Control Of Nonlinear Equations Research Articles

Nonlinear statics of magneto-electro-elastic nanoplates considering flexomagnetoelectric effect based on nonlocal strain gradient theory

The nonlinear static behavior of hygrothermal magnetoelectroelastic(MEE) nanoplates considering the flexomagnetoelectric (FME) effect is researched by engaging the first-order shear deformation theory (FSDT). The constitutive equations of MEE nanoplates take into account the FME effect and hygrothermal effect. Leveraging the FSDT, von Karman's nonlinear equation and Hamilton's principle, the nonlinear control equation for hygrothermal MEE nanoplates can be derived by using the variational approach. The nonlocal strain gradient theory (NSGT) has application in the size effect of MEE nanoplates. The nonlocal nonlinear term in the control equation is handled by employing the Airy stress function, and then the non-linear mechanical model is solved by the Galerkin method. Thus, the nonlinear load-deflection curves (NLDC) of the MEE nanoplate are obtained via the introduction of material parameters, enabling an examination of the impact of various factors such as the FME effect, two small size parameters of NSGT and other parameters on the nonlinear bending behavior of MEE nanoplates. In conclusion, this study offers a theoretical foundation for taking into account the FME effect in the development of nanodevices, thereby contributing to advancements in this field.

Analysis of the Mechanical Properties and Study of Influential Factors of Different Materials in Tape Spring

This paper analyzes and calculates the mechanical properties of composite tape spring structures during folding and bending and establishes a non-linear control equation for the folding and bending of composite laminate tape spring structures. Accurate expressions for folding and bending displacements are obtained. The influence of the cross-section’s central angle and the composite tape spring’s ply thickness on their mechanical properties are analyzed. Finite element numerical analysis is performed on [−45 45]s laminated composite tape springs, and the correctness of the theoretical derivation is proved by comparing the curvature radius-bending moment curve. Based on previous research, the mechanical properties of different tape spring materials and structures are compared, further studying the lightweight design of space deployment mechanisms. The results show that the steady-state bending moment performance of composite tape springs is excellent, with a 162.1% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs. Additionally, the critical bending moment performance of negative Poisson ratio honeycomb structure tape springs is also excellent, with a 62.3% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs.

Static and dynamic characteristics of post-buckling of porous functionally graded pipes under thermal shock

The study of thermal post-buckling characteristics of functionally graded pipelines is of great significance for promoting the application of functionally graded materials in spacecraft thermal protection design and marine pipelines. In this study, the static buckling of functionally graded pipes with porosity and the pseudo-linear vibration near the first buckling position of post-buckling are studied. Based on the modified power-law distribution, it is assumed that the material properties of porous FGM pipes change continuously and smoothly along the radial direction. For porosity, it generally occurs in the manufacturing process of functionally graded materials, so the classical Voigt model is selected to describe the material properties of functionally graded material pipelines with pores. Based on Hamilton principle, the nonlinear control equations and corresponding boundary conditions of the pipeline are derived. Firstly, the Routh-Hurwitz criterion is used to discuss the influence of temperature and porosity volume fraction on the critical flow velocity of instability, and then the post-buckling structure of the pipeline and the dynamic characteristics of post-buckling are discussed. The numerical results discussed the influence of important parameters such as power law index, porosity volume fraction and temperature on the buckling and post-buckling behaviors of the system.

A Mixed Stream of Viscoelastic Liquid Through a Porous Medium is Situated in a Vertical Channel with Permeable Walls

We examined the completely developed mixed convection flow of a visco-elastic fluid via a porous medium in a vertical channel with a permeable wall. The non-linear control equations have been resolved using the conventional disturbing method for the speed and temperature domain. Graphs will be used to detail the effects on speed and temperature of the viscoelastic Reynold number, the cross flow parameter, the number of Grashof , and Prandtl temperature.

Multiple Slip Effects on Magnetohydrodynamic Axisymmetric Buoyant Nanofluid Flow above a Stretching Sheet with Radiation and Chemical Reaction

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

Dynamic response of temperature-seepage-stress coupling in asphalt pavement

Abstract Temperature-seepage-stress coupling exists in asphalt pavement and directly affects force and failure mechanisms in the pavement structure. The objective of this paper is to propose a systematic approach to simulate the dynamic characteristics of asphalt pavement, under the combined effects of vehicle dynamic load and environmental factors. In the simulation, the asphalt viscoelastic constitutive equation was established using Burger’s model, to derive the nonlinear control equation of thermal-hydraulic-mechanical coupling of asphalt pavement. Then, a finite element model of asphalt pavement was built using the software ABAQUS. The thermal stress and pore water pressure in pavement structure were analyzed under the condition of rainfall infiltration. Moreover, vertical stress, longitudinal stress, transverse stress and shear stress of different structural layers were analyzed and computed under the multi-field condition. These stresses were then compared to the stresses in the single stress field. The results show that when seepage and temperature are considered, stress change of the subbase is insignificant. However, the transverse stress in the modified fine-grained asphalt concrete layer (AC-1) and the vertical shear stress in the asphalt macadam layer (AM) increased 30% and 53% respectively, compared to the single stress field. This would lead to the occurrence of rutting and cracks in asphalt pavement, which accordingly seriously affects the road performance in hot and rainy weather. The field test was carried out in the DaGuang Highway, and the validity of the simulation model was verified.

Unsteady heat transfer performance of heat pipe with axially swallow-tailed microgrooves

A mathematical model is developed for predicting the transient heat transfer and fluid flow of heat pipe with axially swallow-tailed microgrooves. The effects of liquid convective heat transfer in the microgrooves, liquid-vapor interfacial phase-change heat transfer and liquid-vapor interfacial shear stress are accounted for in the present model. The coupled non-linear control equations are solved numerically. Mass flow rate at the interface is obtained from the application of kinetic theory. Time variation of wall temperature is studied from the initial startup to steady state. The numerical results are verified by experiments. Time constants for startup and shutdown operation are defined to determine how fast a heat pipe responds to an applied input heat flux, which slightly decreases with increasing heat load.

The estimation of the dynamics of indirect control switching systems

Abstract The paper deals with the time switching hybrid systems described by nonlinear control equations with nonlinearity of a sector form. The estimation of the solution of the control system at any moment is established through the method of Lyapunov function. Both cases, stable and unstable control systems are considered. The final estimation of the solution of the hybrid system is obtained from the composition of perturbations of the separate control systems using the condition of solution continuity in the points of switching.

Stochastic Optimal Control for the Stochastic Heat Equation with Exponentially Growing Coefficients and with Control and Noise on a Subdomain

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain.

Stochastic Optimal Control Problems and Parabolic Equations in Banach Spaces

We consider stochastic optimal control problems in Banach spaces. These problems are related to nonlinear controlled equations with dissipative nonlinearity and are treated via the backward stochastic differential equation approach, which also allows us to solve, in a mild sense, Hamilton-Jacobi-Bellman equations in Banach spaces. We apply the results to controlled stochastic heat and wave equations with a cost functional that is well defined on continuous functions, and to delay equations in spaces of $p$-integrable functions.

Fitting of a neural network to control the intelligent operation of a high voltage circuit breaker

‘Intelligent operation (IO)’ can improve the reliability of a high voltage circuit breaker and prolong its life. In this paper an artificial neural network (ANN) is used in the control of circuit breaker intelligent operation. Thus, during real-time control, it can save a lot of calculating time spent in the very complicated opening process of the circuit breaker. In the design of the controller of a circuit breaker IO, the structure of feedforward multilayer network is used, and two kinds of back-propagation learning algorithms, the self-adapting adjusting learning and the momentum method, are applied to the supervised training of the neural network. Both algorithms greatly enhance the training speed, shorten the training time and speed up the convergence. After training, an artificial neural network controller (ANNC) of the system is formed. It is proved that the ANNC has a higher accuracy and can meet the controlling requirement of the circuit breaker IO. This method can be used for reference by other control systems for solving complicated nonlinear control equations.

LINEAR AND NONLINEAR AERODYNAMIC THEORY OF INTERACTION BETWEEN FLEXIBLE LONG STRUCTURE AND WIND

In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci = Ci(β(t), Θ), (i = D, L, M). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with “strip theory” and modified “quasi-static theory”, and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called “flutter derivatives” corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bohm's.

On the Optimal Control for Nonlinear Equations with Impulses

On the Optimal Control for Nonlinear Equations with Impulses

Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions

This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. The emphasis is placed on hyperbolic and parabolic systems. Related subjects such as spectral determination, control of nonlinear equations, linear quadratic cost criteria and time optimal control are also discussed.

The Maximum Principle and Controllability of Nonlinear Equations

The main result proved is that a nonlinear control equation is controllable if a related linear equation is controllable. The result allows the set of control values to be discrete and it is not assumed that “small” values of the control are available. The methods used are closely related to the Pontryagin maximum principle.

Dynamic computer regulation of a dry-process cement kiln

The paper describes the application of adigital computer to the dynamic regulation of a dry-process Humboldt cement kiln and its associated Fuller cooler. The background to the project and an outline of this particular process and its control problems are given. The control hardware is then briefly outlined, together with details of the kiln models and their method of derivation. Particular attention is paid to the problem of measuring the burning-zone temperature, and the close correlation of this measurement with kiln power, which can be used as an alternative indication of burning zone temperature in the short term. The control system and the discrete equations for control of the kiln are also given, together with a discussion of their functions. One feature of this application, which greatly reduced commissioning time, was the implementation of the linear and nonlinear control equations entirely by a standard conversational control package online via a control panel without programming in the conventional sense. The commissioning procedure and the results obtained under control are discussed.

Hydrogen bubble flow visualization at low Reynolds numbers.

where /i and /2 are the control variables and the arM depend on various sensitivity coefficients and on the measured density parameter and initial condition deviations. Setting the expressions for the terminal velocity and range angle errors equal to zero then gives two nonlinear algebraic equations in /i and /2 which must be solved simultaneously. To insure convergence, the aforementioned problem was converted to an ordinary minimum problem which was solved numerically using a gradient technique.5 The performance of the first- and second-order sensitivity guidance schemes is compared in Table 2. First, the uncontrolled terminal velocity and range angle deviations due to atmospheric parameter differences are given. Then the results of the first-order sensitivity guidance with updating are given. Next, first-order guidance without updating is simulated. In this case, the controls determined at the beginning of entry are applied all the way down to 20,000 ft. Finally, second-order guidance without updating is implemented. Conclusions Second-order sensitivity analysis is introduced to improve the accuracy of the error prediction equations. A new vectormatrix differential equation for the second-order sensitivity coefficients of a general system is derived. A difference in form between the first- and second-order sensitivity equations is noted. For the first-order case, it was possible to describe all the terminal values by using the adjoint sensitivity equation. For the second-order coefficients, this procedure is possible only for a certain approximation to the second-order sensitivity forcing function. Numerical simulation of second sensitivity guidance including solution of the nonlinear control equations is performed and the results summarized in Table 2.

Stability of Following in Two Dimensions

The mechanism by which objects follow each other on a two-dimensional surface is considered, with the movement of a convoy of ships in mind as a physical example. This is to be compared with single-lane traffic dynamics, which is essentially a one-dimensional following theory applied to cars on a straight highway. At first the assumed laws of following are linear in the position and velocity vectors of the ships, and the form of relation used is one suggested partly by previous work on traffic dynamics and partly from the theory of guided missiles. As a measure of imperfections in speed control and steering, various types of time constants are introduced and the resulting equations tested for stability, yielding criteria for the maximum permissible size of the time constants. Nonlinear control equations are also investigated, and by making linear approximations to the trajectories in these cases, stability criteria are again suggested. Finally a few computed trajectories have been obtained, including an interesting example where the following ship suddenly reverses its direction of motion in course.