Exact and simple expressions for the permanent solutions corresponding to two oscillatory motions of incompressible upper-convected Maxwell fluids with exponential dependence of viscosity on the pressure between parallel plates have been established using suitable changes of the spatial variable and the unknown function and the Laplace transform technique. The solutions that have been obtained satisfy the boundary conditions and governing equations but are independent of the initial conditions. They are important for those who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids as well as known results for the Newtonian fluids performing the same motions were obtained as limiting cases. The convergence of starting solutions to the corresponding permanent components that has been graphically proved could constitute an asset on the correctness of obtained results. The influence of pertinent parameters on the fluid motion and the spatial profiles of starting solutions have been graphically depicted and discussed. The oscillations’ amplitude is an increasing function with respect to the dimensionless pressure–viscosity coefficient and the Weissenberg number. It is lower for the shear stress as compared to the fluid velocity. The three-dimensional distribution of the starting velocity fields has been numerically visualized by means of the two-dimensional contour graphs.

利用空间变量和未知函数的适当变化以及拉普拉斯变换技术，建立了与不可压缩的上对流麦克斯韦流体的两个振荡运动相对应的永久解的精确且简单的表达式，其粘度与平行板之间的压力呈指数关系。 。已获得的解满足边界条件和控制方程，但与初始条件无关。对于想从实验中消除瞬变的人来说，它们很重要。作为极限情况，获得了相同流体的简单Couette流的相似解决方案以及执行相同运动的牛顿流体的已知结果。已经通过图形证明的起始解决方案与相应的永久组件的收敛性可能对所获得结果的正确性构成资产。有关参数对流体运动和起始溶液的空间分布的影响已通过图形方式描绘和讨论。相对于无因次压力-粘度系数和魏森伯格数，振荡幅度是一个增加的函数。与流体速度相比，剪切应力较低。起始速度场的三维分布已通过二维轮廓图进行了数字可视化。有关参数对流体运动和起始溶液的空间分布的影响已通过图形方式描绘和讨论。相对于无因次压力-粘度系数和魏森伯格数，振荡幅度是一个增加的函数。与流体速度相比，剪切应力较低。起始速度场的三维分布已通过二维轮廓图进行了数字可视化。有关参数对流体运动和起始溶液的空间分布的影响已通过图形方式描绘和讨论。相对于无因次压力-粘度系数和魏森伯格数，振荡幅度是一个增加的函数。与流体速度相比，剪切应力较低。起始速度场的三维分布已通过二维轮廓图进行了数字可视化。