Search results for: nonlinear viscoelastic

Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Hendradi Hardhienata, Tony Sumaryada, Sri Setyaningsih

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Current progress in the field of nonlinear optics has enabled precise surface characterization in semiconductor materials. Nonlinear optical techniques are favorable due to their nondestructive measurement and ability to work in nonvacuum and ambient conditions. The advance of the bond hyperpolarizability models opens a wide range of nanoscale surface investigation including the possibility to detect molecular orientation at the surface of silicon and zincblende semiconductors, investigation of electric field induced second harmonic fields at the semiconductor interface, detection of surface impurities, and very recently, study surface defects such as twin boundary in wurtzite semiconductors. In this work, we show using nonlinear optical techniques, e.g. nonlinear bond models how arbitrary polarization of the incoming electric field in Rotational Anisotropy Spectroscopy experiments can provide more information regarding the origin of the nonlinear sources in zincblende and wurtzite semiconductor structure. In addition, using hyperpolarizability consideration, we describe how the nonlinear susceptibility tensor describing SHG can be well modelled using only few parameter because of the symmetry of the bonds. We also show how the third harmonic intensity feature shows considerable changes when the incoming field polarization angle is changed from s-polarized to p-polarized. We also propose a method how to investigate surface reconstruction and defects in wurtzite and zincblende structure at the nanoscale level.

Keywords: surface characterization, bond model, rotational anisotropy spectroscopy, effective hyperpolarizability

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Authors: Shahrokh Barati

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In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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Authors: A. Brouri, F. Giri, A. Mkhida, A. Elkarkri, M. L. Chhibat

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Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the linear subsystem is allowed to be parametric or not, continuous- or discrete-time. The input and output nonlinearities are polynomial and may be noninvertible. A two-stage identification method is developed such the parameters of all nonlinear elements are estimated first using the Kozen-Landau polynomial decomposition algorithm. The obtained estimates are then based upon in the identification of the linear subsystem, making use of suitable pre-ad post-compensators.

Keywords: nonlinear system identification, Hammerstein-Wiener systems, frequency identification, polynomial decomposition

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Authors: E. Feulefack Songong, A. Zingoni

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A vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Although vibrations can be linear or nonlinear depending on the basic components of the system, the interest is mostly pointed towards nonlinear vibrations. This is because most structures around us are to some extent nonlinear and also because we need more accurate values in an analysis. The goal of this research is the integration of nonlinearities in the development and validation of structural models and to ameliorate the resistance of structures when subjected to loads. Although there exist many types of nonlinearities, this thesis will mostly focus on the vibration of free and undamped systems incorporating nonlinearity due to stiffness. Nonlinear stiffness has been a concern to many engineers in general and Civil engineers in particular because it is an important factor that can bring a good modification and amelioration to the response of structures when subjected to loads. The analysis of systems will be done analytically and then numerically to validate the analytical results. We will first show the benefit and importance of stiffness nonlinearity when it is implemented in the structure. Secondly, We will show how its integration in the structure can improve not only the structure’s performance but also its response when subjected to loads. The results of this study will be valuable to practicing engineers as well as industry practitioners in developing better designs and tools for their structures and mechanical devices. They will also serve to engineers to design lighter and stronger structures and to give good predictions as for the behavior of structures when subjected to external loads.

Keywords: elastic foundation, nonlinear, plates, stiffness, structures, vibration

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Authors: Ali Anwar, Hu Qinglei, Li Bo, Muhammad Taha Ali

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In this paper a generic model of perturbed nonlinear systems is considered which is affected by hard backlash nonlinearity at the input. The nonlinearity is modelled by a dynamic differential equation which presents a more precise shape as compared to the existing linear models and is compatible with nonlinear design technique such as backstepping. Moreover, a novel backstepping based nonlinear control law is designed which explicitly incorporates a continuous-time adaptive backlash inverse model. It provides a significant flexibility to control engineers, whereby they can use the estimated backlash spacing value specified on actuators such as gears etc. in the adaptive Backlash Inverse model during the control design. It ensures not only global stability but also stringent transient performance with desired precision. It is also robust to external disturbances upon which the bounds are taken as unknown and traverses the backlash spacing efficiently with underestimated information about the actual value. The continuous-time backlash inverse model is distinguished in the sense that other models are either discrete-time or involve complex computations. Furthermore, numerical simulations are presented which not only illustrate the effectiveness of proposed control law but also its comparison with PID and other backstepping controllers.

Keywords: adaptive control, hysteresis, backlash inverse, nonlinear system, robust control, backstepping

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Authors: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: Ali Ballouch, Nourelhouda Choukri, Zouhair Soufiani, Mohamed El Jouad, Mohamed Addou

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For several years, significant research has been developed in the areas of applications of semiconductor wide bandgap such as ZnO in optoelectronics. This oxide has the advantage of having a large exciton energy (60 meV) three times higher than that of GaN (21 meV) or ZnS (20 meV). This energy makes zinc oxide resistant for laser irradiations and very interesting for the near UV-visible optic, as well as for studying physical microcavities. A high-energy direct gap at room temperature (Eg > 1 eV) which makes it a potential candidate for emitting devices in the near UV and visible. Our work is to study the nonlinear optical properties, mainly the nonlinear third-order susceptibility of europium doped Zinc oxide thin films. The samples were prepared by chemical vapor spray method (Spray), XRD, SEM technique, THG were used for characterization. In this context, the influence of europium doping on the nonlinear optical response of the Zinc oxide was investigated. The nonlinear third-order properties depend on the physico-chemical parameters (crystallinity, strain, and surface roughness), the nature and the level of doping, temperature.

Keywords: ZnO, characterization, non-linear optical properties, optoelectronics

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: Mohammad Moeini, Mehrdad Ghyabi, Kiarash Mohtasham Dolatshahi

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This paper investigates seismic soil-pile interaction using the Beam on Nonlinear Winkler Foundation (BNWF) approach. Three soil types are considered to cover all the possible responses, as well as nonlinear site response analysis using finite element method in OpenSees platform. Excitations at each elevation that are output of the site response analysis are used as the input excitation to the soil pile system implementing multi-support excitation method. Spectral intensities of acceleration show that the extent of the response in sand is more severe than that of clay, in addition, increasing the PGA of ground strong motion will affect the sandy soil more, in comparison with clayey medium, which is an indicator of the sensitivity of soil-pile systems in sandy soil.

Keywords: BNWF method, multi-support excitation, nonlinear site response analysis, seismic soil-pile interaction

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Authors: Juliette Harper, Yu Yang

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Biofuels have gained significant attention recently due to the new regulations and agreements regarding fossil fuels and greenhouse gases being made by countries around the globe. One of the most common types of biofuels is biodiesel, primarily made via the transesterification reaction. We model this nonlinear process in MATLAB using the standard kinetic equations. Then, a nonlinear Model predictive control (NMPC) was developed to regulate this process due to its capability to handle process constraints. The feeding flow uncertainty and kinetic disturbances are further incorporated in the model to capture the real-world operating conditions. The simulation results will show that the proposed NMPC can guarantee the final composition of fatty acid methyl esters (FAME) above the target threshold with a high chance by adjusting the process temperature and flowrate. This research will allow further understanding of NMPC under uncertainties and how to design the computational strategy for larger process with more variables.

Keywords: NMPC, biodiesel, uncertainties, nonlinear, MATLAB

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Authors: A. Chegenizadeh, M. Keramatikerman, H. Nikraz

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Bitumen is one of the most applicable materials in pavement engineering. It is a binding material with unique viscoelastic properties, especially when it mixes with polymer. In this study, to figure out the viscoelastic behaviour of the polymer modified with bitumen (PMB), a series of dynamic shearing rheological (DSR) tests were conducted. Four percentages of lime (i.e. 1%, 2%, 4% and 5%) were mixed with PMB and tested under four different temperatures including 64ºC, 70ºC, 76ºC and 82ºC. The results indicated that complex shearing modulus (G*) increased by increasing the frequency due to raised resistance against deformation. The phase angle (δ) showed a decreasing trend by incrementing the frequency. The addition of lime percentages increased the complex modulus value and declined phase angle parameter. Increasing the temperature decreased the complex modulus and increased the phase angle until 70ºC. The decreasing trend of rutting factor with increasing temperature revealed that rutting factor improved by the addition of the lime to the PMB.

Keywords: rheological properties, DSR test, polymer mixed with bitumen (PMB), complex modulus, lime

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Authors: Kang-Gyu Park, Sun-Jong Park, Hong Jae Yim, Hyo-Gyung Kwak

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This paper attempts to evaluate the effect of fire damage on concrete by using nonlinear resonance vibration method, one of the nonlinear nondestructive method. Concrete exhibits not only nonlinear stress-strain relation but also hysteresis and discrete memory effect which are contained in consolidated materials. Hysteretic materials typically show the linear resonance frequency shift. Also, the shift of resonance frequency is changed according to the degree of micro damage. The degree of the shift can be obtained through nonlinear resonance vibration method. Five exposure scenarios were considered in order to make different internal micro damage. Also, the effect of post-fire-curing on fire-damaged concrete was taken into account to conform the change in internal damage. Hysteretic non linearity parameter was obtained by amplitude-dependent resonance frequency shift after specific curing periods. In addition, splitting tensile strength was measured on each sample to characterize the variation of residual strength. Then, a correlation between the hysteretic non linearity parameter and residual strength was proposed from each test result.

Keywords: nonlinear resonance vibration method, non linearity parameter, splitting tensile strength, micro damage, post-fire-curing, fire damaged concrete

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust model predictive controller (RMPC) for uncertain nonlinear system under actuator saturation is designed to control a DC-DC buck converter in PV pumping application, where this system is subject to actuator saturation and parameter uncertainties. The considered nonlinear system contains a linear constant part perturbed by an additive state-dependent nonlinear term. Based on the saturating actuator property, an appropriate linear feedback control law is constructed and used to minimize an infinite horizon cost function within the framework of linear matrix inequalities. The proposed approach has successfully provided a solution to the optimization problem that can stabilize the nonlinear plants. Furthermore, sufficient conditions for the existence of the proposed controller guarantee the robust stability of the system in the presence of polytypic uncertainties. In addition, the simulation results have demonstrated the efficiency of the proposed control scheme.

Keywords: PV pumping system, DC-DC buck converter, robust model predictive controller, nonlinear system, actuator saturation, linear matrix inequality

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh

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This paper presents a new method to design nonlinear feedback linearization controller for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA_II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.

Keywords: nonlinear dynamic model, polymer electrolyte membrane fuel cells, feedback linearization, optimal control, NSGA_II

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: E. Menga, S. Hernandez

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Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Nesrine Gaaliche

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This study provides a finite element dynamic model for analyzing rolling bearing system vibration response. The vibration responses of polypropylene bearings with and without defects are studied using FE analysis and compared to experimental data. The viscoelastic behavior of thermoplastic is investigated in this work to evaluate the influence of material flexibility and damping viscosity. The vibrations are detected using 3D dynamic analysis. Peak vibrations are more noticeable in an inner ring defect than in an outer ring defect, according to test data. The performance of thermoplastic bearings is compared to that of metal parts using vibration signals. Both the test and numerical results show that Polypropylene bearings exhibit less vibration than steel counterparts. Unlike bearings made from metal, polypropylene bearings absorb vibrations and handle shaft misalignments. Following validation of the overall vibration spectrum data, Von Mises stresses inside the rings are assessed under high loads. Stress is significantly high under the balls, according to the simulation findings. For the test cases, the computational findings correspond closely to the experimental results.

Keywords: viscoelastic, FE analysis, polypropylene, bearings

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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Authors: Anna Makuch, Grzegorz Kokot, Konstanty Skalski, Jakub Banczorowski

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Cancellous bone is a porous composite of a hierarchical structure and anisotropic properties. The biological tissue is considered to be a viscoelastic material, but many studies based on a nanoindentation method have focused on their elasticity and microhardness. However, the response of many organic materials depends not only on the load magnitude, but also on its duration and time course. Depth Sensing Indentation (DSI) technique has been used for examination of creep in polymers, metals and composites. In the indentation tests on biological samples, the mechanical properties are most frequently determined for animal tissues (of an ox, a monkey, a pig, a rat, a mouse, a bovine). However, there are rare reports of studies of the bone viscoelastic properties on microstructural level. Various rheological models were used to describe the viscoelastic behaviours of bone, identified in the indentation process (e. g Burgers model, linear model, two-dashpot Kelvin model, Maxwell-Voigt model). The goal of the study was to determine the influence of creep effect on the mechanical properties of human cancellous bone in indentation tests. The aim of this research was also the assessment of the material properties of bone structures, having in mind the energy aspects of the curve (penetrator loading-depth) obtained in the loading/unloading cycle. There was considered how the different holding times affected the results within trabecular bone.As a result, indentation creep (CIT), hardness (HM, HIT, HV) and elasticity are obtained. Human trabecular bone samples (n=21; mean age 63±15yrs) from the femoral heads replaced during hip alloplasty were removed and drained from alcohol of 1h before the experiment. The indentation process was conducted using CSM Microhardness Tester equipped with Vickers indenter. Each sample was indented 35 times (7 times for 5 different hold times: t1=0.1s, t2=1s, t3=10s, t4=100s and t5=1000s). The indenter was advanced at a rate of 10mN/s to 500mN. There was used Oliver-Pharr method in calculation process. The increase of hold time is associated with the decrease of hardness parameters (HIT(t1)=418±34 MPa, HIT(t2)=390±50 MPa, HIT(t3)= 313±54 MPa, HIT(t4)=305±54 MPa, HIT(t5)=276±90 MPa) and elasticity (EIT(t1)=7.7±1.2 GPa, EIT(t2)=8.0±1.5 GPa, EIT(t3)=7.0±0.9 GPa, EIT(t4)=7.2±0.9 GPa, EIT(t5)=6.2±1.8 GPa) as well as with the increase of the elastic (Welastic(t1)=4.11∙10-7±4.2∙10-8Nm, Welastic(t2)= 4.12∙10-7±6.4∙10-8 Nm, Welastic(t3)=4.71∙10-7±6.0∙10-9 Nm, Welastic(t4)= 4.33∙10-7±5.5∙10-9Nm, Welastic(t5)=5.11∙10-7±7.4∙10-8Nm) and inelastic (Winelastic(t1)=1.05∙10-6±1.2∙10-7 Nm, Winelastic(t2) =1.07∙10-6±7.6∙10-8 Nm, Winelastic(t3)=1.26∙10-6±1.9∙10-7Nm, Winelastic(t4)=1.56∙10-6± 1.9∙10-7 Nm, Winelastic(t5)=1.67∙10-6±2.6∙10-7)) reaction of materials. The indentation creep increased logarithmically (R2=0.901) with increasing hold time: CIT(t1) = 0.08±0.01%, CIT(t2) = 0.7±0.1%, CIT(t3) = 3.7±0.3%, CIT(t4) = 12.2±1.5%, CIT(t5) = 13.5±3.8%. The pronounced impact of creep effect on the mechanical properties of human cancellous bone was observed in experimental studies. While the description elastic-inelastic, and thus the Oliver-Pharr method for data analysis, may apply in few limited cases, most biological tissues do not exhibit elastic-inelastic indentation responses. Viscoelastic properties of tissues may play a significant role in remodelling. The aspect is still under an analysis and numerical simulations. Acknowledgements: The presented results are part of the research project founded by National Science Centre (NCN), Poland, no.2014/15/B/ST7/03244.

Keywords: bone, creep, indentation, mechanical properties

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Authors: T. Sanches, K. Bousson

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As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Sonia Sonia

Abstract:

This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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