Investigation of dynamic behavior of a cable-stayed cantilever beam under two-frequency excitations

Abstract

Many civil structures and facilities can be modeled using cable-stayed cantilever beams. This study is to investigate the nonlinear dynamic response and dynamic behavior of a cable-stayed cantilever beam subjected to two different external excitations through theoretical analyses. First, the equations of motion of the cable and the beam are established. Then, based on the Galerkin method, dynamic structural responses are expressed into the superimposition of mode shapes, with the generalized time coordinates as unknown coefficients. To obtain the unknown coefficients, modulation equations governing the amplitude and phase are derived by using the method of multiple scales. Four representative cases of simultaneous resonances (four representative excitation cases) are considered. Based on the derived analytical solutions, for each case, the frequency response and amplitude response of the system are obtained through parametric studies and nonlinear dynamic behavior of the system are explored. The obtained results demonstrate: (1) both the beam and the cable can behave the harden spring properties and the soften spring property in the frequency response; and the cable experiences larger response than the beam although excitations are applied on the beam; (2) the effect of the amplitude variation of secondary resonance on the responses of the beam and the cable is smaller than the primary resonance; and (3) the addition of a secondary resonance, such as Order 1/2 and 1/3 sub-harmonic resonance and Order 2 and 3 super-harmonic resonance, to the primary resonance can suppress the response of the beam or the cable to a certain extent.