移动车辆非定常气动力时域模拟及分析

为了在时域中考虑复数导纳函数，精细化模拟作用在移动列车上的非定常气动力，提出列车复数导纳函数时频变换方法，并建立同时考虑顺风向、横风向和竖向脉动风的移动列车非定常气动力数学模型。首先，推导出相对于移动列车的瞬时风速，并将瞬时风速代入到移动列车风荷载模型中，通过泰勒级数展开和忽略脉动风速、三角函数高阶项，将移动列车非定常气动力表示成关于顺风向、横风向和竖向脉动风的函数。然后，基于有理函数逼近法，将频域的复数导纳函数展开成有理函数项表示，再通过拉普拉斯逆变换实现导纳函数的时频变换，并将变换后的时域导纳函数代入推导的气动力模型中，精细化模拟移动列车非定常气动力。最后，通过与加权函数法对比，验证基于有理函数逼近法模拟移动列车非定常气动力方法的正确性，分析复数导纳函数相位、横风向和竖向脉动风对列车非定常气动力的影响。研究结果表明：有理函数逼近法可以成功实现列车复数导纳函数的时频变换，能够在非定常气动力时域模拟中有效考虑复数导纳函数的相位特性；导纳函数能够降低气动力的峰值，其相位可以使得非定常气动力时程产生“延迟”；横风向和竖向脉动风对列车非定常气动力的贡献不容忽视，能够使得气动力峰值显著增大；在列车非定常气动力模拟中，应该综合考虑复数导纳函数以及横风向和竖向脉动风的影响。研究结果可为移动列车风荷载及风-车-桥耦合振动等相关研究提供参考。

Simulation and Analysis of Unsteady Aerodynamic Forces Relative to Moving Vehicle

In order to consider a complex-valued admittance function in the time domain, and precisely simulate the unsteady aerodynamic forces relative to a moving vehicle, a method was proposed for transferring the complex-valued admittance function of a vehicle from the frequency domain to the time domain, and the mathematical model for the unsteady aerodynamic forces of a moving vehicle was derived by considering the longitudinal, lateral, and vertical turbulence components. First, the instantaneous wind speed relative to the moving vehicle was derived and substituted into the models for the wind loads of the moving vehicle. With Taylor's series expansion and neglecting the higher-order items of the fluctuations and trigonometric functions, the unsteady aerodynamic forces relative to the moving vehicle were expressed as functions that considered the longitudinal, lateral, and vertical turbulence components. Then, based on the rational function approximation approach, the frequency-domain complex-valued admittance function was expressed with rational functions; hence, it was transformed from the frequency domain to the time domain using inverse Laplace transformation. The time-domain admittance function was submitted to the derived aerodynamic functions to precisely simulate the unsteady aerodynamic forces relative to the moving vehicle. Finally, by comparing with the weighting function method, the method for simulating the unsteady aerodynamic forces of a moving vehicle using the rational function approximation approach was validated to be accurate. The influences of the complex-valued admittance function and lateral and vertical turbulence components on the unsteady aerodynamic forces of the moving vehicle were analyzed. The results indicated that the rational function approximation approach could successfully transfer a complex-valued admittance function from the frequency domain to the time domain, and the phase of the admittance function could be considered in the time-domain simulation of the unsteady aerodynamic forces. The admittance function could reduce the peak values, and its phase led to time lags for the unsteady aerodynamic forces. The contributions of the lateral and vertical turbulence components to the unsteady aerodynamic forces of a moving vehicle could not be ignored, which could significantly increase the peak values of the aerodynamic forces. It is necessary to consider the complex-valued admittance function and lateral and vertical turbulence components when simulating the unsteady aerodynamic forces of a vehicle. The results of the present study could be used for relevant research such as on the wind loads relative to moving vehicles and wind-vehicle-bridge coupled vibrations.