Effect of Higher Transition Foundation on Dynamic Stability Boundaries of Simply Supported Beam

Abstract

Abstract Accurate closed form solution to predict the dynamic stability behavior of simply supported (SS) beam on elastic foundation, subjected to an end axial periodic load, has been derived using simple single term trigonometric function which satisfies the geometric boundary conditions. The effect of higher transition foundation on dynamic stability regions is studied. The energy method is used in the present work to evaluate the dynamic stability boundaries. Euler - Bernoulli beam theory is used for the analysis. Numerical results are presented using proper non-dimensional parameters with varying foundation parameters below and above the second transition foundation value of elastic foundation, in both the digital and analogue forms for better comprehension of the dynamic stability behavior of the beams. The effect of the higher transition foundation value of the elastic foundation on the dynamic stability behavior is brought out in the present work.