Theoretical analysis of non-linear dynamic response of a bridge pier under two-phase flow excitation

In this paper, analytical and numerical approaches are used to investigate the vibration and non-linear dynamic responses of a bridge pier under two harmonic excitations, caused by aero- and hydro-flows, acting on different portions of the beam. The mechanical system is reduced using the Galerkin method to an ordinary differential equation, and the multiple scale method (MSM) is employed to analyse sub- and super-harmonic resonances. The variation of beam amplitude of vibration caused by a significant effect due to axial force, and two-frequency excitations due to flows are captured. These conduct to the evaluation of nonlinear dynamic behaviour through some frequency-response curves, time history curves of amplitudes vibrations, and phase diagrams presented. In order to gain more features of this system, the discrete general equation is treated numerically. The results show a good accordance between the analytical and numerical solutions.