Using Shaban transformation for solving equations of the deflection curve

Shaban, Rehab Ali; Baqir, Nakheel Mohammed

doi:10.1080/09720502.2021.1960709

Cited by 1 publication

(1 citation statement)

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“…The idea of "integral transforms give us power and ease to solve such fundamental problems as initial value ones of a linear and of an integral differential equation, and numerous mathematicians across the world became interested in this problem during the last decades" of their applications of fluid mechanics was of great interest to the authors such as Sumudu, ARA, Saban, SEA, and SEJI [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis of Squeeze Lubrication Using Double ZZ Transform: Application of Non-Newtonian Fluids

Khudair,

Abdullah,

Albukhuttar

2024

MMEP

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This paper highlights the flow of non-Newtonian fluids through porous elastic layers of human articular cartilage and describes the effect of lubricating fluid flow on the performance of daily activities and various activities with high accuracy through the design of a mathematical model. The current work includes the equations of motion, the equation of continuity, and squeeze lubrication as influencing factors on phases (stance phase-swing phase) in the gait cycle. In other words, study the characteristics of lubrication through the cohesive force of particles, initial concentration, smoothness of the surface, vertical roughness, and the weight of the human body. These expressions are computed using the double ZZ transformation and are used to describe many problems in the field of science, including the heat equation, Klein-Gordon equation, and others, all of which are crucial for physical applications and fractional differential equation because of its frequent appearance in fluid mechanics, mathematical biology, electrochemistry, and physics. The current findings show that solving these equations by Using single transforms is more difficult than using the double transform, because using a double transform the partial equation is converted directly into an algebraic equation, while the single transform converts the partial equation into an ordinary equation firstly and then into an algebraic equation, which requires more calculation and methods to obtain the exact solution. Besides, the theoretical and applied description of the lubrication mechanism is evident when hydrodynamic pressure is generated between the different layers, which plays an important role in the kinematic friction force between layers and particles. Furthermore, the results are presented graphically. From the analysis and computations of the results, it is found that the pressure and friction forces increase with an increase in the cycle of time. Cycle time greatly affects (pressure -friction force). It is known that the walking pattern varies depending on the daily activities that a person performs, which is greatly reflected in the increased pressure on the synovial joints, which is reflected in the increased friction between the (layer -molecules) responsible for lubricating articular.

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