Buckling mode localization in randomly disordered multispan continuous beams

Abstract

Buckling mode localization in large randomly disordered multispan continuous beams is studied. When the cross-sections of each span are uniform, an exact formulation is employed to establish the equations of equilibrium in terms of the angles of rotations at the supports. When the cross-sections of each span are not uniform, a finite element method is applied to set up the governing equations. Two approaches are applied to determine the localization factors, which characterize the average exponential rates of growth or decay of amplitudes of deformation. The first method applies a transfer matrix formulation and Furstenberg's theorem on the asymptotic behavior of products of random matrices. The second method uses a Green's function formulation for a linear eigenvalue problem of a block tridiagonal form.