Nonlinear Physical Models Research Articles

A Distributed Plasticity Approach for Steel Frames Analysis Including Strain Hardening Effects

This paper focuses on the creation and numerical application of physically nonlinear plane steel frames analysis problems. The frames are analysed using finite elements with axial and bending deformations taken into account. Two nonlinear physical models are used and compared – linear hardening and ideal elastic-plastic. In the first model, distributions of plastic deformations along the elements and across the sections are taken into account. The proposed method allows for an exact determination of the stress-strain state of a rectangular section subjected to an arbitrary combination of bending moment and axial force. Development of plastic deformations in time and distribution along the length of elements are determined by dividing the structure (and loading) into the parts (increments) and determining the reduced modulus of elasticity for every part. The plastic hinge concept is used for the analysis based on the ideal elastic-plastic model. The created calculation algorithms have been fully implemented in a computer program. The numerical results of the two problems are presented in detail. Besides the stress-strain analysis, the described examples demonstrate how the accuracy of the results depends on the number of finite elements, on the number of load increments and on the physical material model. COMSOL finite element analysis software was used to compare the presented 1D FEM methodology to the 3D FEM mesh model analysis.

The expa function method and the conformable time-fractional KdV equations

Abstract The nonlinear fractional differential equations (FDEs) are produced by mathematical modelling of some nonlinear physical systems. The study of such nonlinear physical models through wave solutions analysis corresponding to their FDEs, has a dynamic role in applied sciences. In this paper, we are going to explore the conformable time-fractional KdV equations using the expa function method. The way to reach explicit exact wave solutions is to transform the fractional order PDE into a nonlinear ODE of discrete order through travelling wave transforms. The subsequent equation has been explored by utilizing the exp a function approach. Consequently, some new explicit exact wave solutions of the said equations are effectively formulated and graphically conveyed with the help of numerical simulation.

Optimized Control Based on Nonlinear Modelling and Parameter Estimation of the Electro-Hydraulic Servo System

In this paper, a nonlinear physical model of the electro-hydraulic system is built and described in Bond Graph in order to show its physical structure and flow of energy. The nonlinear model is simplified based on response bandwidth of different parts of system and nonlinear degree. A series of typical parameters of the model are chosen based on the effect on nonlinear response of system and estimated with the experiment response. A simple and useful model based nonlinear feedforward PID control methods is proposed based on the steady state response of system and dynamic stribeck friction force. The simulation and experiment results of parameter estimation and feedforward control are presented, which shows that the model response with estimated parameters can fit the experimental data very well, and the simulation and experiment response of the optimized control can eliminate the nonlinear response very well. Therefore, the nonlinear model and control method used in this paper have a guiding significance and application value, and have theory value for the further research of hydraulic servo system with the similar structure.

Application of $$\tan (\Phi (\xi )/2)$$tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model

Based on the $$\tan (\Phi (\xi )/2)$$-expansion method, five nonlinear fractional physical models for obtaining the solutions containing three types hyperbolic function, trigonometric function and rational function solutions are investigated. These equations are the time fractional biological population model, time fractional Burgers, time fractional Cahn–Hilliard, space–time fractional Whitham–Broer–Kaup, space–time fractional Fokas equations. The fractional derivative is described in the Caputo sense. We obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these equations to ordinary differential equations which subsequently resulted into number of exact solutions.

Analytical Solution of Two Dimensional Nonlinear Space–Time Fractional Burgers–Huxley Equation Using Fractional Sub-Equation Method

The analytical solution of nonlinear two dimensional space–time fractional Burgers–Huxley equation involving Jumarie’s modified Riemann–Liouville derivative is derived using the tool fractional sub equation method. The obtained results clearly exhibit that the mathematical tool is quite effective, efficient and appropriate for solving various kinds of nonlinear fractional order physical models compared to other existing schemes.

Dark and singular optical solutions with dual-mode nonlinear Schrödinger's equation and Kerr-law nonlinearity

Recently, a new family of nonlinear physical models under the name of dual-mode nonlinear equations has been arisen. Several real-valued dual-mode equations associated with well-known single-mode equations such as KdV, mKdV, and Burgers’ have been established and studied. In this study, we provide the first attempt to establish a complex-valued dual-mode equation that corresponds to the single-mode nonlinear Shrödinger equation. Accordingly, necessary conditions on the nonlinearity and dispersion parameters for the existence of two right-left (R-L) moving wave solutions are explored. Finally, graphical analysis is provided to validate the findings of this work.

Solitons in an inhomogeneous Murnaghan’s rod

In this paper, we construct a family of wave solutions to the doubly dispersive equation, such as topological, non-topological, singular, compound topological-non-topological bell-type and compound singular, soliton-like, singular periodic wave and exponential function solutions. These analytical solutions are obtained by using the extended sinh-Gordon equation expansion method and the modified $\exp(-\varphi(\zeta))$ -expansion function method. The doubly dispersive equation is an important nonlinear physical model describing the nonlinear wave propagation in the elastic inhomogeneous Murnaghan’s rod. Under a suitable choice of parameters, the 2D, 3D and contour graphics to the reported results are also plotted.

Robust model predictive control for greenhouse temperature based on particle swarm optimization

Application of model predictive control (MPC) in horticultural practice requires detailed models. However, even highly sophisticated greenhouse climate models are often known to have unknown dynamics affected by bounded uncertainties. To enforce robustness during the controller design stage, this paper proposes a particle swarm optimization (PSO)-based robust MPC strategy for greenhouse temperature systems. The strategy is based on a nonlinear physical temperature affine model. The robust MPC technique requires online solution of a minimax optimal control problem, which optimizes the tradeoff between set point tracking and cost requirements reduction. The minimax optimization problem is reformulated to a nonlinear programming problem with constraints. PSO is used to solve the reformulated problem and priority ranking of constraint fitness is proposed to guarantee that the constraints are satisfied. The results of simulations performed using the proposed control system show that the controller can effectively achieve the set point in the presence of disturbances and that it offers more suitable control variables, higher control precision, and stronger robustness than the conventional MPC.

Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity

This study is devoted to analyze the influence of variable diffusion coefficient and variable thermal conductivity on heat and mass transfer in Casson fluid flow. The behavior of concentration and temperature profiles in the presence of Joule heating and viscous dissipation is also studied. The dimensionless conversation laws with suitable BCs are solved via Modified Gegenbauer Wavelets Method (MGWM). It has been observed that increase in Casson fluid parameter $$ (\beta ) $$ and parameter $$ \epsilon $$ enhances the Nusselt number. Moreover, Nusselt number of Newtonian fluid is less than that of the Casson fluid. The phenomenon of mass transport can be increased by solute of variable diffusion coefficient rather than solute of constant diffusion coefficient. A detailed analysis of results is appropriately highlighted. The obtained results, error estimates, and convergence analysis reconfirm the credibility of proposed algorithm. It is concluded that MGWM is an appropriate tool to tackle nonlinear physical models and hence may be extended to some other nonlinear problems of diversified physical nature also.

Nonlinear Model-Based Multivariable Control for Air & Charging System of Diesel Engine with Short and Long Route EGR Valves

The objective of this study is to investigate a nonlinear model-based multivariable (MIMO, Multi Input Multi Output) technique to decouple actuators interaction and to reduce the calibration effort, while increasing control performances, above all in transient conditions, and robustness with respect to model uncertainties and system parameter variations. The presented control technique is based on the development of a nonlinear dynamical physical model of the diesel air and charging system. Feedback Linearization control is then applied to decouple actuators’ interactions and compensate for nonlinearities. A new set of virtual inputs are defined inverting the system differential equations. Relation among the new virtual inputs and the outputs is purely linear and decoupled, meaning that each virtual input affects linearly only one output. Moreover, a linear control block is added to guarantee transient and steady state performances and closed loop robustness. The proposed control approach has been validated through small diesel engine dyno and vehicle activities. Transient test bench maneuvers show that the control is able to coordinate the actuators in order to fulfill the targets and to guarantee similar performances in different operating points. In addition the robustness to environmental changes has been demonstrated by vehicle tests at different ambient conditions.

Modified Chebyshev Wavelet-Picard Technique for Thin Film Flow of Non-Newtonian Fluid Down an Inclined Plane

For the past few decades, solutions of the nonlinear differential equations are of great importance and interest for researchers and scientists around the globe. Most of the physical phenomena’s around us can easily be modeled into nonlinear differential equations. In this article, a new method is proposed by using shifted Chebyshev wavelets and Picard iteration technique to tackle with the nonlinearity of these physical problems. The proposed scheme is very user friendly and extremely accurate. The accuracy of the proposed scheme is verified by the help of a nonlinear physical model representing the thin film flow of a third grade fluid down an inclined plane. Numerical solution is also sought using Runge–Kutta order 4 method. Results are obtained by shifted Chebyshev wavelets at different iterations of Picard technique for different values of parameters are described in table and graphs which confirms the accuracy and stability of the proposed technique.

An improved instrumental variable method for industrial robot model identification

Industrial robots are electro-mechanical systems with double integrator behaviour, necessitating operation and model identification under closed-loop control conditions. The Inverse Dynamic Identification Model (IDIM) is a mechanical model based on Newton’s laws that has the advantage of being linear with respect to the parameters. Existing Instrumental Variable (IDIM-IV) estimation provides a robust solution to this estimation problem and the paper introduces an improved IDIM-PIV method that takes account of the additive noise characteristics by adding prefilters that provide lower variance estimates of the IDIM parameters. Inspired by the prefiltering approach used in optimal Refined Instrumental Variable (RIV) estimation, the IDIM-PIV method identifies the nonlinear physical model of the robot, as well as the noise model resulting from the feedback control system. It also has the advantage of providing a systematic prefiltering process, in contrast to that required for the previous IDIM-IV method. The issue of an unknown controller is also considered and resolved using existing parametric identification. The evaluation of the new estimation algorithms on a six degrees-of-freedom rigid robot shows that they improve statistical efficiency, with the controller either known or identified as an intrinsic part of the IDIM-PIV algorithm.

On the solitary wave solutions to the longitudinal wave equation in MEE circular rod

This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences.

Two-Degree-of-Freedom H∞ Control of Diesel Engine Air Path System with Nonlinear Feedforward Controller

In this research, we developed a two-degree-of-freedom control system for a Diesel engine air path system. First, a physical air path model of the Diesel engine was developed. Then, a feedforward controller was designed based on the inverse of the developed physical model, thus reducing the computational effort in real-time calculation. The feedback controller was designed by using an H∞ control theory by regarding the plant nonlinearities and the response delay of the actuators as uncertainties to the nominal model. The feedforward and feedback controllers were implemented as a two-degree-of-freedom control scheme. Further, an anti-windup scheme was introduced in the feedback controller to reduce the overshoot in the intake manifold pressure response. The effectiveness of the proposed method was evaluated by conducting not only simulations using the nonlinear physical model, but also experiments using a real Diesel engine.

Advance Exp (-Φ(ξ)) Expansion Method and Its Application to Find the Exact Solutions for Some Important Coupled Nonlinear Physical Models

The theoretical investigations of resonance physical phenomena by nonlinear coupled evolution equations are become important in currently. Hence, the purpose of this paper is to represent an advance exp (-Φ(ξ))-expansion method with nonlinear ordinary differential equation for finding exact solutions of some nonlinear coupled physical models. The present method is capable of evaluating all branches of solutions simultaneously and this difficult to distinguish with numerical technique. To verify its computational efficiency, the coupled classical Boussineq equation and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashili equation are considered. The obtained solutions in this paper reveal that the method is a very effective and easily applicable of formulating the exact traveling wave solutions of the nonlinear coupled evolution equations arising in mathematical physics and engineering.

Linear Quadratic Optimal Control Applied to the Greenhouse Temperature Hierarchal System

Optimal greenhouse temperature management systems as hierarchical systems have been employed to achieve suitable conditions for crop growth. The system is generally decomposed into upper and lower layers. The lower layer usually includes online controllers that try to cancel tracking errors of temperature set points obtained from the upper layer. However, as the greenhouse temperature is highly non-linear, the problem of lower layer controller design becomes very complex and the online computational demands are great, which limit the practical applications of hierarchical systems. This paper presents the design of a practical greenhouse temperature hierarchical control approach. In lower layer, a linear quadratic optimal controller with heater inputs is used. The strategy is based on a linearised model achieved by using an accurate linearisation method for an inside temperature non-linear physical model which can be described as an affine non-linear one. The controller is designed by means of finding a tradeoff between set point tracking and cost requirements reduction. The upper layer calculates optimal temperature trajectories by minimising net costs. Performance of the hierarchical control system is studied in simulation. The results show that the upper layer controller can effectively achieve the set point and that the lower layer controller can contribute to a good control performance with a minor cost increment.

Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation

This study uses two mathematical approaches in constructing dark, bright, kink-type and singular soliton solutions to the Heisenberg ferromagnetic spin chain equation. The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation describes nonlinear dynamics of magnets. The acquired results in this study may help in explaining some physical meanings of some nonlinear physical models arising in electromagnetic waves. For instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic cotangent arises in the Langevin function for magnetic polarization. The 2-, 3-dimensional and the contour plots of all the acquired solutions are presented.

A High-Frequency Compact Model for Graphene Resonant Channel Transistors Including Mechanical Nonlinear Effects

This paper presents a physical-based high-frequency nonlinear model of graphene resonant channel transistors (G-RCTs), including a nonlinear electromechanical model of doubled clamped graphene mechanical resonators. To accurately describe the temperature-dependent modal dispersion, both bias- and temperature-dependent effects are considered. The temperature-dependent built-in strain, the bias-based electrostatic force, and the spring restoring force, including the nonlinear term upon deformation, are used to describe the mechanical motion of the suspended beam. The nonlinear model is validated by the measured results of G-RCTs, which indicate that our model can predict the experimental results well. Moreover, the nonlinear effects, including harmonic distortion, third-order intermodulation distortion, and the hysteresis and nonlinear behavior of G-RCTs, are also studied. The results show that the nonlinear physical model can predict the response of G-RCTs very well. These results also show that the mechanical nonlinearity has strong effects on nonlinear distortion for G-RCTs. The nonlinear equivalent circuit model could be useful for nanoelectromechanical system in the applications of high-frequency integrated circuits.

Frequency sensitivity in mammalian hearing from a fundamental nonlinear physics model of the inner ear

A dominant view holds that the outer and middle ear are the determining factors for the frequency dependence of mammalian hearing sensitivity, but this view has been challenged. In the ensuing debate, there has been a missing element regarding in what sense and to what degree the biophysics of the inner ear might contribute to this frequency dependence. Here, we show that a simple model of the inner ear based on fundamental physical principles, reproduces, alone, the experimentally observed frequency dependence of the hearing threshold. This provides direct cochlea modeling support of the possibility that the inner ear could have a substantial role in determining the frequency dependence of mammalian hearing.

Formation of Kerr waveguide and microgratings on a germanium surface under the action of femtosecond radiation of the mid-IR range

A new nonlinear physical model of the formation of ordered structures of a surface topography of a semiconductor by ultrashort pulses of linearly polarized laser radiation has been proposed. The model is based on the formation of the dynamic near-surface waveguide due to the optical Kerr effect, interference with the part of waveguide modes, and the formation of microgratings on the surface, which are oriented by polarization of radiation. The model is confirmed by experimental data.