Search results for: non-linear dynamic characteristics

Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior

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Authors: Jun Tian, Yu Yang, Liping Zhang, Qianhua Kan

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Experimental results show that SA 508-3 steel exhibits temperature dependent cyclic softening characteristic and obvious ratcheting behaviors, and dynamic strain age was observed at temperature range of 200 ºC to 350 ºC. Based on these observations, a temperature dependent cyclic plastic constitutive model was proposed by introducing the nonlinear cyclic softening and kinematic hardening rules, and the dynamic strain age was also considered into the constitutive model. Comparisons between experiments and simulations were carried out to validate the proposed model at elevated temperature.

Keywords: constitutive model, elevated temperature, ratcheting, SA 508-3

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, safety margin

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Authors: Chunying Fang, Haifeng Li, Lin Ma, Mancai Zhang

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Speech intelligibility assessment is an important measure to evaluate the functional outcomes of surgical and non-surgical treatment, speech therapy and rehabilitation. The assessment of pathological speech plays an important role in assisting the experts. Pathological speech usually is non-stationary and mutational, in this paper, we describe a multi-granularity combined feature schemes, and which is optimized by hierarchical visual method. First of all, the difference granularity level pathological features are extracted which are BAFS (Basic acoustics feature set), local spectral characteristics MSCC (Mel s-transform cepstrum coefficients) and nonlinear dynamic characteristics based on chaotic analysis. Latterly, radar chart and F-score are proposed to optimize the features by the hierarchical visual fusion. The feature set could be optimized from 526 to 96-dimensions.The experimental results denote that new features by support vector machine (SVM) has the best performance, with a recognition rate of 84.4% on NKI-CCRT corpus. The proposed method is thus approved to be effective and reliable for pathological speech intelligibility evaluation.

Keywords: pathological speech, multi-granularity feature, MSCC (Mel s-transform cepstrum coefficients), F-score, radar chart

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Authors: Kawser Ahmed, K. Bousson, Milca F. Coelho

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4D flight trajectory optimization is one of the key ingredients to improve flight efficiency and to enhance the air traffic capacity in the current air traffic management (ATM). The present paper explores the iterative dynamic programming (IDP) as a potential numerical optimization method for 4D flight trajectory optimization. IDP is an iterative version of the Dynamic programming (DP) method. Due to the numerical framework, DP is very suitable to deal with nonlinear discrete dynamic systems. The 4D waypoint representation of the flight trajectory is similar to the discretization by a grid system; thus DP is a natural method to deal with the 4D flight trajectory optimization. However, the computational time and space complexity demanded by the DP is enormous due to the immense number of grid points required to find the optimum, which prevents the use of the DP in many practical high dimension problems. On the other hand, the IDP has shown potentials to deal successfully with high dimension optimal control problems even with a few numbers of grid points at each stage, which reduces the computational effort over the traditional DP approach. Although the IDP has been applied successfully in chemical engineering problems, IDP is yet to be validated in 4D flight trajectory optimization problems. In this paper, the IDP has been successfully used to generate minimum length 4D optimal trajectory avoiding any obstacle in its path, such as a no-fly zone or residential areas when flying in low altitude to reduce noise pollution.

Keywords: 4D waypoint navigation, iterative dynamic programming, obstacle avoidance, trajectory optimization

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Authors: George D. Hatzigeorgiou, Nikos G. Pnevmatikos

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This study examines the inelastic behavior of adjacent planar reinforced concrete (R.C.) frames subjected to strong ground motions. The investigation focuses on the effects of vertical ground motion on the seismic pounding. The examined structures are modeled and analyzed by RUAUMOKO dynamic nonlinear analysis program using reliable hysteretic models for both structural members and contact elements. It is found that the vertical ground motion mildly affects the seismic response of adjacent buildings subjected to structural pounding and, for this reason, it can be ignored from the displacement and interstorey drifts assessment. However, the structural damage is moderately affected by the vertical component of earthquakes.

Keywords: nonlinear seismic behavior, reinforced concrete structures, structural pounding, vertical ground motions

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Authors: Dehini Rachid, Ferdi Brahim

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The shunt active power filter (SAPF) is not destined only to improve the power factor, but also to compensate the unwanted harmonic currents produced by nonlinear loads. This paper presents a SAPF with identification and control method based on artificial neural network (ANN). To identify harmonics, many techniques are used, among them the conventional p-q theory and the relatively recent one the artificial neural network method. It is difficult to get satisfied identification and control characteristics by using a normal (ANN) due to the nonlinearity of the system (SAPF + fast nonlinear load variations). This work is an attempt to undertake a systematic study of the problem to equip the (SAPF) with the harmonics identification and DC link voltage control method based on (ANN). The latter has been applied to the (SAPF) with fast nonlinear load variations. The results of computer simulations and experiments are given, which can confirm the feasibility of the proposed active power filter.

Keywords: artificial neural networks (ANN), p-q theory, harmonics, total harmonic distortion

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Authors: Ali Y Al-Attraqchi, P. Rajeev, M. Javad Hashemi, Riadh Al-Mahaidi

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This paper presents a probabilistic incremental dynamic analysis (IDA) of a full reinforced concrete building subjected to column loss scenario for the assessment of progressive collapse. The IDA is chosen to explicitly account for uncertainties in loads and system capacity. Fragility curves are developed to predict the probability of progressive collapse given the loss of one or more columns. At a broader scale, it will also provide critical information needed to support the development of a new generation of design codes that attempt to explicitly quantify structural robustness.

Keywords: fire, nonlinear incremental dynamic analysis, progressive collapse, structural engineering

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: M. J. Uddin, M. M. Rahman

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Transient natural convective flow dynamics of nanofluids in a horizontal homocentric annulus using nonhomogeneous dynamic model has been experimented numerically. The simulation is carried out for four different shapes of the inner wall, which is either cylindrical, elliptical, square or triangular. The outer surface of the annulus is maintained at constant low temperature while the inner wall is maintained at a uniform temperature; higher than the outer one. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic deposition phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To find the best performer, the local Nusselt number is demonstrated for different shapes of the inner wall. The heat transfer enhancement for different nanofluids for four different shapes of the inner wall is exhibited.

Keywords: nanofluids, annulus, nonhomogeneous dynamic model, heat transfer

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Authors: Hamza Nejib, Okba Taouali

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This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Luis F. Caballero-castro, Dirsa Feliciano, Daniela Novoa, Orlando Arroyo, Jesús D. Villalba-morales

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Colombia faces a critical challenge in seismic resilience due to the prevalence of informal housing, which constitutes approximately 70% of residential structures. More than 10 million Colombians (20% of the population), live in homes susceptible to collapse in the event of an earthquake. This, combined with the fact that 83% of the population is in intermediate and high seismic hazard areas, has brought serious consequences to the country. These consequences became evident during the 1999 Armenia earthquake, which affected nearly 100,000 properties and represented economic losses equivalent to 1.88% of that year's Gross Domestic Product (GDP). Despite previous efforts to reinforce informal housing through methods like externally reinforced masonry walls, alternatives related to seismic protection systems (SPDs), such as Buckling-Restrained Braces (BRB), have not yet been explored in the country. BRBs are reinforcement elements capable of withstanding both compression and tension, making them effective in enhancing the lateral stiffness of structures. In this study, the use of low-cost and easily installable BRBs for the retrofit of informal housing in Colombia was evaluated, considering the economic limitations of the communities. For this purpose, a case study was selected involving an informally constructed dwelling in the country, from which field information on its structural characteristics and construction materials was collected. Based on the gathered information, nonlinear models with and without BRBs were created, and their seismic performance was analyzed and compared through incremental static (pushover) and nonlinear dynamic analyses. In the first analysis, the capacity curve was identified, showcasing the sequence of failure events occurring from initial yielding to structural collapse. In the second case, the model underwent nonlinear dynamic analyses using a set of seismic records consistent with the country's seismic hazard. Based on the results, fragility curves were calculated to evaluate the probability of failure of the informal housings before and after the intervention with BRBs, providing essential information about their effectiveness in reducing seismic vulnerability. The results indicate that low-cost BRBs can significantly increase the capacity of informal housing to withstand earthquakes. The dynamic analysis revealed that retrofit structures experienced lower displacements and deformations, enhancing the safety of residents and the seismic performance of informally constructed houses. In other words, the use of low-cost BRBs in the retrofit of informal housing in Colombia is a promising strategy for improving structural safety in seismic-prone areas. This study emphasizes the importance of seeking affordable and practical solutions to address seismic risk in vulnerable communities in earthquake-prone regions in Colombia and serves as a model for addressing similar challenges of informal housing worldwide.

Keywords: buckling-restrained braces, fragility curves, informal housing, incremental dynamic analysis, seismic retrofit

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Authors: Kunwar Mrityunjai Sharma, Trilok Nath Singh

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The Navier-Stokes equation is used to study nonlinear fluid flow in rough 2D fractures. The major goal is to investigate the influence of inertial flow owing to fracture wall roughness on nonlinear flow behavior. Roughness profiles are developed using Barton's Joint Roughness Coefficient (JRC) and used as fracture walls to assess wall roughness. Four JRC profiles (5, 11, 15, and 19) are employed in the study, where a higher number indicates higher roughness. A parametric study has been performed using varying pressure gradients, and the corresponding Forchheimer number is calculated to observe the nonlinear behavior. The results indicate that the fracture roughness has a significant effect on the onset of nonlinearity. Additionally, the validity of the cubic law is evaluated and observed that it overestimates the flow in rough fractures and should be used with utmost care.

Keywords: fracture flow, nonlinear flow, cubic law, Navier-stokes equation

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Authors: Hyung-Joon Kim, Jin-Young Park

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Energy dissipating devices (EDDs) have become more popular as seismic-force-resisting systems for building structures. However, there is little information on the collapse capacities of frames employing EDDs which are an important criterion for their seismic design. This study investigates the collapse capacities of steel frames with TADAS hysteric energy dissipative devices (HEDDs) that become an alternative to steel braced frames. To do this, 5-story steel ordinary concentrically braced frame and steel frame with HEDDs are designed and modeled. Nonlinear dynamic analyses and incremental dynamic analysis with 40 ground motions scaled to maximum considered earthquake are carried out. It is shown from analysis results that the significant enhancement in terms of the collapse capacities is found due to the introduction HEDDs.

Keywords: collapse capacity, incremental dynamic analysis, steel braced frame, TADAS hysteric energy dissipative device

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Authors: Paul V. Thomas, Mostafa S. A. Elsayed, Denis Walch

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Airframe structural optimization at different design stages results in new mass and stiffness distributions which modify the critical design loads envelop. Determination of aircraft critical loads is an extensive analysis procedure which involves simulating the aircraft at thousands of load cases as defined in the certification requirements. It is computationally prohibitive to use a Global Finite Element Model (GFEM) for the load analysis, hence reduced order structural models are required which closely represent the dynamic characteristics of the GFEM. This paper presents the implementation of Component Mode Synthesis (CMS) method for the generation of high fidelity Reduced Order Model (ROM) of complex airframes. Here, sub-structuring technique is used to divide the complex higher order airframe dynamical system into a set of subsystems. Each subsystem is reduced to fewer degrees of freedom using matrix projection onto a carefully chosen reduced order basis subspace. The reduced structural matrices are assembled for all the subsystems through interface coupling and the dynamic response of the total system is solved. The CMS method is employed to develop the ROM of a Bombardier Aerospace business jet which is coupled with an aerodynamic model for dynamic aeroelasticity loads analysis under gust turbulence. Another set of dynamic aeroelastic loads is also generated employing a stick model of the same aircraft. Stick model is the reduced order modelling methodology commonly used in the aerospace industry based on stiffness generation by unitary loading application. The extracted aeroelastic loads from both models are compared against those generated employing the GFEM. Critical loads Modal participation factors and modal characteristics of the different ROMs are investigated and compared against those of the GFEM. Results obtained show that the ROM generated using Craig Bampton CMS reduction process has a superior dynamic characteristics compared to the stick model.

Keywords: component mode synthesis, craig bampton reduction method, dynamic aeroelasticity analysis, model order reduction

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Authors: Amin H. Almasria, Rajai Z. Alrousanb, Al-Harith Manasrah

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The collapse of a light weight pedestrian bridges due to vehicle collision is investigated and studied in detail using a dynamic nonlinear finite element analysis. Typical bridge widely used in Jordan is studied and modeled under truck collision using one dimensional beam finite element in order to minimize analysis time due to the dynamic nature of the problem. Truck collision with the bridge is simulated at different speeds and locations of collisions using dynamic explicit finite element scheme with material nonlinearity taken into account. Energy absorption of bridge is investigated through principle of energy conservation, where truck kinetic energy is assumed to be stored in the bridge as strain energy. Weak failure points in the bridges were identified, and modifications are proposed in order to strengthen the bridge structure and prevent total collapse. The proposed design modifications on bridge structure were successful in allowing the bridge to fail locally rather than globally and expected to help in saving lives.

Keywords: finite element method, dynamic impact, pedestrian bridges, strain energy, collapse failure

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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Authors: Kazuhisa Takagi

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This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: dynamic mathematical object, javascript, google drive, transfer jet

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Authors: Hamid Havasi, Mohamad Reza Gholami Dehbalaei, Hamed Khorami, Shahram Karimi, Hamdi Abdi

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Doubly-fed induction generator (DFIG) equipped with a power converter is an efficient tool for converting mechanical energy of a variable speed system to a fixed-frequency electrical grid. Since electrical energy sources faces with production problems such as harmonics caused by nonlinear loads, so in this paper, compensation performance of DPC and FOC method on harmonics reduction of a DFIG wind turbine connected to a nonlinear load in MATLAB Simulink model has been simulated and effect of each method on nonlinear load harmonic elimination has been compared. Results of the two mentioned control methods shows the advantage of the FOC method on DPC method for harmonic compensation. Also, the fifth and seventh harmonic components of the network and THD greatly reduced.

Keywords: DFIG machine, energy conversion, nonlinear load, THD, DPC, FOC

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Authors: Biaou Jean-Baptiste Kouchoro, Anissa Meziane, Philippe Micheau, Mathieu Renier, Nicolas Quaegebeur

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Numerous experimental and numerical studies have shown the interest of the local defects resonance (LDR) for the Non-Destructive Testing of metallic and composite plates. Indeed, guided ultrasonic waves such as Lamb waves, which are increasingly used for the inspection of these flat structures, enable the generation of local resonance phenomena by their interaction with a damaged area, allowing the detection of defects. When subjected to a large amplitude motion, a nonlinear behavior can predominate in the damaged area. This work presents a 2D Finite Element Model of the local resonance of a 12 mm long and 5 mm deep Flat Bottom Hole (FBH) in a 6 mm thick aluminum plate under the excitation induced by an incident A0 Lamb mode. The analysis of the transient response of the FBH enables the precise determination of its resonance frequencies and the associate modal deformations. Then, a linear parametric study varying the geometrical properties of the FBH highlights the sensitivity of the resonance frequency with respect to the plate thickness. It is demonstrated that the resonance effect disappears when the ratio of thicknesses between the FBH and the plate is below 0.1. Finally, the nonlinear behavior of the FBH is considered and studied introducing geometrical (taken into account the nonlinear component of the strain tensor) nonlinearities that occur at large vibration amplitudes. Experimental analysis allows observation of the resonance effects and nonlinear response of the FBH. The differences between these experimental results and the numerical results will be commented on. The results of this study are promising and allow to consider more realistic defects such as delamination in composite materials.

Keywords: guided waves, non-destructive testing, dynamic field testing, non-linear ultrasound/vibration

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Authors: Jui-Pin Hung, Qiao-Wen Chang, Kung-Da Wu, Yong-Run Chen

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This study was aimed to investigate the machining stability of a spindle tool with different preloaded amount. To this end, the vibration tests were conducted on the spindle unit with different preload to assess the dynamic characteristics and machining stability of the spindle unit. Current results demonstrate that the tool tip frequency response characteristics and the machining stabilities in X and Y direction are affected to change for spindle with different preload. As can be found from the results, a high preloaded spindle tool shows higher limited cutting depth at mid position, while a spindle with low preload shows a higher limited depth. This implies that the machining stability of spindle tool system is affected to vary by the machine frame structure. Besides, such an effect is quite different and varied with the preload of the spindle.

Keywords: bearing preload, dynamic compliance, machining stability, spindle

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: identification, Hammerstein-Wiener, optimization, quantization

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Authors: Luiz Carlos Wrobel, Matjaz Hribersek, Jure Marn, Jurij Iljaz

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Dynamic thermography has been clinically proven to be a valuable diagnostic technique for skin tumor detection as well as for other medical applications such as breast cancer diagnostics, diagnostics of vascular diseases, fever screening, dermatological and other applications. Thermography for medical screening can be done in two different ways, observing the temperature response under steady-state conditions (passive or static thermography), and by inducing thermal stresses by cooling or heating the observed tissue and measuring the thermal response during the recovery phase (active or dynamic thermography). The numerical modelling of heat transfer phenomena in biological tissue during dynamic thermography can aid the technique by improving process parameters or by estimating unknown tissue parameters based on measured data. This paper presents a nonlinear numerical model of multilayer skin tissue containing a skin tumor, together with the thermoregulation response of the tissue during the cooling-rewarming processes of dynamic thermography. The model is based on the Pennes bioheat equation and solved numerically by using a subdomain boundary element method which treats the problem as axisymmetric. The paper includes computational tests and numerical results for Clark II and Clark IV tumors, comparing the models using constant and temperature-dependent thermophysical properties, which showed noticeable differences and highlighted the importance of using a local thermoregulation model.

Keywords: boundary element method, dynamic thermography, static thermography, skin tumor diagnostic

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Authors: Md. S. Ansari, S. S. Motsa

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In this paper, an analysis has been made on the flow of non-Newtonian viscoelastic nanofluid over a linearly stretching sheet under the influence of uniform magnetic field. Heat transfer characteristics is analyzed taking into the effect of nonlinear radiation and non-uniform heat source/sink. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into ordinary differential equations by using appropriate similarity transformations. The transformed, highly nonlinear, ordinary differential equations are solved by spectral local linearisation method. The numerical convergence, error and stability analysis of iteration schemes are presented. The effects of different controlling parameters, namely, radiation, space and temperature-dependent heat source/sink, Brownian motion, thermophoresis, viscoelastic, Lewis number and the magnetic force parameter on the flow field, heat transfer characteristics and nanoparticles concentration are examined. The present investigation has many industrial and engineering applications in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Keywords: magnetic field, nonlinear radiation, non-uniform heat source/sink, similar solution, spectral local linearisation method, Rosseland diffusion approximation

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: M. Seguini, D. Nedjar

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An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability

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Authors: Hao Chen, Bo Guo, Ping Jiang

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Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: Kahil Amar, Nekmouche Aghiles, Titouche Billal, Hamizi Mohand, Hannachi Naceur Eddine

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The ductility is an important parameter in the nonlinear behavior of portal structures reinforced concrete. It may be explained by the ability of the structure to deform in the plastic range, or the geometric characteristics in the map may influence the overall ductility. Our study is based on the influence of geometric slenderness (Lx / Ly) on the overall ductility of these structures, a study is made on a structure has 05 floors with varying the column section of 900 cm², 1600 cm² and 1225 cm². A slight variation in global ductility is noticed as (Lx/Ly) varies; however, column sections can control satisfactorily the plastic behavior of buildings.

Keywords: ductility, nonlinear behavior, pushover analysis, geometric slenderness, structural behavior

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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