清洗活塞通道时,主燃气管道开路段的强迫振荡

V. Grudz, T. Tutko, O. Dubei
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引用次数: 0

摘要

清洗活塞通道中燃气管道开口段的强迫振荡问题属于一维弹性物体在运动惯性载荷作用下的强迫振荡问题。目前,解决这类问题的方法有两种。第一种方法与偏微分方程的积分有关,这类问题的解是特征振荡和伴随振荡的叠加。第二种方法不涉及偏微分方程的积分。广义坐标法、广义位移法和各种数值方法属于第二类求解。上述方法都不简单。因此,作者提出了一种方法,其中第一个数学模型提供了在清洁活塞通过过程中气体管道截面强迫振荡的确定,而不考虑其对气体管道的惯性载荷。将来,在第一个模型的基础上,计划开发第二个数学模型,该模型将提供管道轴的挠度的近似确定,同时考虑到活塞对管道的惯性载荷。本文的目的是在不考虑管道上惯性力的情况下,得到清洗活塞通过过程中管道截面强迫振荡问题的解。采用偏微分方程求解,采用傅里叶方法求解。非齐次微分方程的右侧被分解成一个无穷级数,该无穷级数是管道截面自由振荡的特征函数和未知时间函数的乘积之和。在找出这个函数后,作者用傅里叶方法确定了未知的时间函数,从而用无穷级数的形式求解了这个问题,无穷级数的和迅速减少。作者计算了管道轴线在不同时间点沿天然气管道整段的挠度,以及随时间和挠度变化的个别部分的挠度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Forced oscillations of the main gas pipeline open section during the cleaning piston passage
The problem of forced oscillations of an open section of a gas pipeline during the cleaning piston passage belongs to the type of problems of forced oscillations of one-dimensional elastic objects under the influence of a moving inertial load on them. Currently, there are two ways to solve such problems. The first way is related to the integration of the partial differential equation and the solution of such problems is a superposition of eigen-oscillations and accompanying oscillations. The second way does not involve the integration of the partial dif-ferential equation. Methods of generalized coordinates, generalized displacements and various numerical methods belong to the second type of solving. None of the mentioned methods is simple. Therefore, the authors suggest the method, in which the first mathematical model provides the determination of forced oscillations of the gas pipeline section during the passage of the cleaning piston without taking into account its inertial load on the gas pipeline. In future, on the basis of the first model it is planned to develop the second mathematical model which will provide an approximate determination of the deflections of the pipeline axis, taking into account the inertial load of the piston on the pipeline. The purpose of this article is to obtain a solution to the problem of forced oscillations of the pipeline section during the passage of the cleaning piston without taking into account the inertial forces on the pipeline. The problem is solved by partial differential equation, Fourier method is applied. The right side of the non-homogeneous differential equation is decomposed into an infinite series, which is the sum of the produc-tions of the eigenfunctions of the pipeline section free oscillations and the unknown function of time. After finding out this function, the authors determine the unknown time function in the Fourier method and hence the solution of the problem in the form of an infinite series, the summands of which lessen rapidly. The authors calculate the deflections of the pipeline axis along the entire section of the gas pipeline for different points of time, as well as deflections of individual sections changing in time and moments of deflection.
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