An Introduction to Structural Dynamics, Experimental Modal Analysis and Substructuring by Matt Allen, May 2021

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Introduction to Structural Dynamics Matt Allen May112021
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An Introduction to Structural Dynamics, Experimental Modal Analysis and Substructuring

Matthew S. Allen

Professor, Brigham Young University

May 11, 2021


Dynamic loads have destroyed countless aircraft, vehicles, machines, and civil structures, and so significant effort is invested in modeling various structures to ensure that they can survive their dynamic environments. These models always include simplifications, especially near the joints or interfaces between parts, and so testing is required to verify that the simulation models are correct, especially for high-consequence systems such as launch vehicles. This talk provides an overview of some key concepts in structural dynamics, including modes and modal analysis, frequency response, experimental modal analysis, and adaptations of the concept of modes for systems with weak nonlinearities. Substructuring concepts are also reviewed, in which the dynamics of an assembly are predicted from the dynamics of its parts. Particular attention is given to the joints between parts and the uncertainties and damping that they can introduce.


Matt Allen is a Professor in the Mechanical Engineering Department at Brigham Young University. Prior to that, he taught for 15 years in the Department of Engineering Physics at the University of Wisconsin-Madison. He received a B.S. in Mechanical Engineering from BYU, M. S., and Ph.D. degrees from Georgia Tech in 2005 and was a post-doc at Sandia National Laboratories. He enjoys playing sheep’s head (Bavarian card game) during breaks at IMAC, trying new kinds of ice cream and skiing, hiking, biking or almost anything to do with mountains.

Video Presentation


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Associated Papers

  1. E. Jewell, M. S. Allen, I. Zare, and M. Wall, “Application of Quasi-Static Modal Analysis to a Finite Element Model and Experimental Correlation,” J. Sound Vib., vol. 479, no. 4 August, Art. no. 4 August, 2020, available:
  2. H. Festjens, G. Chevallier, and J.-L. Dion, “A numerical tool for the design of assembled structures under dynamic loads,” Int. J. Mech. Sci., vol. 75, pp. 170–177, 2013, available:
  3. M. R. W. E. Brake, The Mechanics of Jointed Structures. Springer, 2017.
  4. E. H. Dowell, “Damping In Beams And Plates Due To Slipping At The Support Boundaries,” J. Sound Vib., vol. 105, no. 2, Art. no. 2, 1986, available:
  5. M. P. J. Wall, A. Allen Matthew S., and R. J. Kuether, “Observations of Modal Coupling due to Bolted Joints in an Experimental Benchmark Structure,” Mech. Syst. Signal Process., vol. (submitted), Dec. 2020.
  6. R. M. Lacayo and M. S. Allen, “Updating Structural Models Containing Nonlinear Iwan Joints Using Quasi-Static Modal Analysis,” Mech. Syst. Signal Process., vol. 118, no. 1 March 2019, Art. no. 1 March 2019, 2019.
  7. M. Griebel, A. Johnson, B. Erickson, J. Sills, and M. S. Allen, “Orion MPCV Nonlinear Dynamic Correlation and Model Updating using Quasi-Static Modal Analysis,” presented at the 2021 Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, CA, Jun. 2021.
  8. D. A. Najera-Flores and R. J. Kuether, “A Study of Whole Joint Model Calibration Using Quasi-Static Modal Analysis,” J. Vib. Acoust., vol. 142, no. 051109, Jun. 2020, available:
  9. S. Baek and B. Epureanu, “Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers,” J. Vib. Acoust., vol. 139, no. 061011, Aug. 2017, available:
  10. D. J. Segalman, “A Four-Parameter Iwan Model for Lap-Type Joints,” J. Appl. Mech., vol. 72, no. 5, Art. no. 5, Sep. 2005.
  11. D. J. Segalman et al., “Handbook on Dynamics of Jointed Structures,” Sandia National Laboratories, Albuquerque, NM 87185, 2009.
  12. W. D. Iwan, “ON DEFINING EQUIVALENT SYSTEMS FOR CERTAIN ORDINARY NONLINEAR DIFFERENTIAL EQUATIONS,” Int. J. Non-Linear Mech., vol. 4, no. 4, Art. no. 4, 1969, available:
  13. D. Shetty and M. S. Allen, “Fast Simulation of a Single Degree-of-Freedom system consisting of an Iwan element using the Method of Averaging,” ASME J. Vib. Acoust., vol. 142, no. 5, Oct. 2020, available:
  14. I. Zare and A. Allen Matthew S., “Time-Domain Numerical Continuation of Periodic Orbits for Harmonically Forced Hysteretic Nonlinear Systems,” J. Sound Vib., vol. (Submitted Sept 2020).