Nonlinear Slip Research Articles

Analytical and numerical study of an eccentric continuous cable bracing system with friction slip mechanism

This study proposes a very simple and low-cost friction mechanism using a pre-stressed cable passing over two fixed pulleys without rotation along with an eccentric continuous cable bracing as a lateral-resistant system for structures subjected to lateral loading such as earthquake. The performance of this mechanism is investigated using analytical solution method and finite element modeling. The purpose of this system is to provide a structure with sufficient stiffness and lateral resistance as well as energy dissipation through frictional slip between the cable and pulleys. The system exhibits two-phase behavior. In case of a small lateral displacement, the system exhibits high stiffness in the linear elastic phase (first phase) and behaves well under normal winds and small earthquakes. In case of large lateral displacement such as a strong earthquake, the system experiences a nonlinear slip phase (second phase) and, accordingly, exhibits a nonlinear behavior with an increase in stiffness and input energy dissipation which protects the structure from displacement. The seismic performance of the proposed system is investigated in terms of three parameters: friction coefficient, initial pre-stressing force, and span length. As the friction coefficient value increases, the lateral resistance of the system rises. In the event of extra rotation of the cable around the pulleys, the coefficient values at static and dynamic friction phases are 5.6 and 5.1 times those in the frictional state, respectively. The rise of the span length and reduction of initial pre-stressing force decrease the system lateral resistance and the initial stiffness of the system, respectively. Upon increasing the initial pre-stressing force up to twice that of the base state, the slip threshold of the system lateral resistance force increases by 33% and as a result, the system remains more at the static friction phase. Also, by reducing the initial pre-stressing to half of its value in the base state, the lateral resistance force corresponding to the slip threshold of system is decreased by 52%; therefore, the slip of the cable on pulleys is initiated earlier. Finally, the cyclic behavior of the steel moment frame with the proposed system is investigated with ATC24 protocol, which increases the stiffness and energy dissipation by 19% compared to the moment frame without the proposed system.

Nonlinear MPC-Based Acceleration Slip Regulation for Distributed Electric Vehicles

To address the problem in which wheel longitudinal slip rate directly affects the dynamics and handling stability of a vehicle under driving conditions, front and rear dual-motor four-wheel drive electric vehicles (4WD EVs) were selected as the research object in this study. An acceleration slip regulation (ASR) control strategy based on nonlinear model predictive control (NMPC) is proposed. First, the vehicle dynamics model and the Simulink/CarSim co-simulation platform were built. Second, an ASR controller with intervention and exit mechanisms was designed with the control objective of tracking reference speed or optimal slip rate. Then, considering the problem that the left and right wheels could not freely distribute torque under the condition of a split road surface, the motor output torque was determined in accordance with the wheel with the larger slip rate to enhance passibility. Finally, on the basis of the built Simulink/CarSim co-simulation platform, slip rate control simulation experiments were performed on a snow-covered road, a wet asphalt road, a docking road, and a split road. The designed controller can better track target slip rate and it exhibits better dynamic performance and stability than the method with PID control under different road conditions, especially under low speed and low adhesion road conditions, and its robustness can also meet the requirements.

Radiative couple stress Casson hybrid nanofluid flow over an inclined stretching surface due to nonlinear convection and slip boundaries

The study of fluid dynamics due to the stretching surface is one of the most eminent topics due to its potential industrial applications viz. drawing wire and plastic films, metal and polymer extrusion, fiber and glass production. In the present article, the author is going to study the effects of hybrid nanofluids flow on an inclined plate including CuO (Copper Oxide), and Cu (Copper). The Casson fluid with a couple-stress term has been used in the flow analysis. The surface of the plate is considered slippery. The convection has been taken nonlinear with thermal radiation. The governing equation of the flow of hybrid nanofluids with energy equation has been transformed into highly nonlinear ODEs through similarity transformation. The proposed model has been solved through a numerical RK-4 method. Significant variables of the physical process such as solar radiation, nonlinear convection parameters, heat transfer rates, and their effect on the solar power plant have been noticed.

Hydrothermal stagnation point flow of Carreau nanofluid over a moving thin needle with non-linear Navier's slip and cubic autocatalytic chemical reactions in Darcy-Forchheimer medium

The present analysis deals with the hydrothermal and stagnation point flow of non-Newtonian fluid characterized by Carreau model over a moving thin needle. Darcy-Forchheimer medium is introduced. Homogeneous and heterogeneous chemical reactions are involved in the flow model. Non-linear Navier's slip condition is taken into account. Buongiorno model is adopted. The present hydrothermal flow model is useful in many complex industrial processes. The required numerical solution is obtained by 4th order Runge Kutta method along with shooting technique. The some remarkable outcomes of the current study are that axial velocity whittles down with rise in Weissenberg number and exhibits reverse trend in response to increase in non-linear slip parameter. Amplification of homogeneous and heterogeneous reaction parameters leads to diminution of nanoparticles concentration. Surface viscous drag intensify due to increment in Forchheimer number and heat transfer rate ameliorates with hike in Weissenberg number for both power law behavior (shear thinning and shear thickening) of Carreau nanofluid.

Mixed electroosmotic/pressure-driven flow for a generalized Phan–Thien–Tanner fluid in a microchannel with nonlinear Navier slip at the wall

This work derives an approximate solution of the laminar viscoelastic fluid flow through a parallel flat plate microchannel, driven by electroosmotic and external pressure forces. In contrast to other works published in the past, in the present analysis, the fluid’s rheology obeys the generalized Phan–Thien–Tanner model that has been proposed recently, which uses the Mittag-Leffler function instead of linear or exponential functions of the trace for the stress tensor. The hydrodynamic analysis considers a non-linear Navier slip law at the wall that follows a power-law behavior on the shear stress. For the electric potential in the electric double layer, the Debye–Hückel approximation was used, and it is assumed that the wall’s zeta potentials are symmetric. The solution obtained in this work depends on several dimensionless parameters that allow controlling the flow: ɛWi2 characterizes the fluid’s viscoelasticity, the electrokinetic parameter κ̄, the dimensionless slip coefficient L̄, the slip-power exponent m, and the ratio between pressure and electroosmotic forces, G. Besides, the influence of two parameters of the Mittag-Leffler function, α and β, notably affects the flow’s characteristics. Our results evidence the important consequences of considering the generalized Phan–Thien–Tanner model and the slippage effect on the flow field compared to that described by the Phan–Thien–Tanner model.

Electro-osmotic optimized flow of Prandtl nanofluid in vertical wavy channel with nonlinear thermal radiation and slip effects

The simulations have been performed for the nonlinear radiative flow of Prandtl nanofluid following the peristaltic pumping in a wavy channel. The applications of entropy generation for the electrokinetic pumping phenomenon are also focused as a novelty. The complex wavy channel induced the flow of Prandtl nanofluid. Moreover, the formulated problem is solved by using the convective thermal and concentration boundary conditions. The Keller Box numerical procedure is adopted as a tool for the simulation task. The results are also verified by implementing the built-in numerical technique bvp4c. The comparison tasked against obtained numerical measurement has been done with already reported results with excellent manner. The physical characteristics based on the flow parameters for velocity, heat transfer phenomenon, concentration field, and entropy generation pattern is visualized graphically. It has been observed that the presence of thermal slip and concentration enhanced the heat transfer rate and concentration profile, respectively. The skin friction coefficient declines with electro-osmotic force and slip parameter. The increasing variation in Nusselt number is observed for electro-osmotic parameter for both linear and non-linear radiative phenomenon.

Non-isothermal non-Newtonian flow problem with heat convection and Tresca's friction law

We consider an incompressible non-isothermal fluid flow with non-linear slip boundary conditions governed by Tresca's friction law. We assume that the stress tensor is given as where θ is the temperature, π is the pressure, u is the velocity and is the strain rate tensor of the fluid while p is a real parameter. The problem is thus given by the p-Laplacian Stokes system with subdifferential type boundary conditions coupled to a elliptic equation describing the heat conduction in the fluid. We establish first an existence result for a family of approximate coupled problems where the coupling term in the heat equation is replaced by a bounded one depending on a parameter , by using a fixed point technique. Then we pass to the limit as δ tends to zero and we prove the existence of a solution to our original coupled problem in Banach spaces depending on p for any .

Influence of nonlinear radiation on MHD nanofluid flow over a cone with second‐order velocity and thermal slips: A numerical study

AbstractThis computational study discovered the influence of magnetohydrodynamics nanofluid flow over a vertical cone. The nonlinear form of thermal radiation and irregular heat generation/sink takes an active part in this study. The influences of chemical reactions and second‐order slip parameters (velocity and temperature) are taken into account. Copper nanoparticles were mixed with water as base fluid in the present investigation. The leading partial differential equations which model the flow are altered as a set of nonlinear ordinary differential equations by means of self‐similarity alterations and then a numerical solution is cultivated with the support of fourth order Runge–Kutta Fehlberg method with the shooting method. The influence of appropriate parameters such as nonlinear radiation, chemical reaction, and slip parameters (velocity and temperature) on common fields (concentration, temperature, and velocity) are visualized through graphs. Also, we have analyzed the effects of identical parameters on the coefficient of skin friction and rate of transfer (mass and heat) by means of tables. The skin friction coefficient is boosted when the magnetic parameter is incremented. For larger values of nonlinear radiation parameter , the rate of heat transfer was reduced.

A three-step stabilized algorithm for the Navier-Stokes type variational inequality

In the light of two-grid finite element discretization, this paper is concerned with a three-step stabilized algorithm for the Navier-Stokes equations with nonlinear slip boundary conditions of friction type. The proposed algorithm proceeds three steps: the first step solves a stabilized nonlinear variational inequality problem on a coarse grid, the second step solves a stabilized linear variational inequality problem based on Newton iteration on a fine grid, and the third step solves the same stabilized linear problem with only different right-hand sides on a fine grid. We analyze the stability of the presented algorithm, and derive error estimate of the approximate solutions in L2 norms of the velocity gradient and pressure. Finally, we demonstrate the effectiveness of the present algorithm by two numerical tests.

Simulation Study on Mechanical Characteristics of Rock Bolt in Rock Mass with Bedding Separation Based on the Nonlinear Bond Slip Relationship

The mechanical equation on the mechanical characteristics of rock bolt in rock mass with bedding separation is established, based on the bond slip relationship of anchoring interface by the load transfer method. The validity of the numerical simulation is verified by the analytical solution of mechanical equation, when the bond slip relationship is linear. Further, the nonlinear bond slip relationship of anchoring interface is input into Flac3D by FISH. The mechanical characteristics of rock bolt are studied with the single and multiple bedding separation by numerical simulation. The results show that the axial force and the interfacial shear stress distribution curves on both sides are symmetrically distributed with the single bedding separation in rock mass, when the bedding separation is located in the center of the anchoring segment. When the bedding separation positions are not located in the center of the anchoring segment, the bedding separation value at different positions versus the axial force curves shows a single peak distribution. The axial force of rock bolt is mainly controlled by the side with the shorter anchoring length. Compared with the single bedding separation in rock mass, the additional stress of rock bolt occurred by the multiple bedding separation will superimpose each other. This paper leads to a better understanding for the load transfer mechanism for grouted rock bolt systems in rock mass with bedding separation and provides a reference for scientific support design and evaluation method.

A finite difference scheme for non-Cartesian mesh: Applications to rarefied gas flows

A novel numerical scheme based on the finite-difference framework is developed, which allows us to model moderately rarefied gas flows in irregular geometries. The major hurdle in constructing numerical methods for rarefied gas flows is the prescription of the velocity-slip and temperature-jump boundary conditions as well as the discretization of an intricate set of partial differential equations. The proposed scheme is demonstrated to solve the non-linear coupled constitutive relations model along with the corresponding non-linear slip and jump boundary conditions. The computation of the discretized weights is proposed using two approaches: (i) polynomial shape functions and (ii) a generalized inverse distance approach. The non-linear terms are discretized using the fixed-point iteration method. The numerical method is validated for the Laplace equation over an annulus, and results are presented for a lid-driven curved cavity and a triangular lid-driven cavity, which delineates its performance on a skewed non-Cartesian grid. The results are validated with direct simulation Monte Carlo data from the literature, and a robust convergence for the solutions is demonstrated.

The Cox–Voinov law for traveling waves in the partial wetting regime* *The first author is grateful to Lorenzo Giacomelli and Felix Otto for discussions on work preceding this paper. The second author thanks Floris Roodenburg for discussions. This work is partially based on the second author’s bachelor thesis in applied mathematics prepared under the advice of the first author at

We consider the thin-film equation in {h > 0} with partial-wetting boundary conditions and inhomogeneous mobility of the form m(h) = h 3 + λ 3−n h n , where h ⩾ 0 is the film height, λ > 0 is the slip length, y > 0 denotes the lateral variable, and n ∈ (0, 3) is the mobility exponent parameterizing the nonlinear slip condition. The partial-wetting regime implies the boundary condition ∂ y h = const. > 0 at the triple junction ∂{h > 0} (nonzero microscopic contact angle). Existence and uniqueness of traveling-wave solutions to this problem under the constraint as h → ∞ have been proved in previous work by Chiricotto and Giacomelli (2011 Commun. Appl. Ind. Math. 2 e-388, 16). We are interested in the asymptotics as h ↓ 0 and h → ∞. By reformulating the problem as h ↓ 0 as a dynamical system for the difference between the solution and the microscopic contact angle, values for n are found for which linear as well as nonlinear resonances occur. These resonances lead to a different asymptotic behavior of the solution as h ↓ 0 depending on n. Together with the asymptotics as h → ∞ characterizing the Cox–Voinov law for the velocity-dependent macroscopic contact angle as found by Giacomelli, the first author of this work, and Otto (2016 Nonlinearity 29 2497–536), the rigorous asymptotics of traveling-wave solutions to the thin-film equation in partial wetting can be characterized. Furthermore, our approach enables us to analyze the relation between the microscopic and macroscopic contact angle. It is found that the Cox–Voinov law for the macroscopic contact angle depends continuously differentiably on the microscopic contact angle.

An LMIs‐based back‐stepping sliding mode control framework for robust velocity tracking of the automatic driving vehicle on sloped roads

AbstractAutomatic driving has received a broad of attention from academia and industry since it is effective in greatly reducing the severity of potential traffic accidents and achieving the ultimate automobile safety and comfort. This article presents a back‐stepping sliding mode controller (BSMC) through linear matrix inequalities (LMIs) for the highly automatic driving vehicle on sloped roads. It includes three key modules, namely, an extended Kalman filter (EKF)‐based road slope estimation module, a robust BSMC‐LMIs velocity‐tracking controller based on the input–output feedback linearization, as well as a longitudinal inverse vehicle dynamics module. The nonlinear combined slip tire model with the transient behavior is introduced to calculate the tire forces properly, which would be further proven to offer more accurate road slope estimations even in a fierce acceleration or deceleration situation. The proposed BSMC‐LMIs controller for velocity tracking can handle the lumped uncertainties which include the modeling error, the parameter perturbation, external disturbances, and noises, and guarantee the reachability of the sliding surface, meanwhile, alleviating the chattering phenomenon inherited from the sliding mode structure. Besides, a sufficient condition for the existence of the proposed BSMC is derived by using the LMIs, which ensures the asymptotical stability on the sliding surface. Finally, the robustness, feasibility, and effectiveness of the proposed BSMC‐LMIs controller for velocity‐tracking are verified by simulation tests in various working scenarios, which shows satisfying results when dealing with the lumped uncertainties on sloped roads. Moreover, the comparative study also shows that the proposed BSMC‐LMIs controller has the best tracking performance when compared to the model predictive control, conventional sliding mode control, and the cubic proportional‐integral controller.

Effect of Non-Linear Thermal Radiation and Partial slip on Unsteady MHD Flow of a Nanofluid Past a Permeable Stretching Sheet through a Porous Medium with Suction/Injection, convective Heat Transfer

We discuss the effect of non-linear thermal radiation on the boundary layer flow of a thermophoretic magnetohydrodynamics dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and temperature dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. We observed that the Radiation parameter (Rd) to enhance the velocity, temperature profiles, heat and mass transfer rates of the fluid and reduce the concentration profiles. An increase in slip parameter (A11), reduces the velocity, enhances the temperature and nano-concentration., Nu and Sh reduce with increasing Rd & A11 on =0. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.

Vehicle yaw stability control with a two-layered learning MPC

This paper proposes a novel framework to address the model-vehicle mismatch (MVM) challenge of yaw stability control, which introduces the Gaussian Process-based Model Predictive Control into the classical two-layer structure. In the upper layer, the supervisor controller calculates the compensation torque required for vehicle turning. Gaussian Process regression is employed to compensate model mismatch and unmodelled dynamics. The chance constraints on sideslip angle are converted into double half-space constraints by the normal distribution quantile function. In the lower layer, the subordinate controller utilises the nonlinear slip rate model to distribute torque to the wheels in the form of braking torque. A new assignment rule of braking torque weight is proposed according to the yaw torque analysis. The stability of the two-layered learning MPC is ensured through proof and simulation. In the Simulink and Carsim co-simulation environment, the superiority of the proposed method is verified in the task of rapid double-lane change. Compared with the traditional MPC-based yaw stability controller, the proposed method has increased the stability tracking index and energy consumption index by around 13% and 8%.

Soret & Dufour and Triple Stratification Effect on MHD Flow with Velocity Slip towards a Stretching Cylinder

The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. The effects of nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) and diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) flow towards a stretching cylinder in the presence of triple stratification (TSF) are investigated in this paper. The governing equations are transformed into an ODE by suitable transformations. The homotopy analysis method (HAM) is used to solve the ODE. The revamping of fluid flow, and heat transfer due to the presence of the Soret and Dufour effect, concentration slip and concentration stratification are analyzed. The temperature and local Sherwood number increases as the Dufour number rises, whereas the local Nusselt number decreases. While elevating the Soret number, the Sherwood number diminishes, whereas the concentration profile rises. The thermal boundary layer thickness enhances when thermal radiation increases. The rate of solute transport reduces while the concentration slip increases.

Unsteady MHD radiative-dissipative flow of Cu-Al[formula omitted]O[formula omitted]/H[formula omitted]O hybrid nanofluid past a stretching sheet with slip and convective conditions: A regression analysis

The current investigation is concerned with the study of unsteady laminar flow with heat and mass transfer of an incompressible and hydromagnetic Cu-Al2O3/H2O hybrid nanofluid near a nonlinearly permeable stretching sheet in the presence of nonlinear thermal radiation, viscous-Ohmic dissipation and velocity slip. Further, the impacts of heat generation/absorption, chemical reaction, convective heat and mass conditions at the boundary are also considered. The prevailing model equations are converted into dimensionless form with the implementation of some suitable similarity transformations. A shooting technique along with Runge–Kutta–Fehlberg method is used to develop the solutions for momentum, thermal and mass fields. The impingements of several controlling parameters on the velocity as well as heat and mass distributions are demonstrated and exhibited graphically. Also, the variations in the physical quantities like skin-friction coefficient, Nusselt and Sherwood numbers are delineated with the help of graphs. The analysis reveals that Hartree pressure gradient and wall velocity slip have the tendency to slow down the flow. On the other side, the velocity ratio parameter, thermal radiation and Biot number boost the fluid temperature. Furthermore, the regression analysis presents that skin-friction is more prone to the suction parameter than the Hartree pressure gradient while the Nusselt number is much sensitive to the radiation parameter as compared to the Eckert number. However, the Sherwood number is dominated by the solutal Biot number.

Qualitative analysis of magnetohydrodynamics stagnation point flow with a novel numerical approach through Shifted Chebyshev collocation method

This paper investigates the third-order nonlinear boundary value problem, resulting from the exact reduction of the Navier-Stokes equation caused by the magnetohydrodynamics boundary layer flow near a stagnation point on a rough plate. The governing partial differential equations are transformed into a nonlinear ordinary differential equation and partial slip boundary conditions by an appropriate similarity transformation. In this previous work, the boundary value problem (BVP) was investigated numerically, and a lot of speculations regarding the existence and behavior of the solutions were carried out. The primary objective of this article is to verify these speculations mathematically. In this work, we have proved that there is a unique solution for all parameters values, and further, the solution has monotonic increasing first derivative. Moreover, the resulting nonlinear boundary value problem is solved by shifted Chebyshev collocation method. We compare the present numerical results with the previous results for the particular physical parameters, concluding that the results are highly accurate. The velocity profiles and streamlines are also plotted to address the significance of the parameters. Our manuscript is a judicial mix between mathematical and numerical methods.

Comparison of flexural capacity of different hollow slab beams with/without pavement layer reinforced by steel plates

PurposeReinforcement of reinforced concrete (RC) beams in-service have always been an important research field, anchoring steel plate in the bottom of the beams is a kind of common reinforcement methods. In actual engineering, the contribution of pavement layer to the bearing capacity of RC beams is often ignored, which underestimates the bearing capacity and stiffness of RC beams to a certain extent. The purpose of this paper is to study the effect of pavement layer on the RC beams before and after reinforcement.Design/methodology/approachFirst, static load experiments are carried out on three in-service RC hollow slab beams, meanwhile, nonlinear finite element models are built to study the bearing capacity of them. The nonlinear material and shear slip effect of studs are considered in the models. Second, the finite element models are verified, and the numerical simulation results are in good agreement with the experimental results. Last, the finite element models are adopted to carry out the research on the influence of different steel plate thicknesses on the flexural bearing capacity and ductility.FindingsThe experimental results showed that pavement layers increase the flexural capacity of hollow slab beams by 16.7%, and contribute to increasing stiffness. Ductility ratio of SPRCB3 and PRCB2 was 30% and 24% lower than that of RCB1, respectively. The results showed that when the steel plate thickness was 1 mm–6 mm, the bearing capacity of the hollow slab beam increased gradually from 2158.0 kN.m to 2656.6 kN.m. As the steel plate thickness continuously increased to 8 mm, the ultimate bearing capacity increased to 2681.0 kN.m. The increased thickness did not cause difference to the bearing capacity, because of concrete crushing at the upper edge.Originality/valueIn this paper, based on the experimental study, the bearing capacity of hollow beam strengthened by steel plate with different thickness is extrapolated by finite element simulation, and its influence on ductility is discussed. This method not only guarantees the accuracy of the bearing capacity evaluation, but also does not require a large number of samples, and has certain economy. The research results provide a basis for the reinforcement design of similar bridges.

Thermophysical impact on the squeezing motion of non-Newtonian fluid with quadratic convection, velocity slip, and convective surface conditions between parallel disks

The present paper considers suction/injection, constant and variable thermophysical influence in squeezing flow of magnetized blood rheological (Casson) fluid model between two parallel disks subjected to nonlinear convection process, slip and convective surface conditions. The unsteady, squeezing, magnetized, and chemically reacting dissipative fluid flowing between parallel disks is modeled and non-dimensionalized via an applicable similarity transformation. An approximate solution of the flow distributions is sought by employing the Chebyshev Collocation Approach (CCA). In the limiting scenario, an excellent agreement in the present results with the existing literature is obtained. The analysis reveals the dominance of constant thermophysical effect over the variable thermo-properties on velocities and temperature field. Higher thermal/solutal Biot number highlighted the dominance of positive squeezing number while its minimal values showcase the dominance of negative squeezing number on flow and energy field. Therein, the squeezing effect remains invariant for some range values of thermal/solutal Biot number, while a rise in velocity slip and suction parameter enhanced the fluid velocities and concentration profiles respectively. Moreover, the current analysis is applicable in moving engines such as in parallel disk gate valve, locomotion of piston in ring where oil is viewed as Casson fluid, thermoforming, injection molding, biomedical use among others.