To study the dynamic behavior of cable-stayed bridges, a linear multi-cable-stayed beam model is developed to investigate its in-plane and out-of-plane transverse vibrations. From the full-bridge perspective, an in-plane nonlinear single-mode discrete model is established. First, the in-plane and out-of-plane motion equations of the system and their boundary conditions are derived. Second, by employing the separation of variables method, the linear eigenvalue problems are solved. The influences of the mass ratio, stiffness ratio, and cable sag on the occurrence of global, local, and coupled vibration modes are studied. Third, frequency response, amplitude response, phase diagram, time history, and power spectrum are extracted to investigate the system’s nonlinear dynamic behaviors. The obtained results demonstrate that for the in-plane motion, the occurrence of global and local modes of the system depends on the mass and stiffness ratios between cable and beam significantly; for the out-of-plane motion, without the elastic support of the cable, the global modes occur, which can be suppressed by adjusting the mass and stiffness ratios between cable and beam but may in turn induce the cable’s local vibration modes; for the nonlinear analysis, the single-degree-of-freedom system behaves like a hardening spring. Its lower branch behaves more complicated than the higher one and has a double-periodic steady-state solution. The system with large damping ratio behaves shows weak hardening spring property.

中文翻译：

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多斜拉梁模型的建模、动力学和参数化研究

为了研究斜拉桥的动力行为，开发了线性多斜拉梁模型来研究其平面内和平面外横向振动。从全桥的角度，建立了面内非线性单模离散模型。首先，推导了系统的平面内和平面外运动方程及其边界条件。其次，采用变量分离法解决了线性特征值问题。研究了质量比、刚度比和缆索垂度对全局、局部和耦合振动模式发生的影响。第三，提取频率响应、幅度响应、相图、时间历程和功率谱来研究系统的非线性动态行为。所得结果表明，对于面内运动，系统全局和局部模态的出现显着取决于索梁之间的质量和刚度比；对于面外运动，在没有拉索弹性支撑的情况下，会出现全局模态，可以通过调整拉索与梁之间的质量和刚度比来抑制全局模态，但反过来可能会引起拉索的局部振动模态；对于非线性分析，单自由度系统就像一个硬化弹簧。其较低的分支比较高的分支表现得更复杂，并且具有双周期稳态解。阻尼比大的系统表现出弱的硬化弹簧特性。在没有电缆弹性支撑的情况下，会出现全局模态，这可以通过调整电缆和梁之间的质量和刚度比来抑制，但反过来可能会引起电缆的局部振动模式；对于非线性分析，单自由度系统就像一个硬化弹簧。其较低的分支比较高的分支表现得更复杂，并且具有双周期稳态解。阻尼比大的系统表现出弱的硬化弹簧特性。在没有电缆弹性支撑的情况下，会出现全局模态，这可以通过调整电缆和梁之间的质量和刚度比来抑制，但反过来可能会引起电缆的局部振动模式；对于非线性分析，单自由度系统就像一个硬化弹簧。其较低的分支比较高的分支表现得更复杂，并且具有双周期稳态解。阻尼比大的系统表现出弱的硬化弹簧特性。其较低的分支比较高的分支表现得更复杂，并且具有双周期稳态解。阻尼比大的系统表现出弱的硬化弹簧特性。其较低的分支比较高的分支表现得更复杂，并且具有双周期稳态解。阻尼比大的系统表现出弱的硬化弹簧特性。