AXIAL TENSILE STRENGTH ANALYSIS OF UNBONDED FLEXIBLE PIPE CONTAINING COMPOSITE TENSILE ARMORS by MA JinSheng, DU FaXi, LUO Dan

“…As offshore oil industry moves into ultra-deep water,replacing the steel tensile armors of unbonded flexible pipe with composite is becoming a scheme that can effectively reduce weight and provide better mechanical properties.The anisotropic parameters of composite are obtained by meso-mechanical method,then a model of axisymmetric structure response for composite flexible pipe with composite armored layer is established,which is based on both thick-wall cylinder theory and the differential equation of curved beam,and also the algorithm of cyclic iterative is combined.Failure models of different type of flexible pipes are obtained,and iso-strength method is used for composite armored pipe.A case study shows that composite armors can effectively enhance the tensile strength of unbonded flexible pipe while effectively reduce the overall weight.Results state that volume fraction,elastic modulus and strength of fiber are the important parameters which affect the axial stiffness and tensile strength of unbonded flexible pipe.…”
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Scaling Laws of Droplet Coalescence: Theory and Numerical Simulation by M. Irshad Khodabocus, Mathieu Sellier, Volker Nock

“…The twofold objective of the present contribution is to propose a simple theoretical framework which leads to an Ordinary Differential Equation, the solution of which predicts the different scaling laws in various limits, and to validate these theoretical predictions numerically by modelling the phenomenon in the commercial Finite Element software COMSOL Multiphysics.…”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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DESIGN AND DYNAMIC ANALYSIS OF A NEW CHAOTIC VIBRATING SCREEN by WANG ChengJun, ZHU Tao

“…A new type of chaotic vibrating screen with one redundant degree of freedom is developed, the dynamic model of the new chaotic vibrating screen is established, the vibration differential equation of the vibrating screen is obtained by the Lagrange method, and its dynamic characteristic diagram is obtained through simulink simulation analysis. …”
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. …”
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An Improved C-V Model and Application to the Coal Rock Mesocrack Images by Yulong Chen, Hongwei Zhang

“…In order to accurately and comprehensively obtain information about coal rock mesocrack images, image processing technique based on partial differential equation (PDE) is introduced in order to expound on the active contour model without edges and overcome the deficiency of the C-V model. …”
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Kinematics and Stiffness Characteristics of Orientation Adjustment and Vibration Isolation Platform with Active-passive Closed-loop Fusion by Geng Mingchao, Li Erwei, Li Yanan, Ma Hong, Wang Zhanying, Li Xin

“…Based on this, the first and second order influence coefficients of the mechanism are derived, which are concise and compact, and lay a foundation for the establishment of the motion differential equation and the analysis of the vibration characteristics of the mechanism. …”
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A robust, exponentially fitted higher-order numerical method for a two-parameter singularly perturbed boundary value problem by Adisie Fenta Agmas, Fasika Wondimu Gelu, Meselech Chima Fino

“…The derivatives in the governing ordinary differential equation are substituted by second-order central finite difference approximations, after which the fitting parameter is introduced and determined. …”
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Importance of Activation Energy on Magnetized Dissipative Casson-Maxwell Fluid through Porous Medium Incorporating Chemical Reaction, Joule Heating, and Soret Effects: Numerical St... by Nesreen Althobaiti

“…The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. …”
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Time Series Prediction Based on Complex-Valued S-System Model by Bin Yang, Wenzheng Bao, Yuehui Chen

“…The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R2, and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system.…”
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Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation by Javad Alinejad, Sina Samarbakhsh

“…The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field 𝑓 and differential equation by variable coefficient for the temperature field 𝜃, are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. …”
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Iterative Learning Control with Forgetting Factor for Linear Distributed Parameter Systems with Uncertainty by Xisheng Dai, Senping Tian, Wenguang Luo, Yajun Guo

“…Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm.…”
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Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions by Jiaquan Xie, Yongjiang Zheng, Zhongkai Ren, Tao Wang, Guangxian Shen

“…In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. …”
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Chaotic numerical instabilities arising in the transition from differential to difference nonlinear equations by Alicia Serfaty de Markus

“…For computational purposes, a numerical algorithm maps a differential equation into an often complex difference equation whose structure and stability depends on the scheme used. …”
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A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field by Abdul-Sattar J. A. Al-Saif, Abeer Majeed Jasim

“…The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. …”
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In Situ Bioremediation of Crude Petroleum Oil Polluted Soil Using Mathematical Experimentation by Modupe Elizabeth Ojewumi, Moses Eterigho Emetere, Damilola Elizabeth Babatunde, Joshua Olusegun Okeniyi

“…The parabolic partial differential equation developed was resolved into a system of ordinary differential equations (ODEs) by orthogonal collocation method and the necessary boundary condition was used. …”
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VIBRATION SUPPRESSION CHARACTERISTICS ANALYSIS OF TWO-PLANE AUTOMATIC BALL BALANCING DEVICE by WANG Zhi, CHEN HaiWei, SUN Zhen

“…The mathematical models of two-plane automatic ball balancing device for double eccentric disk were established and derived the vibration differential equation by the Lagrange equation,the autonomous system was obtained by rotating coordinate transformation. …”
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Per‐unit transformation for the combined analysis of multi‐energy integration by Zhang Zhang, Fei Wang, Hui Fan

“…Abstract To handle numerical issues caused by dimensional differences among heterogeneous states in integrated energy systems (IES), this paper proposes a novel per‐unit transformation method and explores its applications to the partial differential equation‐governed models. Initially, a unified IES model is developed, which encompasses both fast and slow dynamics in a generalized form. …”
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Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium by Alexander I. Zemlyanukhin, Andrey V. Bochkarev, Lev I. Mogilevich, Ekaterina G. Tindova

“…A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. …”
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Dynamic Load Performance of a Face Gear Drive in a Spent Fuel Reactor by Guo Mingchao, Zhang Ju, Xu Lei, Kan Chen

“…The dynamic model of the face gear drive is established based on the centralized mass method.The influence of factors such as manufacturing errors and misalignments, time-varying meshing stiffness, corrosion on tooth surfaces, earthquakes on the dynamic performance are taken into consideration to deduce the differential equations of the face gear drive. Runge-Kutta method is applied to solve the differential equation, the dynamic loads under excitations of misalignment, earthquake and corrosion are obtained, and the influence law of these excitations on the dynamic load coefficient is further analyzed. …”
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