Сalculation of parameters of forced steady - state fluctuations of the pipeline

2021 ◽  
pp. 51-59
Author(s):  
А.Л. Мелконян ◽  
Д.А. Николаев ◽  
М.В. Чуклин
Keyword(s):  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Discrete Version ◽  
Inertial Load ◽  
Calculation Algorithm ◽  
Flowing Liquid ◽  
Internal Forces ◽  
Stiffness Characteristics ◽  
Vibration Parameters ◽  
Pipeline Model

Для расчета параметров вибрации трубопроводов (амплитуды смещений, внутренних усилий и опорных реакций) разработаны модель, алгоритм и программа. Модель – квазиодномерная конечноэлементная система. Алгоритм расчета построен на базе метода парциальных откликов в его дискретном варианте. Выведены формулы для парциальных откликов и парциальных параметров, необходимые при реализации предложенного алгоритма. Влияние протекающей жидкости учтено приложением дополнительной инерционной нагрузки, которая, в свою очередь, учитывается коррекцией и модификацией инерционно-жесткостных характеристик модели трубопровода. В качестве примера рассмотрена задача о вибрации прямого трубопровода постоянного поперечного сечения, опирающегося на две опоры. Выполнено исследование влияния составляющих инерционной нагрузки на параметры вибрации, значения собственных частот и величину критической скорости жидкости. Оценена сходимость процесса в случае необходимости применения метода последовательных приближений. To analyze vibration parameters of the pipeline (displacement amplitudes, internal forces, and support reactions) the model, algorithm, and program were created. The model is a quasi-one-dimensional (quasi-1D) finite element system. The calculation algorithm is based on the discrete version of the partial responses method. Formulas for partial responses and partial parameters necessary for the implementation of the proposed algorithm were derived. The influence of the flowing liquid is compensated by applying an additional inertial load, which, in turn, is taken into account by correcting and modifying the inertia-stiffness characteristics of the pipeline model. The problem of the vibration of a straight pipeline of a constant cross-section with two points of support is given as an example. The influence of inertial load components on vibration parameters, own frequency values, and the critical velocity of the liquid were studied. The convergence of the process in case of using method of successive approximations was estimated.

scholarly journals Calculation algorithm and software for pipeline vibrations with consideration of internal flow

2020 ◽  
Vol S-I (2) ◽  
pp. 260-265
Author(s):  
A. Melkonyan ◽  
◽  
M. Chuklin ◽  
Keyword(s):  
Cross Section ◽  
Internal Flow ◽  
Complex Model ◽  
Constant Cross Section ◽  
Inertial Load ◽  
Calculation Algorithm ◽  
Perfect Incompressible Fluid ◽  
Adopted Model ◽  
Vibration Parameters ◽  
Pipeline Model

This paper discusses the development of calculation complex (model, algorithm and software) needed to investigate vibration parameters (amplitudes of displacements, internal forces and support responses) of a constant cross-section pipeline with a perfect incompressible fluid flowing inside it. This paper presents a pipeline model as quasi-monomeric finite-element system. Presently, the study discusses vibration of a straight constant cross-section pipeline resting on two elastic supports. Calculation algorithm is based on the discrete variant of partial-response method. The effect of fluid flow is taken into account as an additional inertial load incorporated, in its turn, by means of corrections and modifications of inertia & stiffness parameters of pipeline model. The study gives calculation expressions for partial responses and partial parameters, needed to implement the algorithm suggested by the authors. The problem formulated in this paper was solved as per specially developed mathematical model taking into account the forces due to the flow in the pipe. The paper also suggests calculation algorithm for vibration parameters of the adopted model. These vibration parameters were obtained in specially developed Koriolis software. The study also investigated the effect of additional inertial load components upon vibration parameters and natural frequencies of the structure at question. All these activities made it possible to accomplish the task of the whole study, i.e. to develop the calculation complex for determination of pipeline vibration parameters.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals A new method of successive approximations when calculating elements of electromechanical machines

2020 ◽  
Vol 5 (2) ◽  
pp. 168-172
Author(s):  
K. Ismayilov ◽  
◽  
S.T. Suleymanov ◽  
S.T. Ruziev ◽  
M.B. Aripjanova ◽  
...  
Keyword(s):  
New Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

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