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为得到悬浮隧道锚索模态耦合内共振特性,建立了悬浮隧道锚索面内、外耦合非线性振动偏微分方程。根据锚索的线性振动模态,通过Galerkin方法,将该偏微分方程转化为常微分方程,得到锚索面内一阶模态与面外一阶模态的耦合振动方程。采用数值分析方法,研究悬浮隧道锚索的1∶1模态耦合内共振特性。结果表明:锚索在面内简谐荷载作用下,在一定的激励频率和激励幅值的作用下容易产生模态耦合内共振;在模态耦合内共振频率区间内,随着频率比的增大,锚索产生模态耦合内共振所需激励幅值逐渐增大;且在此区间内,随着激励幅值的逐渐增大,锚索的面内跨中振幅逐渐增大,而锚索的面外跨中振幅由零逐渐增大,达到峰值后逐渐减小,直至恢复纯平面振动。
In order to obtain the modal coupling internal resonance characteristics of suspended tunnel anchor cables, a nonlinear partial differential equation of the in-plane and out-coupled suspension cables for suspended tunnels is established. According to the linear vibration mode of anchor cable, this partial differential equation is transformed into an ordinary differential equation by Galerkin method, and the coupling vibration equation of the first-order mode and the first-order modes in the anchor plane is obtained. The numerical analysis method is used to study the 1: 1 mode coupling internal resonance characteristics of suspended tunnel anchor cables. The results show that the mode coupling internal resonance easily occurs under the action of simple excitation and in-plane excitation frequency under the effect of simple in-plane harmonic load. In the mode coupling internal resonance frequency range, with the increase of frequency ratio The amplitudes of excitation needed for the large and anchor cables to produce mode coupling internal resonance increase gradually; and in this interval, as the amplitude of excitation gradually increases, the amplitude of in-plane cross-cables of the cables gradually increases, while the anchor cables The amplitude of the out-of-plane crosstalk gradually increases from zero to peak and then decreases until it returns to pure-plane vibration.