Stability of beams on modified Vlasov foundation subjected to lateral loads acting on the ends

Using the variational principle,an analytical method for the stability analysis of beams on modified Vlasov foundation subjected to lateral loads acting on the ends was developed.The buckling loads and the corresponding mode shapes of the beams could be determined by solving the eigenvalues of the boundary conditions of the beams.It was shown by the parametric study that the effect of the lateral loads acting on the ends was negligible when the height length ratio of the beams was large.Meanwhile,the effect should be considered when the value of the height-length ratio was small.