Auto-parametric vibration of a cable-stayed-beam structure under random excitation

Auto-parametric vibration of a cable-stayed-beam structure under a random excitation is first studied numerically with emphasis on cable local vibration. A simplified 3-degree-of-freedom model that includes linear as well as nonlinear coupling terms between the cable and beam is employed. The general equivalent linearization method is applied to obtain the random response of the nonlinear system. Results show that when the vertical random excitation to the beam exceeds a critical value, the horizontal motions of the cable and beam are excited due to the auto-parametric nonlinear coupling. In this motion, the structural response possesses a nonstationary characteristic, even though the loading is a stationary random process. The Lyaponov exponent technique is applied to investigate the stability property of the auto-parametric vibration, under harmonic, random, and combined excitations. Effects of the natural frequency ratio and damping on the stability are also investigated.