路面非周期一维温度场的傅里叶级数解

首先把路面温度场简化为非周期一维温度场,用分离变量法得到齐次边界条件下与温度场基本方程相容的傅里叶级数;然后用格林公式在边界展开热传导方程,得到傅里叶级数系数的常微分方程组,并用拉普拉斯变换求解;最后用实测数据标定的材料参数预测路面温度场。分析结果表明：傅里叶级数第4项仅在-0.1℃～0.1℃范围内波动;初始温度扰动对温度场有短时影响,如果扰动深度增大则影响时间变长;用实测数据标定模型后,模型可以较准确地预测路面温度场,标准差为1.88℃。

Fourier Series Solution of Non-periodic 1-D Temperature Field of Pavement

Pavement temperature field was simplified as non-periodic 1-D temperature field.Under homogeneous boundary conditions,Fourier series that was compatible with the basic equation of temperature field was obtained by separation of variables.Then,employing Green’s formula to expand heat conduct equation at boundary,equations about coefficient of Fourier series were obtained.Using Laplace transform,the solutions were gotten.Finally,pavement temperature field was predicted by calibration of the material parameter with measured data.Analysis results show that Fourier series convergence is rapid,series No.4 ranges from-0.1 ℃ to 0.1 ℃.Initial temperature perturbation has effect on the temperature field for short time.The deeper the disturbance is,the longer the influenced time becomes.The model can predict the pavement temperature field with standard deviation of 1.88 ℃ after the model is calibrated with the measured data.