195 Modal Analysis for Structural Validation

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

Objectives  Engineers and designers need to understand and determine the magnitude of vibration and modal characteristics of a structural system in its operating conditions. There are two ways to achieve this:

  • modal analysis (the theoretical approach), and
  • modal testing (the experimental approach).

Brief Course Description  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, 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.

This TTi course begins with a review of structural and dynamic theory before examining methods of measuring frequency response from the structure under test. Next, 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 presentation of the modal test results.

Diploma Programs  This course is a recommended optional course for TTi’s Mechanical Design Specialist (MDS) Diploma Program. It may be used as an optional course for any TTi specialist diploma program.

Related Courses See course 142-4, Mechanical Shock and Modal Test Techniques. Course 142-4 includes many chapters of course 195 and is available as a completed OnDemand Internet course.

Prerequisites  There are no definite prerequisites for this course. However, this course is aimed toward individuals involved in a related technical field.

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.

OnDemand Internet Short Topics Many chapters of course 195 are available as OnDemand Internet Short Topics. See the course outline below for details.

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.

Click for a printable course outline (pdf).

Course Outline

Chapter 1 - Background and Theory of Modal Testing

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OnDemand Short Topics$50.00
  • 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 2 - Single-Degree-of-Freedom (SDoF) and 2DoF Systems

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OnDemand Short Topics$200.00
  • 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 3 - Multiple-Degrees of Freedom (MDoF) Systems

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OnDemand Short Topics$150.00
  • 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 4 - Some Essentials of Signal Processing

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OnDemand Short Topics$200.00
  • 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 5 - Modal Test Planning and Set-up

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OnDemand Short Topics$250.00
  • 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 6 - Meshing

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OnDemand Short Topics$50.00
  • 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 7 - Setting up the Modal Test

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OnDemand Short Topics$150.00
  • 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 8 - Modal Parameter Extraction

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OnDemand Short Topics$50.00
  • Natural Frequencies, Modal Damping, and Modal Constant
  • Modal Inferposition
  • Using Single Mode Methods
    • “Quadrature” Method
    • “Circle Fit” Method
    • Modal Residues
  • Multiple Mode Methods

Chapter 9 - Documenting Modal Test Results

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OnDemand Short Topics$50.00
  • 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

Appendix A - Glossary of Symbols and Units

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OnDemand Short Topics$25.00

Appendix B - A Brief Run through an EMA Computer Session

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OnDemand Short Topics$25.00
  • Introduction
  • Mesh
  • FRB Program
    • Plots
    • Locate Resonances
    • Curve Fitting
    • Damping, Mode Shapes

Appendix C - Finite Element Analysis

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OnDemand Short Topics$25.00
  • The FEA Model
  • Nodes and Elements
  • The Element Shape Function
  • General Analysis Considerations
  • Linear vs. Nonlinear Analysis
  • General Steps of the Finite Element Method
  • Engineering Applications of the Finite Element Method
  • Warning: The Computed Answer May Be Wrong

Appendix D - Matrix Math Revisited

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OnDemand Short Topics$25.00

Summary, Final Review

Award of certificates for successful completion

Click for a printable course outline (pdf).

Updated 190910