A Simple Formula for Evaluating the Fundamental Frequency Parameter of Initially Stressed Uniform Beams on Elastic Foundation

Abstract

A simple design formula is derived here to evaluate the fundamental frequency parameter of initially stressed (subjected to axial concentrated load at the ends) uniform beams resting on elastic foundation. Even though the basis for derivation of the formula is based on the finite element method, the applicability of the formula is general and can be used effectively, once the buckling load parameter, stress free frequency parameter and the applied concentrated load parameter are known, to obtain the fundamental frequency parameter of the stressed beam. The assumption involved in deriving the formula is that the mode shapes of buckling, stress free vibration and stressed vibration are the same. The effectiveness of the formula is demonstrated through numerical examples.