Dynamic stability of beams on elastic foundation

Abstract

Accurate closed form solution to predict the dynamic stability behavior of simply supported beams on elastic foundation, subjected to a concentrated end axial periodic load, has been derived using single term trigonometric function which satisfy the geometric boundary conditions in conjunction with the variational formulation. Euler - Bernoulli beam theory is used for the analysis. Numerical results are presented in the nondimensional form with varying foundation parameters below and above the first transition value of elastic foundation in both the digital and analogue forms. The present results show a good agreement when compared with those obtained by the versatile finite element method. The effect of the first transition value of the elastic foundation on the dynamic stability behavior is brought out in the present work.