Simple Mechanical Models
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.
KeywordsSaddle Point Critical Load Total Potential Initial Kinetic Energy Static Equilibrium Position
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