Modeling of vibration of a pipeline on the theory of Timoshenko
In this paper the oscillatory process of a viscoelastic pipeline is investigated numerically according to the theory of Timoshenko lying on an elastic foundation, described by the Winkler model. To describe the deformation processes of viscoelastic materials, the Boltzmann-Volterra integral model with weakly singular nuclei was used: a = E(1 - R* )e = E je - JR(t - т)е(т)Л j, here E is the modulus of elasticity of the material; R(t -x) is the relaxation kernel; t is the observation time; x is the time preceding the moment of observation. A mathematical model of pipelines conveying fluid flow has been developed with account for viscosity properties of structure material and the base of the pipeline: °!w , 2m V, m V2 , k w = G A K (1 D-)f02w , (mp + mf)fT ^ 2mjV - +f ^ +kww = GpApKs(1- R*)(^ + £ (P Л + P A) §=epIp (1 - R*) 0X2 - GpApKs (1 - R*) (fw Here mp , mf are the masses of the pipe and fluid, respectively, referred to the unit of length; If = J z 1dA; Af is the area limiting Af the volume of fluid flow; pf , p are the densities of the fluid and the pipe material, respectively. When modeling problems, a number of new dynamic effects were investigated: it was found that an account of viscoelastic properties of the pipeline material led to a decrease in the amplitude and frequency of vibrations; it was shown that an increase in the base parameter led to an increase in the vibration frequency of the pipeline; it was found that a decrease in the pipe mass per unit length led to an increase in the amplitude and frequency of vibrations.
Keywords
математическая модель,
вычислительный алгоритм,
вязкоупругость,
трубопровод,
теория Тимошенко,
mathematical model,
viscoelasticity,
pipeline,
computational algorithm,
Timoshenko theoryAuthors
| Khudayarov Bakhtiyar Alimovich | Tashkent Institute of Irrigation and Agricultural Mechanization Engineers | bakht-flpo@yandex.ru |
| Kucharov Olimzhon Ruzimurotovich | Scientific and Innovation Center of Information and Communication Technologies | k.r.olimjon@mail.ru |
Всего: 2
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