Simple Mechanical Models

  • George J. Simitses


Two single-degree-of-freedom mechanical models and one two-degree-of-freedom model are employed in this chapter to demonstrate the concept of dynamic stability for the extreme cases of the ideal impulse and sudden constant load of infinite duration. These models are typical of imperfection-sensitive structural configurations. They are kept as simple as possible, so that the emphasis can easily be placed on the concepts rather than on complex mathematical theories. For each model, the static stability analysis, based on the total potential energy approach, is given in detail. In addition, the total energy-phase plane approach is used for one model. For the same model, the equations of motion approach is also used, for demonstration and comparison purposes. The main emphasis, though, is placed on the total potential energy approach.


Saddle Point Critical Load Total Potential Initial Kinetic Energy Static Equilibrium Position 
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  1. 1.
    Hoff, N.J. Dynamic stability of structures. Dynamic Stability of Structures (edited by G. Herrmann). Pergamon, New York, 1967.Google Scholar
  2. 2.
    Budiansky, B., Roth, R.S. Axisymmetric dynamic buckling of clamped shallow spherical shells. Collected Papers on Instability of Shell Structures. NASA TN D-1510, 1962.Google Scholar
  3. 3.
    Simitses, G.J. An Introduction to the Elastic Stability of Structures. Prentice-Hall, Englewood Cliffs, N.J., 1976.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1990

Authors and Affiliations

  • George J. Simitses
    • 1
    • 2
  1. 1.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiCincinnatiUSA

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