Nonlinear behaviour of quasicrystals

2011 ◽  
pp. 289-316
Author(s):  
Tianyou Fan
Keyword(s):  
Nonlinear Behaviour

Adaptive Control Scheme for Coupled Tank Process

2018 ◽  
pp. 89-95
Author(s):  
Vinodhini M.
Keyword(s):  
Adaptive Control ◽  
Nonlinear Behaviour ◽  
Simulation Studies ◽  
Input Output ◽  
Control Scheme ◽  
Direct Model ◽  
Multivariable Process ◽  
Model Reference Adaptive ◽  
Siso System ◽  
Adaptive Control Scheme

The objective of this paper is to develop a Direct Model Reference Adaptive Control (DMRAC) algorithm for a MIMO process by extending the MIT rule adopted for a SISO system. The controller thus developed is implemented on Laboratory interacting coupled tank process through simulation. This can be regarded as the relevant process control in petrol and chemical industries. These industries involve controlling the liquid level and the flow rate in the presence of nonlinearity and disturbance which justifies the use of adaptive techniques such as DMRAC control scheme. For this purpose, mathematical models are obtained for each of the input-output combinations using white box approach and the respective controllers are developed. A detailed analysis on the performance of the chosen process with these controllers is carried out. Simulation studies reveal the effectiveness of proposed controller for multivariable process that exhibits nonlinear behaviour.

Fuzzy Sets Theory in Comparison with Stochastic Methods to Analyse Nonlinear Behaviour of a Steel Member under Compression

2005 ◽  
Vol 10 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Z. Kala
Keyword(s):  
Fuzzy Sets ◽  
Carrying Capacity ◽  
Stochastic Methods ◽  
Nonlinear Behaviour ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Input Parameters ◽  
Stochastic Solution ◽  
Fuzzy Solution ◽  
Sets Theory

The load-carrying capacity of the member with imperfections under axial compression is analysed in the present paper. The study is divided into two parts: (i) in the first one, the input parameters are considered to be random numbers (with distribution of probability functions obtained from experimental results and/or tolerance standard), while (ii) in the other one, the input parameters are considered to be fuzzy numbers (with membership functions). The load-carrying capacity was calculated by geometrical nonlinear solution of a beam by means of the finite element method. In the case (ii), the membership function was determined by applying the fuzzy sets, whereas in the case (i), the distribution probability function of load-carrying capacity was determined. For (i) stochastic solution, the numerical simulation Monte Carlo method was applied, whereas for (ii) fuzzy solution, the method of the so-called α cuts was applied. The design load-carrying capacity was determined according to the EC3 and EN1990 standards. The results of the fuzzy, stochastic and deterministic analyses are compared in the concluding part of the paper.

SEISMIC CAPACITY OF MEDIUM SIZE CONTINUOUS BRIDGES WITH LEAD-RUBBER BEARINGS

2019 ◽  
Vol 3 (Special Issue on First SACEE'19) ◽  
pp. 199-206
Author(s):  
Bertha Olmos ◽  
José Jara ◽  
José Luis Fabián
Keyword(s):  
Seismic Performance ◽  
Seismic Vulnerability ◽  
Base Isolation ◽  
Elastic Behaviour ◽  
Medium Size ◽  
Nonlinear Behaviour ◽  
Seismic Capacity ◽  
Damage Scenarios ◽  
Isolation Systems ◽  
Rubber Bearings

This paper investigates the effects of the nonlinear behaviour of isolation pads on the seismic capacity of bridges to identify the parameters of base isolation systems that can be used to improve seismic performance of bridges. A parametric study was conducted by designing a set of bridges for three different soil types and varying the number of spans, span lengths, and pier heights. The seismic responses (acceleration, displacement and pier seismic forces) were evaluated for two structural models. The first model corresponded to the bridges supported on elastomeric bearings with linear elastic behaviour and the second model simulated a base isolated bridge that accounts for the nonlinear behaviour of the system. The seismic demand was represented with a group of twelve real accelerograms recorded on the subduction zone on the Pacific Coast of Mexico. The nonlinear responses under different damage scenarios for the bridges included in the presented study were estimated. These results allow determining the seismic capacity of the bridges with and without base isolation. Results show clearly the importance of considering the nonlinear behaviour on the seismic performance of bridges and the influence of base isolation on the seismic vulnerability of medium size bridges.

An elastic phenomenological material law of technical textile with a nonlinear shear behaviour

2021 ◽  
pp. 073168442110058
Author(s):  
Dániel T Karádi ◽  
András A Sipos ◽  
Marianna Halász ◽  
Viktor Hliva ◽  
Dezső Hegyi
Keyword(s):  
Service Level ◽  
Shear Behaviour ◽  
Nonlinear Behaviour ◽  
Exponential Functions ◽  
Normal Stiffness ◽  
Material Parameters ◽  
Fitting Method ◽  
Highly Nonlinear ◽  
Nonlinear Shear ◽  
Magnitude Difference

In technical textile engineering, macro-level phenomenological modelling effectively describes the material’s highly nonlinear behaviour. However, existing material laws concentrate on the normal stiffness in the orthotropic yarns and simplify the shear effect because of the two orders of magnitude difference between shear and normal stiffness. This article introduces an improved phenomenological model that includes nonlinear shear behaviour, and it determines the material parameters with a previously applied data fitting method for exponential functions. The nonlinear shear behaviour is valid for the elastic state, that is, at the service level of the loads. Time-dependent, cyclic loading or plastic behaviour is not considered.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Generation of steady longitudinal vortices in hypersonic boundary layer

2013 ◽  
Vol 729 ◽  
pp. 702-731 ◽  
Author(s):  
A. I. Ruban ◽  
M. A. Kravtsova
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscosity Coefficient ◽  
Momentum Equation ◽  
The Body ◽  
Nonlinear Behaviour ◽  
Hypersonic Boundary Layer ◽  
Stagnation Temperature ◽  
Characteristic Distance

AbstractIn this paper we study the three-dimensional perturbations produced in a hypersonic boundary layer by a small wall roughness. The flow analysis is performed under the assumption that the Reynolds number, $R{e}_{0} = {\rho }_{\infty } {V}_{\infty } L/ {\mu }_{0} $, and Mach number, ${M}_{\infty } = {V}_{\infty } / {a}_{\infty } $, are large, but the hypersonic interaction parameter, $\chi = { M}_{\infty }^{2} R{ e}_{0}^{- 1/ 2} $, is small. Here ${V}_{\infty } $, ${\rho }_{\infty } $ and ${a}_{\infty } $ are the flow velocity, gas density and speed of sound in the free stream, ${\mu }_{0} $ is the dynamic viscosity coefficient at the ‘stagnation temperature’, and $L$ is the characteristic distance the boundary layer develops along the body surface before encountering a roughness. We choose the longitudinal and spanwise dimensions of the roughness to be $O({\chi }^{3/ 4} )$ quantities. In this case the flow field around the roughness may be described in the framework of the hypersonic viscous–inviscid interaction theory, also known as the triple-deck model. Our main interest in this paper is the nonlinear behaviour of the perturbations. We study these by means of numerical solution of the triple-deck equations, for which purpose a modification of the ‘skewed shear’ technique suggested by Smith (United Technologies Research Center Tech. Rep. 83-46, 1983) has been used. The technique requires global iterations to adjust the viscous and inviscid parts of the flow. Convergence of such iterations is known to be a major problem in viscous–inviscid calculations. In order to achieve improved stability of the method, both the momentum equation for the viscous part of the flow, and the equations describing the interaction with the flow outside the boundary layer, are treated implicitly in this study. The calculations confirm the fact that in this sort of flow the perturbations are capable of propagating upstream in the boundary layer, resulting in a perturbation field which surrounds the roughness on all sides. We found that the perturbations decay rather fast with the distance from the roughness everywhere except in the wake behind the roughness. We found that if the height of the roughness is small, then the perturbations also decay in the wake, though much more slowly than outside the wake. However, if the roughness height exceeds some critical value, then two symmetric counter-rotating vortices form in the wake. They appear to support themselves and grow as the distance from the roughness increases.

scholarly journals The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

2001 ◽  
Vol 19 (4) ◽  
pp. 177-188
Author(s):  
B Eitzinger ◽  
G Ederer
Keyword(s):  
Pressure Drop ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Constitutive Equations ◽  
Darcy’S Law ◽  
Stationary Flow ◽  
Darcy's Law ◽  
Nonlinear Behaviour ◽  
Cigarette Paper ◽  
Drop Flow

AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

Linear and nonlinear behaviour of two-stream instabilities in collisionless plasmas

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Y. W. Hou ◽  
M. X. Chen ◽  
M. Y. Yu ◽  
B. Wu
Keyword(s):  
Normal Mode Analysis ◽  
System Size ◽  
Point Of View ◽  
Mode Analysis ◽  
Nonlinear Behaviour ◽  
Initial Growth ◽  
Small Magnitude ◽  
Plasma Oscillations ◽  
Numerical Noise ◽  
Growth Properties

The transient, growth and nonlinear saturation stages in the evolution of the electrostatic two-stream instabilities as described by the Vlasov–Poisson system are reconsidered by numerically following the evolution of the total wave energy of the plasma oscillations excited from (numerical) noise. Except for peculiarities related to the necessarily finite (even though very small) magnitude of the perturbations in the numerical simulation, the existence and initial growth properties of the instabilities from the numerical results are found to be consistent with those from linear normal mode analysis and the Penrose criteria. However, contradictory to the traditional point of view, the growth of instability before saturation is not always linear. The initial stage of the growth can exhibit fine structures that can be attributed to the harmonics of the excited plasma oscillations, whose wavelengths are determined by the system size and the numerical noise. As expected, saturation of the unstable oscillations is due to electron trapping when they reach sufficiently large amplitudes.

The time-asymptotic stability of shocks in cosmic-ray hydrodynamics

1988 ◽  
Vol 39 (3) ◽  
pp. 539-548 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Short Wavelength ◽  
Cosmic Ray ◽  
Hydrodynamical Model ◽  
Shock Formation ◽  
Nonlinear Behaviour ◽  
Two Fluid

The nonlinear behaviour of short-wavelength perturbations in the two-fluid cosmic-ray hydrodynamical model is examined. We show that such a perturbation leads to shock formation and derive the appropriate wave equation. We show that a discontinuous perturbation incident on a weak cosmic-ray shock destabilizes, in a time-asymptotic sense, the shock.

Maximum Power Point Tracking (MPPT) for a Solar Photovoltaic System: A Review

2015 ◽  
Vol 787 ◽  
pp. 227-232 ◽  
Author(s):  
L.A. Arun Shravan ◽  
D. Ebenezer
Keyword(s):  
Solar Energy ◽  
Maximum Power Point Tracking ◽  
Maximum Power ◽  
Nonlinear Behaviour ◽  
Pv System ◽  
Maximum Power Point ◽  
Pv Systems ◽  
Point Tracking ◽  
Power Point Tracking ◽  
Power Point

In recent years there has been a growing attention towards use of solar energy. Advantages of photovoltaic (PV) systems employed for harnessing solar energy are reduction of greenhouse gas emission, low maintenance costs, fewer limitations with regard to site of installation and absence of mechanical noise arising from moving parts. However, PV systems suffer from relatively low conversion efficiency. Therefore, maximum power point tracking (MPPT) for the solar array is essential in a PV system. The nonlinear behaviour of PV systems as well as variations of the maximum power point with solar irradiance level and temperature complicates the tracking of the maximum power point. This paper reviews various MPPT methods based on three categories: offline, online and hybrid methods. Design of a PV system in a encoding environment has also been reviewed here. Furthermore, different MPPT methods are discussed in terms of the dynamic response of the PV system to variations in temperature and irradiance, attainable efficiency, and implementation considerations.

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