142/195 Mechanical Shock and Modal Test Techniques

Applications  The effects of shock are important in many engineering applications ranging from appliances to computers to ships to automobiles, trucks and military vehicles to high-performance aircraft and missiles. Shock is often part of the service and/or transportation environment. Military Standards such as MIL-STD-810 call for shock testing.

The possible effect of shock must be considered for almost every product that has to be shipped and handled. Care can be taken in a controlled environment but during the transportation phase the product within its package must be designed and tested to withstand the anticipated environment.

For Whom Intended  Engineers involved with dynamics and structural test applications.

Most engineers need specialized education in order to properly measure, quantize and analyze this generally unfamiliar environment, and to reproduce it in environmental test laboratories. This course is for packaging designers, test laboratory managers, engineers and aides. It also helps quality and reliability specialists and acquisition personnel in government and military activities, and their contractors.

Instrumentation specialists who will measure transportation, service and laboratory shock need this course. Metrologists learn about shock calibration of accelerometers and systems. Project personnel, structure and packaging engineers learn about developmental shock testing. Product assurance and acquisition specialists learn to evaluate shock test facilities and methods, and to interpret shock test specifications.

This course is designed to serve the varied needs of scientists, engineers, aides and senior technicians. The instructor maintains good balance between practical training and theory.

Brief Course Description  The course begins with a review of structural and dynamic theory before examining methods of measuring frequency response from the structure under test. The causes and effects of shock are reviewed in detail, including the different shock pulse shapes.

Experimental modal testing is introduced by a brief discussion of theoretical modal analysis. The single degree of freedom (SDoF) model enables us to understand the fundamental concepts of free and forced vibration, natural frequency, resonance and damping. However in MDoF systems, resonance may occur at a number of different frequencies, each of which corresponds to a different pattern or shape of the system's motion. These are known as the natural or normal modes of vibration or mode shapes. There is a differential equation of motion for each degree of freedom; a set of n simultaneous equations is needed to mathematically describe a MDoF system. These equations are usually solved using matrix algebra.

In the experimental method of Modal Testing, the structure is excited by applying forced vibration and measuring the responses, from which the vibration modes are determined and a structural model developed. This is the reverse process to the theoretical method. Various methods of input excitation are discussed, such as shaker and impact hammer. Structural preparation and suspension methods are also examined.

A review of transducers and signal processing equipment is made before discussing analysis methods, time-domain curve fitting. Modal test philosophy including the sequence of steps and practical considerations in undertaking the test are discussed. The tabulation of results and derivation of mode shapes and construction of spatial models (mass, stiffness and damping) are covered before discussing the application of the modal test results.

The Shock Response Spectrum (SRS) is discussed as it relates to shock measurement and testing. The course then covers shock measurements, also calibration. The relative merits of various types of shakers and shock test machines are briefly considered before covering various shock test methods, including pyrotechnic shock testing. Some typical shock test procedures and specifications are described, both military and commercial.

Diploma Programs  This course is required for TTi’s Dynamic Test Specialist (DTS) and Mechanical Design Specialist (MDS) Diploma Programs. It may be used as an optional course for any other TTi Specialist Diploma program.

Related Courses See TTi’s Course 142, Mechanical Shock Techniques, and Course 195, Modal Analysis for Structural Validation, which were combined to create this course.

Prerequisites  Prior participation in TTi’s Fundamentals of Vibration would be helpful. Participants will need first-year college mathematics (or equivalent experience) and some facility with fundamental engineering computations. Some familiarity with electrical and mechanical measurements and vibration will be helpful.

Text  Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks 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  OnDemand Internet Complete Course 142-4 features over 18 hours of video as well as more in-depth reading material. All chapters of course 142-4 are also available as OnDemand Internet Short Topics. See the course outline below for details.

Course Outline

Chapter 1 - Single-Degree-of-Freedom and 2-Degree-of-Freedom (SDoF and 2DoF) Systems

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  • The Single Degree Of Freedom System
    • The Spring, k
    • The Mass, m
    • The Damper, c
  • Motion of an SDoF System
  • The Impulse Response Function, h(t)
  • The Frequency Response Function (FRF)
    • Displaying the FRF
  • Structural Dynamic Relationships
    • Receptance, Mobility, Accelerance
  • Two Degrees of Freedom (2DoF)
    • 2DoF Example
  • The 2DoF Frequency Response Function
    • Observations from the 2DoF FRF

Chapter 2 - Multiple-Degrees of Freedom (MDoF) Systems

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  • The Multiple Degrees Of Freedom System (MDoF)
    • Mass Matrix, [M]
    • Stiffness Matrix, [K]
    • Flexibility Matrix, [H]
    • Damping Matrix, [C]
  • Natural Frequencies and Mode Shapes
  • Modal and Frequency Matrices
  • Orthogonality and Normalization
  • Decoupling the Equations
  • Single Point Excitation and Response
  • Observations
  • Mode Shapes
    • Mode Shapes for a Cantilever
    • Mode Shapes for a Plate
  • Mode Shape Animation

Chapter 3 - Some Essentials of Signal Processing

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  • Analog to Digital (A-D) Conversion
  • Aliasing
    • Avoiding Aliasing
  • Fourier Transforms
    • Fast Fourier Transform
    • Discrete Fourier Transform, DFT
  • Windowing
    • Windowing for Continuous, Random Signals
    • Windowing for Transient, Impulsive Signals
  • System Identification Using the FFT
  • Signal Averaging
  • Coherence
    • Coherence—What’s Good and What’s Bad?
  • Some (Almost) Unbreakable Rules of Signal Processing

Chapter 4 - Introduction to Shock

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  • What is Shock?
  • Causes of Shock
  • Effects and Remedies of Shock

Chapter 5 - A Closer Look at Shock

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  • Terms Used in Mechanical Shock
  • Input Pulse and Response of a Sprung Mass
  • Typical Complex Shock Pulses
  • Shock Pulse Shapes
    • Shock Pulse Shape Parameters—Haversine Shape
    • Classical Shock Pulse Shapes
    • Example of 1000 g 1 ms Shock Pulse—Haversine Shape
  • Critical Frequency Response
  • Response to Shock Pulse

Chapter 6 - Background and Theory of Modal Testing

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  • What Is Experimental Modal Analysis (EMA)?
    • Why Experimental Modal Analysis?
  • Theoretical Modes
    • Stretched String
    • Rail Car
  • Experimental Examples
    • Ship Hull Section
    • Bridge Deck
  • Where Does the Modal Model Fit In to the Scheme of Things?
  • The Time Domain Structural Response
  • The Frequency Domain
  • Experimental Modal Analysis (EMA) Procedure

Chapter 7 - Modal Test Planning and Set-up

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  • Selecting a Test Procedure
    • Steady-State
    • Random
    • Impact
    • Burst Random / Chirp
    • Shaker Testing
  • Impact Testing
  • Response Transducers
    • Strain Gages
    • Laser
    • Accelerometers
      • Strain Gage Accelerometers
      • Charge Accelerometers
      • Voltage Accelerometers
      • Voltage vs. Charge Accelerometers
      • Mounting Accelerometers
    • Transducer Selection: General Considerations

Chapter 8 - Meshing

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  • Meshing, Defined
  • Meshing Considerations
  • The “Pretty Picture” Approach
  • Finer Or Coarser – What’s the Difference?
    • Fine Mesh
    • Coarser Mesh
  • An Interpolation Example
  • Practical Aspects of Marking a Mesh

Chapter 9 - Setting up the Modal Test

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  • Support the Structure
  • Support the Structure—Free Boundary
  • Setting up the Test—Mount the Transducers
  • Accelerometer Mounting Considerations
  • Contact Resonance Considerations
  • Mounting Methods
    • Stud
    • Superglue
    • Beeswax
    • Magnet
    • Mounting Base
    • Double-Mount
    • Miscellaneous
  • Setting up the Test—Suggestions for Making Life Easier
  • Setting up the Analyzer
  • Random Excitation
  • Impact Excitation
  • Windowing the Response Signals
  • Data Acquisition
  • Coherence Examples

Chapter 10 - Modal Parameter Extraction

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  • Natural Frequencies, Modal Damping, and Modal Constant
  • Modal Inferposition
  • Using Single Mode Methods
    • “Quadrature” Method
    • “Circle Fit” Method
    • Modal Residues
  • Multiple Mode Methods

Chapter 11 - Documenting Modal Test Results

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  • Average Coherence Example
  • Correct the Viscous Damping Coefficients
  • Tabulate Results
  • Presenting Mode Shapes
    • Deflected Shape
    • Undeflected and Deflected Shapes
    • Deflected Extremes
    • Arrows
    • Persistence
    • Color Rendition
    • Animations
  • Documentation of Results

Chapter 12 - The Shock Response Spectrum

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  • Shock Response Spectrum (SRS)
  • SRS Mechanical Analog
  • Accepted Definition of SRS
  • Terms used in SRS Analysis
  • Developing SRS
  • SRS Maximax Values
  • Maximum Response Spectra for Various Shock Pulse Shapes
  • Some Properties of the SRS
  • Velocity Sensitive Region of SRS
  • Damping and SRS
    • SRS—Damped Spectra
  • Maximum Response Spectra for Linear SDoF System
  • Designing with SRS
  • Absolute and Relative Deflection SRS
  • The Use of the SRS in Shock Testing
    • Required Spectrum and Allowable Tolerances
    • Shock Specifications
  • Shock Spectrum Analyzers
  • Measuring and Analyzing Mechanical Shock
  • Subroutine for the Calculation of the SRS

Chapter 13 - Measurement of Shock

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  • Force Sensors
  • Load Cell Characteristics
  • Motion—Displacement Trackers
    • Characteristics of  Motion Trackers
  • High Speed Photography
  • Electro-Magnetic Induction
  • Motion—Velocity Sensors
  • Motion—Acceleration
  • Seismic Transducers
    • Seismic Transducer Characteristics
  • Pendulum Calibration
  • Dynamic Calibration of Motion Sensors
  • Cabling
  • Accelerator Attachment
  • Accelerometer  Quick-Check Calibration
  • Accelerometer Loading Effect

Chapter 14 - Shock Testing

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  • Types of Mechanical Shock Testing
    • Impulse Shock Test
  • Shock Pulse — Acceleration, Velocity and Displacement
  • Example
  • Drop Test Machines
  • Navy Impact Machines
  • The “Light-Weight” Shock Tester
  • High-Amplitude, High-Frequency “Impact” Transient Simulators
  • Impact Shock Simulators
  • MIPS Table .. Closer Look
  • Programmable Systems
    • Moderate-Level and/or Mid-Frequency Transients
    • Electrodynamic Shakers
    • Electrohydraulic (EH) Shakers
    • Piezoelectric Shakers
    • Shaker Technologies—Stroke vs. Frequency Range
    • Electrodynamic and Electrohydraulic Exciters
    • Optimized Tailoring
  • Generation of Oscillatory Transients
    • Decaying Oscillatory Acceleration
  • Shaker Optimized Cosine (SHOC) Pulses
  • Least Favorable Response
  • Pyrotechnic Shock
    • Simulating the Damage from a PyroShock “Event”
    • Rupture Energy Fixture
    • More Realistic Pyroshock Arrangements
  • Shock Testing Problem Areas
    • Data As We See It.
    • What Our System Has To Handle
  • Drop Machines
    • Objectives
    • Pendulum Type Shock Machine
    • Free-Fall Shock Machine
    • Drop Testing Machine

Chapter 15A - MIL-STD-810G, Method 516.6, Shock

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Chapter 15B - Undex Underwater Explosions And Surface Testing

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Chapter 15C - Typical Free Fall Shock Test Specification

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  • Free Fall Drop Test Methods
  • Tabulation of Test Data
  • Test Procedures, under 55 lbs.
  • Test Procedures, under 220 lbs.
  • Test Procedures, 220–1,000 lbs
  • Surface Drop Test  
  • Edge Drop Test 
  • Corner drop tests 
  • Equipment Handling
  • Test Set-up Using a Mechanical Device 

Chapter 15D - Table-Top Drop Shock Test

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  • Drop Test Sequence

Chapter 15E - Typical Drop Shock and Vibration Test Specification for Disk Drive Assemblies

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  • Purpose
  • Associated Documents
  • Equipment Required
  • Software
  • Drive Configuration
  • Drop Shock Fixturing
  • Design Verification Testing
  • Design Maturity Testing (DMT)
  • Disk Device Shock/Vibration Specification
  • PCB Shock/Vibration Specification
  • Pneumatic Drop Test Shock Machine
  • Orientation of Axes
  • Drop Shock Test Fixture
  • Drop Shock Test Fixture Adapter to Shock Table
  • Typical Drop Shock Pulse

Appendix A - Glossary of Symbols and Units

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Appendix B - A Brief Run through an EMA Computer Session

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  • Introduction
  • Mesh
  • FRB Program
    • Plots
    • Locate Resonances
    • Curve Fitting
    • Damping, Mode Shapes

Appendix C - Finite Element Analysis

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Appendix D - Matrix Math Revisited

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Final Review

Award of certificates for successful completion

Click for a printable course outline (pdf).

Revised 6/18/2018