The Dynamic Analysis Of An X-braced Lattice Girder Subjected To A Support Excitation

Abstract

Based on the assumption that cross-sections at both ends of each bay remain plane after deformation, each bay of a X-braced lattice girder is replaced by an equivalent beam segment. By considering the requirement that the kinetic energy and strain energy of each bay should be equal to its equivalent beam segment, the mass matrix and stiffness matrix of the equivalent beam segment are derived. The assembly of mass matrices and stiffness matrices of all the equivalent beam segments defines the overall mass matrix and stiffness matrix of an equivalent beam corresponding to the entire X-braced lattice girder. The free vibration analysis of a 10-bay X-braced lattice girder and forced vibration analysis of a 12-bay one due to a support excitation are then made based on the simplified equivalent beams. It is found that the first five natural frequencies of the equivalent beam are in good agreement with those of the original 10-bay X-braced lattice girder obtained from the conventional finite element method or micropolar continuum theory.