Modelling with Lagrange’s Method and Experimental Analysis in Cable-Stayed Beam

The dynamic behavior of cable-stayed beam is investigated. Considering the nonlinear of the beam, the equations of the cable-stayed beam are obtained with the help of the Lagrangian multiplier method which can combine the boundary conditions. Then setting the determinant of the coefficient matrix equal to zero, the exact eigenvalues can be given accurately. Following, the results of the parametric analysis on the in-plane and out-of-plane eigen-problems are presented. Afterwards, the global, local and coupled modes are introduced. Then we redefine the three modes on the basis of the frequency contribution theory. Later, the internal resonance that appears with the changes of the parametric is surveyed properly. The system parameters having been carefully measured from the experimental model. Then, steady-state solutions of the coupled nonlinear equations of motion are obtained by the perturbation method of multiple time scales. The model experiments and numerical analyses show that the appropriate design of the damping property will lead to better control performance.