Application of Analytical Methods About Equations of Stokes for Transient Condition in Flow Over Oscillating Plane and Oscillating Flow Over Stationary Plane
Edris Ghonoodi,
Davood Domeiri Ganji
Issue:
Volume 5, Issue 2, December 2021
Pages:
13-21
Received:
18 May 2021
Accepted:
10 July 2021
Published:
15 July 2021
Abstract: In this study, two highly accurate and simple analytical methods (known as semi exact solutions), the variational iteration method (VIM) and Adomian’s decomposition method (ADM) are applied for illustrating transient condition of viscous fluid flow over oscillating plane and also oscillating viscous fluid flow over stationary plane. The flow of an incompressible viscous fluid, caused by the oscillation of a flat wall and also the flow of an oscillating fluid flow over stationary wall are considered by Navier-Stokes equations and are subjected to the behavior of fluid flow in boundary layer at transient condition. The main purpose of this article is to solve transient Navier-Stokes first and second equations in new mathematical solving method which is called semi exact solutions where in each case, the velocity of viscous fluid is determined as a function of time and also vertical distance from plane in boundary layer at transient condition. Results reveal the boundary layer thickness and also the transient fluid flow velocity in boundary layer and even more it shows that the (VIM) and (ADM) methods are very effective and accurate in comparison with the exact solution results. The results demonstrate the velocity of fluid in boundary layer as a function of displacement and time and it is shown that in different time, the value of velocity obtained by “VIM” and “ADM” solving methods is almost equal to velocity which is derived from exact or numerical solutions. So the main background and reason of applying the mentioned methods is to verify the accuracy of “VIM” and “ADM” in solving different fluid mechanics equations especially Navier-Stokes equations.
Abstract: In this study, two highly accurate and simple analytical methods (known as semi exact solutions), the variational iteration method (VIM) and Adomian’s decomposition method (ADM) are applied for illustrating transient condition of viscous fluid flow over oscillating plane and also oscillating viscous fluid flow over stationary plane. The flow of an ...
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Force of Inertia as Sort of Interaction
Parfentev Nikolay Andreevich,
Parfenteva Natalia Andreevna
Issue:
Volume 5, Issue 2, December 2021
Pages:
22-24
Received:
11 June 2021
Accepted:
30 June 2021
Published:
4 August 2021
Abstract: The interaction of the temporal positions of a moving body with mass is now an experimental fact. Models of this interaction are easily determined by the assumption that time is an imaginary coordinate. As a result, the force of inertia can be presented together with other forces as a form of interaction of time positions - characteristic of any kind of movement. The result confirms the universality of Newton's third law, which served as an additional incentive for real work. In particular, with the gravitational interaction of the two bodies, each of them experiences the force determined by the work of interacting masses. According to Newton's third law, this force is confronted by the power of interaction of the temporal positions of each body. The general expressions of force of inertia in the case of rectangular accelerated movement and movement in the circumference are obtained, which leads to classical formulas in any interval of possible body speeds. These formulas are fully in line with modern relativistic laws, but are their natural development and a more complete description of nature. Important results of the study include the formal definition of the sign of the force of interaction. When considering a rectangular accelerated motion, subtracting the force of the interaction of the final moment of movement, occurring at a greater speed, from the force of the interaction of the initial moment (at a lower speed) leads to a negative sign of the resulting force. The proposed model allows to recognize as superfluous experiments to determine the equality of gravitational and inertial masses, as in both cases we are talking about the same mass, participating in different types of interaction.
Abstract: The interaction of the temporal positions of a moving body with mass is now an experimental fact. Models of this interaction are easily determined by the assumption that time is an imaginary coordinate. As a result, the force of inertia can be presented together with other forces as a form of interaction of time positions - characteristic of any ki...
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Mathematical Model of Root Crop Digging with Longitudinal Vibrations
Volodymyr Bulgakov,
Aivars Aboltins,
Hristo Beloev,
Ivan Holovach,
Valerii Adamchuk,
Semjons Ivanovs,
Yevhen Ihnatiev
Issue:
Volume 5, Issue 2, December 2021
Pages:
25-38
Received:
10 June 2021
Accepted:
22 June 2021
Published:
9 August 2021
Abstract: The problem how to reduce damage to tubers when they are dug up is urgent. For the new design of a vibrating digging working body for root crops the mathematical model of longitudinal vibrations of a root crop in the soil is developed as an elastic body in an elastically damped medium. The Ostrogradsky-Hamilton variational principle is applied for the analytical description of the process. The Ritz method was applied to find the frequencies of natural vibrations, the amplitudes of forced vibrations of a root crop as a solid elastic body when it is captured by a vibrating digging body. The frequency equation for the discussed vibrational process was obtained. The values of the first proper frequency of longitudinal vibrations of the considered elastic body of the root crop with specific geometric physical parameters are found. Graphs of the dependence of the first natural frequency upon the elastic deformation coefficient, the damping coefficient of the soil as an elastic damping medium are obtained. When the soil damping coefficient changes within 0 to 10 N∙s2∙m–3, the first proper frequency changes within 500 to 750 s-1 (80 to 119 Hz) at soil elastic deformation coefficient 2∙105 N∙m–3. Dependence of the elastic body forced vibration amplitude upon the change in the amplitude of the disturbing force have been obtained. When the amplitude of the disturbing force changes within 100 to 600 N, the amplitude of forced vibrations of the root crop body changes within 0.30 to 0.68 mm.
Abstract: The problem how to reduce damage to tubers when they are dug up is urgent. For the new design of a vibrating digging working body for root crops the mathematical model of longitudinal vibrations of a root crop in the soil is developed as an elastic body in an elastically damped medium. The Ostrogradsky-Hamilton variational principle is applied for ...
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