ANALYTIC SOLUTION OF DYNAMIC CHARACTERISTICS OF NON-UNIFORM ELASTICALLY SUPPORTED BEAM WITH ARBITRARY ADDED MASSES

A practical model for calculating the dynamic characteristics of non-uniform elastically supported beam (bridge) with arbitrary added masses is given according to the structure characteristics of non-uniform beam bridges. The improved perturbation method (IPM) is obtained by modifying the mode perturbation method based on Bernoulli-Euler beam theory. In the modal subspace of the beam, the variable coefficient differential vibration equation of the beam with arbitrary added masses is converted to nonlinear algebraic equations. IPM is suitable for solving the vibration equation of a simply supported and continuous non-uniform beam (bridge). The examples that are analyzed, demonstrate the high precision and fast convergence speed of the IPM. A timesaving method (SIPM) for the dynamic characteristics of a symmetrical beam (bridge) based on the symmetry of mode shape is developed. SIPM has about half the number of coefficients and unknowns as does IPM. SIPM has higher computational efficiency and the accuracy of SIPM is very close to IPM. Eventually, the effects of elastic supports and added masses on dynamic characteristics of a three-span non-uniform beam bridge are reported.