Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

Abstract

A precise analytical solution has been developed using Energy Method to predict the dynamic instability bounds of simply supported beams on elastic foundation, with a focus on the impact of the higher transition foundation on dynamic stability boundaries. To determine the dynamic instability zones, a trigonometric function with a single term that meets the geometric boundary criteria to represent lateral deflection is used. For the analysis, Euler-Bernoulli beam theory is employed. Numerical results are presented in non-dimensional form in both digital and/or analogue forms, with varying foundation parameters below and above the transition foundation values of an elastic foundation. When compared to those produced using the finite element approach, the current findings exhibit a fair degree of consistency. The impact of the elastic foundation’s first and higher transition foundation values on dynamic stability behavior is amply demonstrated in the current study. According to the studies, when the elastic foundation parameter value increases, the width of the dynamically unstable zones decreases, making the beam less susceptible to the dynamic stability phenomena under periodic loads. By using the precise non-dimensional parameters for the imposed periodic load and its radian frequency, the presence of the master dynamic instability curves is demonstrated in the current work.