Buckling mode localization in nonhomogeneous beams on elastic foundations

Buckling mode localization in nonhomogeneous beams on elastic foundations is studied in this paper. The classical theory of localization for randomly disordered nearly periodic structures is extended to nonhomogeneous continuous structures. Lyapunov exponents, which characterize the average exponential rates of growth or decay of amplitudes of deformation, are determined using the method of transfer matrix. The smallest positive Lyapunov exponent is the localization factor of interest. As an alternative approach, Greenʹs function method coupled with a finite element formulation is applied to evaluate the localization factors. The results obtained in this paper provide an explanation on localized buckling observed in experiments.