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首页> 外文期刊>International journal of non-linear mechanics >Investigation of dynamic behavior of a cable-stayed cantilever beam under two-frequency excitations
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Investigation of dynamic behavior of a cable-stayed cantilever beam under two-frequency excitations

机译：双频激发下电缆延住悬臂梁动态行为的研究

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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.
机译：可以使用电缆延住的悬臂梁进行建模许多民用结构和设施。该研究是通过理论分析研究缆绳悬臂梁的非线性动态响应和动态行为，经过两种不同的外部激励。首先，建立电缆和光束的运动方程。然后，基于Galerkin方法，动态结构响应被表示为模式形状的叠加，具有广义的时间坐标作为未知系数。为了获得未知的系数，通过使用多个尺度的方法导出控制幅度和相位的调制方程。考虑了四种同时共振的代表性病例（四个代表性激励案例）。基于导出的分析解决方案，对于每种情况，通过参数研究获得系统的频率响应和幅度响应，并探讨了系统的非线性动态行为。所得结果表明：（1）梁和电缆都可以在频率响应中表现出硬化弹簧性能和软化弹簧特性;并且电缆经历比光束的响应更大的响应，尽管在光束上施加激动; （2）二次谐振的幅度变化对光束和电缆响应的影响小于初级谐振; （3）添加二次谐振，例如订单1/2和1/3次谐振谐振和订单2和3超声谐振，初级谐振可以抑制光束或电缆的响应一定程度。

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