Search results for: equivalent nonlinear spring

Authors: Kodo Sektani, Apostolos Tsouvalas, Andrei Metrikine

Abstract:

The reassessment of existing movable bridges in The Netherlands has created the need for acceptance/rejection criteria to assess whether the machineries are meet certain design demands. However, the existing design code defines a different limit state design, meant for new machineries which is based on a simple linear spring-mass model. Observations show that existing bridges do not confirm the model predictions. In fact, movable bridges are nonlinear systems consisting of mechanical components, such as, gears, electric motors and brakes. Next to that, each movable bridge is characterized by a unique set of parameters. However, in the existing code various variables that describe the physical characteristics of the bridge are neglected or replaced by partial factors. For instance, the damping ratio ζ, which is different for drawbridges compared to bascule bridges, is taken as a constant for all bridge types. In this paper, a model is developed that overcomes some of the limitations of existing modelling approaches to capture the dynamics of the powertrain of a class of bridge machineries First, a semidefinite dynamic model is proposed, which accounts for stiffness, damping, and some additional variables of the physical system, which are neglected by the code, such as nonlinear braking torques. The model gives an upper bound of the peak forces/torques occurring in the powertrain during emergency braking. Second, a discrete nonlinear dynamic model is discussed, with realistic motor torque characteristics during normal operation. This model succeeds to accurately predict the full time history of the occurred stress state of the opening and closing cycle for fatigue purposes.

Keywords: Dynamics of movable bridges, Bridge machinery, Powertrains, Torque measurements

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Authors: İsmail İnce, Ali Bozdag, Ayla Bozdag, M. Bahadır Tosunlar, M. Ergun Hatır, Mustafa Korkanc

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The building stones used in the construction of historical structures are exposed to atmospheric effects directly or indirectly. As a result of this process, building stones are partially or completely degraded. Historical buildings are important symbols of cultural heritage, so it is very significant to transfer to the future generations by protecting and repairing of these historical buildings. The Eflatunpınar Hitit Monument located near the Eflatunpınar cold water spring was constructed by using natural rock blocks during the Hittites Empire period. The monument has been protected without losing its function until today. The purpose of this study is to evaluate the deteriorations in the Eflatunpınar Hitit Monument and to detect the water chemistry of the Eflatunpınar spring located around the Beysehir County in the west of Konya. For this purpose, the petrographic and mechanical properties of the rocks used in this monument were determined, and the deteriorations in the monument were determined with the aid of non-destructive test methods including Schmidt hardness value, relative humidity measurement, thermal imaging. Additionally, the physical (electrical conductivity (EC), pH and temperature) and chemical characteristics (major anions and cations) of the Eflatunpınar cold water spring have been detected.

Keywords: deteriorations, Eflatunpınar Hitit monument, Eflatunpınar spring, Konya, non-destructıve tests

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Authors: Miladi Yasmine, Bouhlel Salah, David Banks

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The Hammam Zriba (F-Ba-Sr-Pb-Zn) ore deposits of the Zaghouan district are located in northeast Tunisia, 60 Km south of Tunis. The host rocks belong to the Ressas Formation (Tithonian age) and lower Cretaceous layers. Mineralization occurs as stratiform replacement heaps and lenses. The mineral assemblage is composed of fluorite, barite, sphalerite, and galena. Primary fluid inclusions in sphalerite have homogenization temperatures ranging from 83 to 140°C, final melting temperature range from −18 to −7.0, corresponding to salinities of 5 to 21 wt % NaCl equivalent. Fluid inclusions in fluorite homogenize to the liquid phase between 132 and 178°C. Final ice melting temperatures range from −25 to −6.8 °C, corresponding to salinities between 17 and 24 wt% NaCl Equivalent. The LA-ICP-MS analyses of the fluid inclusions in fluorite show that these fluids are dominated by Na>Ca>K>Mg, with the concentration of Fe being equivalent to that of Mg. Microthermometric analyses of the fluid inclusions observed in fluorite and sphalerite show that two distinct fluids were involved in the mineralization deposition: a warmer saline fluid (132-178°C, 17-24 wt % NaCl equivalent) and cooler saline fluid (83°C-140, 5-21 wt %NaCl equivalent). The ore fluid result from highly saline and Na-Ca dominated with lower Mg concentrations come from the leaching of the dolomitic host rocks by the fluids.

Keywords: Hammam Zriba , fluid inclusions, LA-ICP-MS, Zaghouan district

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Authors: Hoda Aleali, Nastran Mansour, Maryam Mirzaie

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In this paper, we study the optical nonlinearities of Silver sulfide (Ag2S) nanostructures dispersed in the Dimethyl sulfoxide (DMSO) under exposure to 532 nm, 15 nanosecond (ns) pulsed laser irradiation. Ultraviolet–visible absorption spectrometry (UV-Vis), X-ray diffraction (XRD), and transmission electron microscopy (TEM) are used to characterize the obtained nanocrystal samples. The band gap energy of colloid is determined by analyzing the UV–Vis absorption spectra of the Ag2S NPs using the band theory of semiconductors. Z-scan technique is used to characterize the optical nonlinear properties of the Ag2S nanoparticles (NPs). Large enhancement of two photon absorption effect is observed with increase in concentration of the Ag2S nanoparticles using open Z-scan measurements in the ns laser regime. The values of the nonlinear absorption coefficients are determined based on the local nonlinear responses including two photon absorption. The observed aperture dependence of the Ag2S NP limiting performance indicates that the nonlinear scattering plays an important role in the limiting action of the sample.The concentration dependence of the optical liming is also investigated. Our results demonstrate that the optical limiting threshold decreases with increasing the silver sulfide NPs in DMSO.

Keywords: nanoscale materials, silver sulfide nanoparticles, nonlinear absorption, nonlinear scattering, optical limiting

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: N. H. Adenan, M. S. M. Noorani

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River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to developed an efficient water management system to optimize the allocation water resources.

Keywords: river flow, nonlinear prediction method, phase space, local linear approximation

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Authors: Kyeong Hoon Park, Taiji Mazuda

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High damping rubber (HDR) bearings are dissipating devices mainly used in seismic isolation systems and have a great damping performance. Although many studies have been conducted on the dynamic model of HDR bearings, few models can reflect phenomena such as dependency of experienced shear strain on initial history. In order to develop a model that can represent the dependency of experienced shear strain of HDR by Mullins effect, dynamic loading test was conducted using HDR specimen. The reaction of HDR was measured by applying a horizontal vibration using a hybrid actuator under a constant vertical load. Dynamic program analysis was also performed after dynamic loading test. The dynamic model applied in program analysis is a bilinear type double-target model. This model is modified from typical bilinear model. This model can express the nonlinear characteristics related to the initial history of HDR bearings. Based on the dynamic loading test and program analysis results, equivalent stiffness and equivalent damping ratio were calculated to evaluate the mechanical properties of HDR and the feasibility of the bilinear type double-target model was examined.

Keywords: base-isolation, bilinear model, high damping rubber, loading test

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Byeong-Sam Kim, Jongmin Park

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The present work is motivated by the industrial challenge to produce complex composite shapes cost-effectively. The model used an anisotropical thermoviscoelastic is analyzed by an implemented finite element solver. The stress relaxation can be constructed by Prony series for the nonlinear thermoviscoelastic model. The calculation of process induced internal stresses relaxation during the cooling stage of the manufacturing cycle was carried out by the spring back phenomena observed from the part containing a cylindrical segment. The finite element results obtained from the present formulation are compared with experimental data, and the results show good correlations.

Keywords: thermoviscoelastic, springback phenomena, FEM analysis, thermoplastic composite structures

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Authors: Toshinori Nawata

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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Fernando P. Silva, Valter J. S. Leite, Erivelton G. Nepomuceno

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In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the first is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties.

Keywords: robust multi inversion, omni-directional robot, robocup, nonlinear control

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

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This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Gül Çevik

Abstract:

This paper summarizes the work conducted to assess the root cause of the failure of a medium commercial vehicle leaf spring failed in service. Macro- and micro-fractographic analyses by scanning electron microscope as well as material verification tests were conducted in order to understand the failure mechanisms and root cause of the failure. Findings from the fractographic analyses indicated that failure mechanism is fatigue. Crack initiation was identified to have occurred from a point on the top surface near to the front face and to the left side. Two other crack initiation points were also observed, however, these cracks did not propagate. The propagation mode of the fatigue crack revealed that the cyclic loads resulting in crack initiation and propagation were unidirectional bending. Fractographic analyses have also showed that the root cause of the fatigue crack initiation and propagation was loading the part above design stress. Material properties of the part were also verified by chemical composition analysis, microstructural analysis by optical microscopy and hardness tests.

Keywords: leaf spring, failure analysis, fatigue, fractography

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Georgi Kalandadze

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For studying the development of world civilizations, textual sources that have undergone textological and worldview changes are of great importance. The conference will discuss the collection of the XVIII century "The Golden Spring", compiled by Gabriel Mtsire, which includes texts of John Chrysostom. John Chrysostom lived in the 4th century and his writings correspond to the culture of readers of that time. In the 10th-11th centuries, the works of John Chrysostom were translated into Georgian by Euthymius of Athos. These texts correspond to the requirements of the Georgian society of the 10th-11th centuries. In the 18th century, Gabriel Mtsire collected and edited these texts to make them more understandable to his modern readers. In the 20th century, these texts were again adapted. Thus, the present study provides an opportunity to evaluate and outline the linguistic and content transformation process of the same work over 16 centuries.

Keywords: gabriel mtsire, john chrysostom, euthymius the athonite, the golden spring

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Authors: Loreine Makki, Marc Anthony Mannah, Christophe Batard, Nicolas Ginot, Julien Weckbrodt

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Planar transformers are extensively utilized in high-frequency, high power density power electronic converters. The breakthrough of wide-bandgap technology compelled power electronic system miniaturization while inducing pivotal effects on system modeling and manufacturing within the power electronics industry. A significant consideration to simulate and model the unanticipated parasitic parameters emerges with the requirement to mitigate electromagnetic disturbances. This paper will present an equivalent circuit model of a shielded pulse planar transformer quantifying leakage inductance and resistance in addition to the interwinding capacitance of the primary and secondary windings. ANSYS Q3D Extractor was utilized to model and simulate the transformer, intending to study the immunity of the simulated equivalent model to high dv/dt occurrences. A convenient correlation between simulation and experimental results is presented.

Keywords: Planar transformers, wide-band gap, equivalent circuit model, shielded, ANSYS Q3D Extractor, dv/dt

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: I. Khabbazi, R. Ghasemi

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This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Kanica Goel, Nilam

Abstract:

Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

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This paper has investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: actuator, piezoelectric, performance, unimorph

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: grey relational degree, multiple linear regression, membership function, nonlinear programming

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

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This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Pengfan Wu, Xiaoan Chen, Ye He, Tianchi Chen

Abstract:

This paper introduces the design of an unpowered knee exoskeleton to assist human walking by redistributing the moment of the knee joint during stair descent (SD). Considering the knee moment varying with the knee joint angle and the work of the knee joint is all negative, the custom-built spring was used to convert negative work into the potential energy of the spring during flexion, and the obtained energy work as assistance during extension to reduce the consumption of lower limb muscles. The human-machine adaptability problem was left by traditional rigid wearable due to the knee involves sliding and rotating without a fixed-axis rotation, and this paper designed the two-direction grooves to follow the human-knee kinematics, and the wire spring provides a certain resistance to the pin in the groove to prevent extra degrees of freedom. The experiment was performed on a normal stair by healthy young wearing the device on both legs with the surface electromyography recorded. The results show that the quadriceps (knee extensor) were reduced significantly.

Keywords: unpowered exoskeleton, stair descent, knee compliant joint, energy redistribution

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