Prediction of dynamic stability behavior of structural members subjected to periodic load through the concept of dynamic stability point

Abstract

The structural members, used in many fields of engineering, are often subjected to the time dependent loads. These loads can be expressed as the sum of a series of periodic loads with discrete frequency content and a constant load by using either Fourier or Harmonic analysis. The periodic load with the least frequency is of practical importance to investigate the dynamic stability behavior of the structural members. Mathematically complex formulations are proposed by several researchers to investigate the dynamic stability phenomenon. However, the design engineers often look for simple design formulas to quickly assess the dynamic stability behavior of structural members. An attempt is made here to evaluate the dynamic stability regions of the structural members, through the concept of the dynamic stability point, which is used, to derive a dynamic stability formula, from which the dynamic stability regions can be easily evaluated. The dynamic stability point has the same value for any structural member, irrespective of boundary conditions and other complicating effects. The usefulness of the proposed point is demonstrated through a uniform thin square plate subjected to periodic load.