Modal Analysis
for Structural Validation

Course No. 195

(Course Outline shown below.)

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 application of the modal test results.

Certificate Programs  This course is required for TTi’s Mechanical Design Specialist (MDS) Certificate Program. It may be used as an elective for any TTi specialist certificate program (see http://www.ttiedu.com/certprog.html).

Related Courses See course 142-4, Mechanical Shock and Modal Test Techniques (see http://www.ttiedu.com/142-4cat.html).

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

Text  Each participant will receive a course workbook, which contains most of the viewgraphs used during the presentation.

Course Hours, Certificate and CEUs  Open courses meet seven hours per day. Upcoming presentation dates can be found on our current open course schedule (see http://www.ttiedu.com/schedule.html). 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.

Course Outline No. 195

• Background and Theory of Modal Testing
  • Experimental Modal Analysis (EMA)
  • Theoretical Modes
  • Experimental Examples - Ship Hull Section, Bridge Deck
  • The Time Domain Structural Response
  • The Frequency Domain
  • Experimental Modal Analysis (EMA) Procedure
• Single-Degree-of-Freedom (SDoF) and 2DoF Systems
  • The Single Degree of Freedom System
    • Spring, k
    • Mass, m
    • Damper, c
  • Motion of an SDoF System
  • The Impulse Response Function, h(t)
  • The Frequency Response Function (FRF)
  • Displaying the FRF
  • Nyquist Plot
  • Structural Dynamic Relationships
  • Two Degrees of Freedom (2DoF)
  • 2DoF Frequency Response
• Multiple-Degrees of Freedom (MDoF) Systems
  • Natural Frequencies and Mode Shapes
  • Modal and Frequency Matrices
  • Orthogonality and Normalization
  • Decoupling the Equations
  • Single Point Excitation and Response
  • Mode Shapes for: Cantilever; Plate
  • Mode Shape Animation
• Some Essentials of Signal Processing
  • Analog to Digital (A-D) Conversion
  • Aliasing
  • FFT
  • DFT
  • Windowing for Continuous, Random and Transient Signals
  • System Identification Using the FFT
  • Signal Averaging
  • Coherence
  • Rules of Signal Processing
  • Time and Frequency Domain Terminology
• Modal Test Planning and Set-up
  • Selecting a Test Procedure
    • Steady-State
    • Random
    • Impact
    • Burst Random / Chirp
    • Shaker Testing
    • Impact Testing
  • Response Transducers
    • Strain gages
    • Laser
    • Accelerometers
    • Charge accelerometers
    • Voltage Accelerometers
    • Voltage vs. Charge Accelerometers
    • Mounting Accelerometers
  • Transducer Selection
• Meshing:
  • Definition, Considerations
  • The “Pretty Picture” Approach
  • Fine Mesh vs. Coarser Mesh
  • An Interpolation Example
  • Practical Aspects of Marking a Mesh
• Setting up the Modal Test
  • Support the Structure
  • Free Boundary
  • Mounting Transducers
  • Contact Resonance
  • Mounting Methods
    • Stud
    • Superglue
    • Beeswax
    • Magnet
    • Mounting Base
    • Double-Mount
  • Suggestions for Making Life Easier
  • Setting up the Analyzer
  • Random Excitation
  • Impact Excitation
  • Windowing the Response
  • Coherence Function
  • Coherence Examples
• Modal Parameter Extraction
  • Natural Frequencies, Modal Damping, and Modal Constant
  • Modal Inferposition Using Single Mode Methods
  • “Quadrature” method
  • “Circle Fit” Method
  • Modal Residues
  • Multiple Mode Methods
• Documenting Modal Test Results
  • Average Coherence Example
  • Viscous Damping Coefficients
  • Presenting Mode Shapes
    • Deflected Shape
    • Undeflected & Deflected Shapes
    • Deflected Extremes
    • Arrows
    • Persistence
  • Color Rendition
  • Presenting Mode Shapes - Animations
• Summary, Final Exam
• Award of certificates for successful completion

For schedules, enrollment information and more, visit http://www.ttiedu.com.

• Fixture Design for Vibration and Shock Testing
• Fundamentals of Vibration for Test Applications
• Mechanical Shock and Modal Test Techniques
• Mechanical Shock Techniques
• Product Noise Control
• Vibration and Shock Test Control Techniques