Torque
		14.7 Rocking Modes and Overturning Moments
		14.8 Oil-Film Slider Tables
		14.9 Vibration Fixture Counterweights
		14.10 A Summary for Good Fixture Design
		14.11 Suspension Systems
		14.12 Mechanical Fuses
		14.13 Distinguishing Bending Modes from Rocking Modes
		14.14 Push-Bar Couplings
		14.15 Slider Plate Longitudinal Resonance
		14.16 Acceleration Force Capability of Shaker
		14.17 Positioning the Servo-Control Accelerometer
		14.18 More Accurate Method for Estimating the Transmissibility Q in Structures
			14.18.1 Sample Problem - Transmissibility Expected for a Plug-in PCB
		14.19 Cross-Coupling Effects in Vibration Test Fixtures
		14.20 Progressive Vibration Shear Failures in Bolted Structures
		14.21 Vibration Push-Bar Couplers with Bolts Loaded in Shear
		14.22 Bolting PCB Centers Together to Improve Their Vibration Fatigue Life
		14.23 Vibration Failures Caused by Careless Manufacturing Methods
		14.24 Alleged Vibration Failure That was Really Caused by Dropping a Large Chassis
		14.25 Methods for Increasing the Vibration and Shock Capability on Existing Systems
	15. Environmental Stress Screening for Electronic Equipment (ESSEE)
		15.1 Introduction
		15.2 Environmental Stress Screening Philosophy
		15.3 Screening Environments
		15.4 Things an Acceptable Screen are Expected to Do
		15.5 Things an Acceptable Screen are Not Expected to Do
		15.6 To Screen or Not to Screen, That is the Problem
		15.7 Preparations Prior to the Start of a Screening Program
		15.8 Combined Thermal Cycling, Random Vibration, and Electrical Operation
		15.9 Separate Thermal Cycling, Random Vibration, and Electrical Operation
		15.10 Importance of the Screening Environment Sequence
		15.11 How Damage Can be Developed in a Thermal Cycling Screen
		15.12 Estimating the Amount of Fatigue Life Used up in a Random Vibration Screen
			15.12.1 Sample Problem - Fatigue Life Used up in a Vibration and Thermal Cycling Screen
	Bibliography
	Index
7685X_01.pdf
	Front Matter
	Table of Contents
	1. Introduction
		1.1 Vibration Sources
		1.2 Definitions
		1.3 Vibration Representation
		1.4 Degrees of Freedom
		1.5 Vibration Modes
		1.6 Vibration Nodes
		1.7 Coupled Modes
		1.8 Fasteners
		1.9 Electronic Equipment for Airplanes and Missiles
		1.10 Electronic Equipment for Ships and Submarines
		1.11 Electronic Equipment for Automobiles, Trucks, and Trains
		1.12 Electronics for Oil Drilling Equipment
		1.13 Electronics for Computers, Communication, and Entertainment
	Bibliography
	Index
7685X_02.pdf
	Front Matter
	Table of Contents
	2. Vibrations of Simple Electronic Systems
		2.1 Single Spring-Mass System without Damping
			2.1.1 Sample Problem - Natural Frequency of a Cantilever Beam
		2.2 Single-Degree-of-Freedom Torsional Systems
			2.2.1 Sample Problem - Natural Frequency of a Torsion System
		2.3 Springs in Series and Parallel
			2.3.1 Sample Problem - Resonant Frequency of a Spring System
		2.4 Relation of Frequency and Acceleration to Displacement
			2.4.1 Sample Problem - Natural Frequency and Stress in a Beam
		2.5 Forced Vibrations with Viscous Damping
		2.6 Transmissibility As a Function of Frequency
			2.6.1 Sample Problem - Relating the Resonant Frequency to the Dynamic Displacement
		2.7 Multiple Spring - Mass Systems without Damping
			2.7.1 Sample Problem - Resonant Frequency of a System
	Bibliography
	Index
7685X_03.pdf
	Front Matter
	Table of Contents
	3. Component Lead Wire and Solder Joint Vibration Fatigue Life
		3.1 Introduction
		3.2 Vibration Problems with Components Mounted High above the PCB
			3.2.1 Sample Problem - Vibration Fatigue Life in the Wires of a TO-5 Transistor
		3.3 Vibration Fatigue Life in Solder Joints of a TO-5 Transistor
		3.4 Recommendations to Fix the Wire Vibration Problem
		3.5 Dynamic Forces Developed in Transformer Wires during Vibration
			3.5.1 Sample Problem - Dynamic Forces and Fatigue Life in Transformer Lead Wires
		3.6 Relative Displacements between PCB and Component Produce Lead Wire Strain
			3.6.1 Sample Problem - Effects of PCB Displacement on Hybrid Reliability
	Bibliography
	Index
7685X_04.pdf
	Front Matter
	Table of Contents
	4. Beam Structures for Electronic Subassemblies
		4.1 Natural Frequency of a Uniform Beam
			4.1.1 Sample Problem - Natural Frequencies of Beams
		4.2 Nonuniform Cross Sections
			4.2.1 Sample Problem - Natural Frequency of a Box with Nonuniform Sections
		4.3 Composite Beams
	Bibliography
	Index
7685X_05.pdf
	Front Matter
	Table of Contents
	5. Component Lead Wires As Bents, Frames, and Arcs
		5.1 Electronic Components Mounted on Circuit Boards
		5.2 Bent with a Lateral Load - Hinged Ends
		5.3 Strain Energy - Bent with Hinged Ends
		5.4 Strain Energy - Bent with Fixed Ends
		5.5 Strain Energy - Circular Arc with Hinged Ends
		5.6 Strain Energy - Circular Arc with Fixed Ends
		5.7 Strain Energy - Circular Arcs for Lead Wire Strain Relief
			5.7.1 Sample Problem - Adding an Offset in a Wire to Increase the Fatigue Life
	Bibliography
	Index
7685X_06.pdf
	Front Matter
	Table of Contents
	6. Printed Circuit Boards and Flat Plates
		6.1 Various Types of Printed Circuit Boards
		6.2 Changes in Circuit Board Edge Conditions
		6.3 Estimating the Transmissibility of a Printed Circuit Board
		6.4 Natural Frequency Using a Trigonometric Series
		6.5 Natural Frequency Using a Polynomial Series
			6.5.1 Sample Problem - Resonant Frequency of a PCB
		6.6 Natural Frequency Equations Derived Using the Rayleigh Method
		6.7 Dynamic Stresses in the Circuit Board
			6.7.1 Sample Problem - Vibration Stresses in a PCB
		6.8 Ribs on Printed Circuit Boards
		6.9 Ribs Fastened to Circuit Boards with Screws
		6.10 Printed Circuit Boards with Ribs in Two Directions
		6.11 Proper Use of Ribs to Stiffen Plates and Circuit Boards
		6.12 Quick Way to Estimate the Required Rib Spacing for Circuit Boards
		6.13 Natural Frequencies for Different PCB Shapes with Different Supports
			6.13.1 Sample Problem - Natural Frequency of a Triangular PCB with Three Point Supports
	Bibliography
	Index
7685X_07.pdf
	Front Matter
	Table of Contents
	7. Octave Rule, Snubbing, and Damping to Increase the PCB Fatigue Life
		7.1 Dynamic Coupling between the PCBs and Their Support Structures
		7.2 Effects of Loose Edge Guides on Plug-In Type PCBs
		7.3 Description of Dynamic Computer Study for the Octave Rule
		7.4 The Forward Octave Rule Always Works
		7.5 The Reverse Octave Rule Must Have Lightweight PCBs
			7.5.1 Sample Problem - Vibration Problems with Relays Mounted on PCBs
		7.6 Proposed Corrective Action for Relays
		7.7 Using Snubbers to Reduce PCB Displacements and Stresses
			7.7.1 Sample Problem - Adding Snubbers to Improve PCB Reliability
		7.8 Controlling the PCB Transmissibility with Damping
		7.9 Properties of Material Damping
		7.10 Constrained Layer Damping with Viscoelastic Materials
		7.11 Why Stiffening Ribs on PCBs are Often Better Than Damping
		7.12 Problems with PCB Viscoelastic Dampers
	Bibliography
	Index
7685X_08.pdf
	Front Matter
	Table of Contents
	8. Preventing Sinusoidal Vibration Failures in Electronic Equipment
		8.1 Introduction
		8.2 Estimating the Vibration Fatigue Life
			8.2.1 Sample Problem - Qualification Test for an Electronic System
		8.3 Electronic Component Lead Wire Strain Relief
		8.4 Designing PCBs for Sinusoidal Vibration Environments
			8.4.1 Sample Problem - Determining Desired PCB Resonant Frequency
		8.5 How Location and Orientation of Component on PCB Affect Life
		8.6 How Wedge Clamps Affect the PCB Resonant Frequency
			8.6.1 Sample Problem - Resonant Frequency of PCB with Side Wedge Clamps
		8.7 Effects of Loose PCB Side Edge Guides
			8.7.1 Sample Problem - Resonant Frequency of PCB with Loose Edge Guides
		8.8 Sine Sweep through a Resonance
			8.8.1 Sample Problem - Fatigue Cycles Accumulated during a Sine Sweep
	Bibliography
	Index
7685X_09.pdf
	Front Matter
	Table of Contents
	9. Designing Electronics for Random Vibration
		9.1 Introduction
		9.2 Basic Failure Modes in Random Vibration
		9.3 Characteristics of Random Vibration
		9.4 Differences between Sinusoidal and Random Vibrations
		9.5 Random Vibration Input Curves
			9.5.1 Sample Problem - Determining the Input RMS Acceleration Level
		9.6 Random Vibration Units
		9.7 Shaped Random Vibration Input Curves
			9.7.1 Sample Problem - Input RMS Accelerations for Sloped PSD Curves
		9.8 Relation between Decibels and Slope
		9.9 Integration Method for Obtaining the Area under a PSD Curve
		9.10 Finding Points on the PSD Curve
			9.10.1 Sample Problem - Finding PSD Values
		9.11 Using Basic Logarithms to Find Points on the PSD Curve
		9.12 Probability Distribution Functions
		9.13 Gaussian or Normal Distribution Curve
		9.14 Correlating Random Vibration Failures Using the Three-Band Technique
		9.15 Rayleigh Distribution Function
		9.16 Response of a Single-Degree-of-Freedom System to Random Vibration
			9.16.1 Sample Problem - Estimating the Random Vibration Fatigue Life
		9.17 How PCBs Respond to Random Vibration
		9.18 Designing PCBs for Random Vibration Environments
			9.18.1 Sample Problem - Finding the Desired PCB Resonant Frequency
		9.19 Effects of Relative Motion on Component Fatigue Life
			9.19.1 Sample Problem - Component Fatigue Life
		9.20 It's the Input PSD That Counts, Not the Input RMS Acceleration
		9.21 Connector Wear and Surface Fretting Corrosion
			9.21.1 Sample Problem - Determining Approximate Connector Fatigue Life
		9.22 Multiple-Degree-of-Freedom Systems
		9.23 Octave Rule for Random Vibration
			9.23.1 Sample Problem - Response of Chassis and PCB to Random Vibration
			9.23.2 Sample Problem - Dynamic Analysis of an Electronic Chassis
		9.24 Determining the Number of Positive Zero Crossings
			9.24.1 Sample Problem - Determining the Number of Positive Zero Crossings
	Bibliography
	Index
7685X_10.pdf
	Front Matter
	Table of Contents
	10. Acoustic Noise Effects on Electronics
		10.1 Introduction
			10.1.1 Sample Problem - Determining the Sound Pressure Level
		10.2 Microphonic Effects in Electronic Equipment
		10.3 Methods for Generating Acoustic Noise Tests
		10.4 One-Third Octave Bandwidth
		10.5 Determining the Sound Pressure Spectral Density
		10.6 Sound Pressure Response to Acoustic Noise Excitation
			10.6.1 Sample Problem - Fatigue Life of a Sheet-Metal Panel Exposed to Acoustic Noise
		10.7 Determining the Sound Acceleration Spectral Density
			10.7.1 Sample Problem - Alternate Method of Acoustic Noise Analysis
	Bibliography
	Index
7685X_11a.pdf
	Front Matter
	Table of Contents
	11. Designing Electronics for Shock Environments
		11.1 Introduction
		11.2 Specifying the Shock Environment
		11.3 Pulse Shock
		11.4 Half-Sine Shock Pulse for Zero Rebound and Full Rebound
			11.4.1 Sample Problem - Half-Sine Shock-Pulse Drop Test
		11.5 Response of Electronic Structures to Shock Pulses
		11.6 Response of a Simple System to Various Shock Pulses
		11.7 How PCBs Respond to Shock Pulses
		11.8 Determining the Desired PCB Resonant Frequency for Shock
			11.8.1 Sample Problem - Response of a PCB to a Half-Sine Shock Pulse
		11.9 Response of PCB to Other Shock Pulses
			11.9.1 Sample Problem - Shock Response of a Transformer Mounting Bracket
		11.10 Equivalent Shock Pulse
			11.10.1 Sample Problem - Shipping Crate for an Electronic Box
		11.11 Low Values of the Frequency Ratio R
			11.11.1 Sample Problem - Shock Amplification for Low Frequency Ratio R
		11.12 Shock Isolators
			11.12.1 Sample Problem - Heat Developed in an Isolator
		11.13 Information Required for Shock Isolators
			11.13.1 Sample Problem - Selecting a Set of Shock Isolators
		11.14 Ringing Effects in Systems with Light Damping
		11.15 How Two-Degree-of-Freedom Systems Respond to Shock
		11.16 The Octave Rule for Shock
		11.17 Velocity Shock
			11.17.1 Sample Problem - Designing a Cabinet for Velocity Shock
		11.18 Nonlinear Velocity Shock
			11.18.1 Sample Problem - Cushioning Material for a Sensitive Electronic Box
		11.19 Shock Response Spectrum
		11.20 How Chassis and PCBs Respond to Shock
			11.20.1 Sample Problem - Shock Response Spectrum Analysis for Chassis and PCB
		11.21 How Pyrotechnic Shock Can Affect Electronic Components
			11.21.1 Sample Problem - Resonant Frequency of a Hybrid Die Bond Wire
	Bibliography
	Index
7685X_12.pdf
	Front Matter
	Table of Contents
	12. Design and Analysis of Electronic Boxes
		12.1 Introduction
		12.2 Different Types of Mounts
		12.3 Preliminary Dynamic Analysis
		12.4 Bolted Covers
		12.5 Coupled Modes
		12.6 Dynamic Loads in a Chassis
		12.7 Bending Stresses in the Chassis
		12.8 Buckling Stress Ratio for Bending
		12.9 Torsional Stresses in the Chassis
		12.10 Buckling Stress Ratio for Shear
		12.11 Margin of Safety for Buckling
		12.12 Center-of-Gravity Mount
		12.13 Simpler Method for Obtaining Dynamic Forces and Stresses on a Chassis
	Bibliography
	Index
7685X_13.pdf
	Front Matter
	Table of Contents
	13. Effects of Manufacturing Methods on the Reliability of Electronics
		13.1 Introduction
		13.2 Typical Tolerances in Electronic Components and Lead Wires
			13.2.1 Sample Problem - Effects of PCB Tolerances on Frequency and Fatigue Life
		13.3 Problems Associated with Tolerances on PCB Thickness
		13.4 Effects of Poor Bonding Methods on Structural Stiffness
		13.5 Soldering Small Axial Leaded Components on Through-Hole PCBs
		13.6 Areas Where Poor Manufacturing Methods Have Been Known to Cause Problems
		13.7 Avionic Integrity Program and Automotive Integrity Program (AVIP)
		13.8 The Basic Philosophy for Performing an AVIP Analysis
		13.9 Different Perspectives of Reliability
	Bibliography
	Index
7685X_14.pdf
	Front Matter
	Table of Contents
	14. Vibration Fixtures and Vibration Testing
		14.1 Vibration Simulation Equipment
		14.2 Mounting the Vibration Machine
		14.3 Vibration Test Fixtures
		14.4 Basic Fixture Design Considerations
		14.5 Effective Spring Rates for Bolts
		14.6 Bolt Preload Torque
			14.6.1 Sample Problem - Determining Desired Bolt Torque
		14.7 Rocking Modes and Overturning Moments
		14.8 Oil-Film Slider Tables
		14.9 Vibration Fixture Counterweights
		14.10 A Summary for Good Fixture Design
		14.11 Suspension Systems
		14.12 Mechanical Fuses
		14.13 Distinguishing Bending Modes from Rocking Modes
		14.14 Push-Bar Couplings
		14.15 Slider Plate Longitudinal Resonance
		14.16 Acceleration Force Capability of Shaker
		14.17 Positioning the Servo-Control Accelerometer
		14.18 More Accurate Method for Estimating the Transmissibility Q in Structures
			14.18.1 Sample Problem - Transmissibility Expected for a Plug-in PCB
		14.19 Cross-Coupling Effects in Vibration Test Fixtures
		14.20 Progressive Vibration Shear Failures in Bolted Structures
		14.21 Vibration Push-Bar Couplers with Bolts Loaded in Shear
		14.22 Bolting PCB Centers Together to Improve Their Vibration Fatigue Life
		14.23 Vibration Failures Caused by Careless Manufacturing Methods
		14.24 Alleged Vibration Failure That was Really Caused by Dropping a Large Chassis
		14.25 Methods for Increasing the Vibration and Shock Capability on Existing Systems
	Bibliography
	Index
7685X_15.pdf
	Front Matter
	Table of Contents
	15. Environmental Stress Screening for Electronic Equipment (ESSEE)
		15.1 Introduction
		15.2 Environmental Stress Screening Philosophy
		15.3 Screening Environments
		15.4 Things an Acceptable Screen are Expected to Do
		15.5 Things an Acceptable Screen are Not Expected to Do
		15.6 To Screen or Not to Screen, That is the Problem
		15.7 Preparations Prior to the Start of a Screening Program
		15.8 Combined Thermal Cycling, Random Vibration, and Electrical Operation
		15.9 Separate Thermal Cycling, Random Vibration, and Electrical Operation
		15.10 Importance of the Screening Environment Sequence
		15.11 How Damage Can be Developed in a Thermal Cycling Screen
		15.12 Estimating the Amount of Fatigue Life Used up in a Random Vibration Screen
			15.12.1 Sample Problem - Fatigue Life Used up in a Vibration and Thermal Cycling Screen
	Bibliography
	Index
7685X_bib.pdf
	Front Matter
	Table of Contents
	Bibliography
	Index
7685X_indx.pdf
	Front Matter
	Table of Contents
	Bibliography
	Index
		A
		B
		C
		D
		E
		F
		G
		H
		I
		J
		K
		L
		M
		N
		O
		P
		Q
		R
		S
		T
		V
		W
                        
Document Text Contents
Page 2

VIBRATION ANALYSIS FOR
ELECTRONIC EQUIPMENT

THIRD EDITION

Dave S. Steinberg
Steinberg & Associates
and University of California, Los Angeles

A WILEY-INTERSCIENCE PUBLICATION

JOHN WILEY & SONS, INC.
New York Chichester Weinheim Brisbane Singapore Toronto

Page 216

INTEGRATION METHOD FOR OBTAINING THE AREA UNDER A PSD CURVE 199

Starting with area 1 in Fig. 9.9, the b intercept on the P axis must be
determined where the frequency f equals 1 Hz. This can be obtained from
point 1 or point 2, since they are both on the same line with the same slope:

P, = 0.0133 G2/Hz

f , = 5 H z

or

P, = 0.20 G*/HZ

f 2 = 75 HZ

The slope S = 1.0 (equivalent to 3 dB/octave). Substitute into Eq. 9.16 for
the intercept b:

0.0133 0.20
b = - or - - - 0.00266 G2/Hz

(5)’ (75)’
(9.18)

Substitute into Eq. 9.17 and integrate between the limits of 5 and 75 Hz
for area 1 as shown in Fig. 9.9:

A, = ~ ~ 0 . 0 0 2 6 6 f ’ df = 0.00266 [;J -
0.00266

A, = 7 [ (75) , - ( 5 ) 2 ] = 7.46 G 2
i-

(9.19)

Comparing the results with Eq. 9.7 shows that the two different methods of
analysis agree very well.

The integration method for finding area 2 will be exactly the same as
Eq. 9.8.

The integration method for finding area 3 will be the same as the method
shown for area 1, except that a new intercept b must be obtained using
Eq. 9.16. The 200-Hz point or the 2000-Hz point can be used in Fig. 9.9,
since they are both on the same line:

P, = 0.2 G2/Hz

f l = 200 Hz

or

p2 = 0.002 G ~ / H ~

f 2 = 2000 Hz

Page 217

200 DESIGNING ELECTRONICS FOR RANDOM VIBRATION

The slope S = - 2 (equivalent to - 6 dB/octave). Substitute into Eq. 9.16 for
the intercept b:

0.20 0.002
b = = 8000 G2/Hz

(200) - 2 Or (2000) - * (9.20)

Substitute into Eq. 9.17 and integrate between the limits of 200 and 2000 Hz
for area 3, as shown in Fig. 9.9:

2000

A , = ~ ~ ~ 0 8 0 0 0 f - 2 df = 8000

8000
A , = ~ [ ( 2 0 0 0 ) - ~ - (200)-’] = 36.0 G2 /Hz (9.21)

Comparing the results with Eq. 9.9 shows the two areas and the two
different methods of analysis agree very well.

9.10 FINDING POINTS ON THE PSD CURVE

Random vibration input PSD curves are often specified in terms of the
frequency break points and the slope in dB, with only one G2/Hz point
defined as shown in Fig. 9.11. When it is necessary to find the PSD level at
these break points, then it is convenient to use the relation

(9.22)

Sample Problem-Finding PSD Values

Determine the PSD values at break points 1 and 2 as shown in Fig. 9.11.

FIGURE 9.11. Locating break points on a PSD
curve.

Slope Sloae

Frequency Hz

Page 431

This page has been reformatted by Knovel to provide easier navigation.

Index Terms Links

Vibration (Cont.)

airplanes and missiles 10 300

automobiles, trucks and trains 156

bending coupled with torsion 308

counter weights 356

die bond wires 297

fixtures 347

design summary 357

wood laminations 348

forced 30

free 17

harmonic modes 5

isolators 275 277 301

sample problem, selecting vibration isolators 278

linear systems 2

mechanical fuse 358

modes 5

nodes 5

nonlinear systems 342 351

nose cones 356

oil film slider 355 356 364

367

qualification tests 168 175 189

224 250

random 188

representation 3

servo control accelerometer 366

effects of location 367

Page 432

This page has been reformatted by Knovel to provide easier navigation.

Index Terms Links

Vibration (Cont.)

shaker machine 347

bolt patterns 361 364

mounting 347

ships and submarines 13

sinusoidal 166

sources 1

suspension systems 358

unsymmetrical fixtures 354

variable cross section 64

beams 64 66 67

electronic chassis 68

W
Wear, connectors 223 224

Wedge clamps 177 179

percent fixity 178

Work 21 22

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