考虑温度影响的斜拉索参数振动模型及响应分析

Analysis of Cable Parametric Vibration Model and Response with Consideration of Temperature Effect

研究超长斜拉索在非均匀温度场和桥面激励联合作用下的振动问题。考虑斜拉索几何非线性和大气梯度温度场的影响,将温度场力作为斜拉索振动的边界条件,提出了梯度温度场和桥面激励联合作用下的斜拉索参数振动模型。基于伽辽金模态截断理论,推导了斜拉索面内主参数振动方程,利用多尺度法获得了温度和桥面联合激励作用下的斜拉索幅频响应方程,并编制程序进行数值计算,分析了梯度温度场、调谐值、桥面激励幅值和阻尼对其参数振动的影响规律。结果表明:梯度温度场中的斜拉索振动亦具有明显的硬弹簧特性,随着调谐值的增大,幅频响应曲线逐渐弯曲成直角,引起多值响应。温度场中拉索振动有明显的"拍"特征,随着温度升高,斜拉索参数共振区域逐渐增大,温度和桥面联合激励下的拉索振幅比单一桥面激励振幅要小;随着桥面激励幅值的增大,拉索共振区和振动幅值均明显增大,但共振区和振幅随阻尼增大而减小。

The vibration of super-long cable under joint effect of non-uniform temperature field and deck excitation was analyzed. A model of cable parametric vibration under the joint effect of gradient temperature field and deck excitation was set up by considering the impacts of cable nonlinearity and atmospheric gradient temperature field and taking force of temperature field as the boundary of cable vibration. Based on Galerkin method,the main parametric vibration equation within cable plane was developed and the equation of cable amplitude-frequency response under joint excitation of temperature and deck was obtained by means of multi-scale method. Program for numerical computation was prepared and the law of influences on their parametric vibrations imposed by gradient temperature field,detuning value and deck excitation amplitude was analyzed and explored. The results show that the cable vibration in gradient temperature field is of apparent hard spring nature. With the increased detuning the amplitude-frequency response curve gradually changed to straight angle and multiple-responses were caused. The cable vibration in the temperature field bears feature of ＂patting＂. With the increase of temperature the cable parametric resonance area gradually expanded. The cable vibration amplitude under joint excitation of temperature and deck is lower than that of single cable plane. With the increased deck excitation amplitude,both the cable resonance area and vibration value increased notably. However,the resonance area and vibration amplitude decrease with increased damping.