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.

可以使用斜拉式悬臂梁对许多民用建筑和设施进行建模。本研究旨在通过理论分析来研究斜拉悬臂梁在两种不同的外部激励作用下的非线性动力响应和动力特性。首先，建立电缆和梁的运动方程。然后，基于Galerkin方法，将动态结构响应表达为模态形状的叠加，而广义时间坐标为未知系数。为了获得未知系数，使用多尺度方法推导了控制振幅和相位的调制方程。考虑了同时共振的四个代表性情况（四个代表性的激发情况）。根据导出的解析解，对于每种情况，通过参数研究获得了系统的频率响应和幅度响应，并探讨了系统的非线性动力学行为。得到的结果表明：（1）梁和电缆在频率响应中都可以表现出硬化弹簧特性和软化弹簧特性。尽管在梁上施加了激励，但电缆比梁具有更大的响应；（2）次级共振幅度变化对梁和电缆响应的影响小于初级共振；（3）在初级共振上增加一个次级共振，例如1/2和1/3阶次谐波共振以及2和3阶超谐波共振，可以抑制光束或电缆对在一定程度上。