Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

Abstract

In the deign of the modern aerospace structural members, due the stringent requirement of light weight and low margins of safety, it is essential to establish the design adequacy by evaluating the stiffness related behavior, like the large lateral amplitude/deflection vibration and postbuckling, through a rigorous geometric nonlinear analysis. Though many complex formulations, either by using the continuum or numerical methods are available in the literature, the heuristic formulae developed recently, for these entirely different nonlinear problems, are similar. Hence, it is possible to unify, these simple formulae, not recognized till now. The unification of these formulae facilitates to obtain the solution for the large amplitude vibration problem from the known solution of the postbuckling of the structural members and vice versa, for a specified lateral amplitude/deflection. This novel concept of the unification is successfully demonstrated through the isotropic uniform beams/columns and thin square plates.