Search results for: nonlinear side force.

Authors: J. B. Seo, K. J. Kim, S. W. Nam

Abstract:

In this paper, a nonlinear acoustic echo cancellation (AEC) system is proposed, whereby 3rd order Volterra filtering is utilized along with a variable step-size Gauss-Seidel pseudo affine projection (VSSGS-PAP) algorithm. In particular, the proposed nonlinear AEC system is developed by considering a double-talk situation with near-end signal variation. Simulation results demonstrate that the proposed approach yields better nonlinear AEC performance than conventional approaches.

Keywords: Acoustic echo cancellation (AEC), Volterra filtering, variable step-size, GS-PAP.

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Authors: Ardeshir Karami Mohammadi, Mohammadreza Saee

Abstract:

A variable structure model reference adaptive control (VS-MRAC) strategy for active steering assistance of a two wheel steering car is proposed. An ideal steering system with fixed properties and moving on an ideal road is used as the reference model, and the active steering assistance system is forced to attain the same behavior as the reference model. The proposed system can treat the nonlinear relationships between the side slip angles and lateral forces on tire, and the uncertainties on friction of the road surface, whose compensation are very important under critical situations. Simulation results show improvements on yaw rate and side slip.

Keywords: Variable Structure, Adaptive Control, Model reference, Active steering assistance.

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Authors: Mohamed M. El-Gendy, Ibrahim A. El-Arabi, Rafik W. Abdel-Missih, Omar A. Kandil

Abstract:

In the present research, a finite element model is presented to study the geometrical and material nonlinear behavior of reinforced concrete plane frames considering soil-structure interaction. The nonlinear behaviors of concrete and reinforcing steel are considered both in compression and tension up to failure. The model takes account also for the number, diameter, and distribution of rebar along every cross section. Soil behavior is taken into consideration using four different models; namely: linear-, nonlinear Winkler's model, and linear-, nonlinear continuum model. A computer program (NARC) is specially developed in order to perform the analysis. The results achieved by the present model show good agreement with both theoretical and experimental published literature. The nonlinear behavior of a rectangular frame resting on soft soil up to failure using the proposed model is introduced for demonstration.

Keywords: Nonlinear analysis, Geometric nonlinearity, Material nonlinearity, Reinforced concrete, Finite element method, Soilstructure interaction, Winkler's soil model, Continuum soil model

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Authors: Hongdeuk Kim, Youngpo Lee, Seokho Yoon

Abstract:

Due to side-peaks of autocorrelation function, the binary offset carrier (BOC) signal acquisition suffers from an ambiguity when one of the side-peaks is acquired. In this paper, we first analyze that the BOC autocorrelation is made up of the sum of subcorrelations, and then, remove the side-peaks causing the ambiguity by recombining the sub-correlations. The proposed scheme is shown to remove the side-peaks completely. From numerical results, it is confirmed that the proposed scheme outperforms the conventional schemes in terms of the receiver operating characteristic and mean acquisition time.

Keywords: Binary offset carrier (BOC), acquisition, ambiguity problem, side-peak.

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Authors: F. Ayça Varol Saraçoğlu, Hayrullah Ağaçcıoğlu

Abstract:

Experimental studies to investigate the depth of the scour conducted at a side-weir intersection located at the 1800 curved flume which located Hydraulic Laboratory of Yıldız Technical University, Istanbul, Turkey. Side weirs were located at the middle of the straight part of the main channel. Three different lengths (25, 40 and 50 cm) and three different weir crest height (7, 10 and 12 cm) of the side weir placed on the side weir station. There is no scour when the material is only kaolin. Therefore, the cohesive bed was prepared by properly mixing clay material (kaolin) with 31% sand in all experiments. Following 24h consolidation time, in order to observe the effect of flow intensity on the scour depth, experiments were carried out for five different upstream Froude numbers in the range of 0.33-0.81. As a result of this study the relation between scour depth and upstream flow intensity as a function of time have been established. The longitudinal velocities decreased along the side weir; towards the downstream due to overflow over the side-weirs. At the beginning, the scour depth increases rapidly with time and then asymptotically approached constant values in all experiments for all side weir dimensions as in non-cohesive sediment. Thus, the scour depth reached equilibrium conditions. Time to equilibrium depends on the approach flow intensity and the dimensions of side weirs. For different heights of the weir crest, dimensionless scour depths increased with increasing upstream Froude number. Equilibrium scour depths which formed 7 cm side-weir crest height were obtained higher than that of the 12 cm side-weir crest height. This means when side-weir crest height increased equilibrium scour depths decreased. Although the upstream side of the scour hole is almost vertical, the downstream side of the hole is inclined.

Keywords: Clay-sand mixed sediments, scour, side weir.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi, F. Rezaie Moghaddam

Abstract:

In the analysis of structures, the nonlinear effects due to large displacement, large rotation and materially-nonlinear are very important and must be considered for the reliable analysis. The non-linear fmite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of fmite element code using the standard Galerkin weighted residual formulation. Two-dimensional plane stress model was carried out to present the shear wall response. Total Lagangian formulation, which is computationally more effective, is used in the formulation of stiffness matrices and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The details of the program formulation are highlighted and the results of the analyses are presented, along with a comparison of the response of the structure with Ansys software results. The presented model in this paper can be developed for nonlinear analysis of civil engineering structures with different material behavior and complicated geometry.

Keywords: Finite element, large displacements, materially nonlinear, shear wall.

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Authors: Nicolò Vaiana, Giorgio Serino

Abstract:

The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: Base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis.

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: B.P. Bezruchko, D.A. Smirnov

Abstract:

Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Keywords: Nonlinear time series analysis, directional couplings, coupled oscillators.

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Authors: Weifeng Wang, Guoqing Huang, Xianwei Zeng

Abstract:

The nearly 21-year-old Jiujiang Bridge, which is suffering from uneven line shape, constant great downwarping of the main beam and cracking of the box girder, needs reinforcement and cable adjustment. It has undergone cable adjustment for twice with incomplete data. Therefore, the initial internal force state of the Jiujiang Bridge is identified as the key for the cable adjustment project. Based on parameter identification by means of static force test data, this paper suggests determining the initial internal force state of the cable-stayed bridge according to the cable force-displacement relationship parameter identification method. That is, upon measuring the displacement and the change in cable forces for twice, one can identify the parameters concerned by means of optimization. This method is applied to the cable adjustment, replacement and reinforcement project for the Jiujiang Bridge as a guidance for the cable adjustment and reinforcement project of the bridge.

Keywords: Cable-stayed bridge, cable force-displacement, parameter identification, internal force state

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Authors: Abuzar.Abazari, Saeed. Ziaei-Rad, Hoseein. Dalayeli

Abstract:

Collision is considered as a time-depended nonlinear dynamic phenomenon. The majority of researchers have focused on deriving the resultant damage of the ship collisions via analytical, experimental, and finite element methods.In this paper, first, the force-penetration curve of a head collision on a container ship with rigid barrier based on Yang and Pedersen-s methods for internal mechanic section is studied. Next, the obtained results from different analytical methods are compared with each others. Then, through a simulation of the container ship collision in Ansys Ls-Dyna, results from finite element approach are compared with analytical methods and the source of errors is discussed. Finally, the effects of parameters such as velocity, and angle of collision on the forcepenetration curve are investigated.

Keywords: Ship collision, Force-penetration curve, Damage

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Authors: Hassen M. Ouakad

Abstract:

In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin method.

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Authors: Hsiang-Wen Tang, Cheng-Ying Lo

Abstract:

In this study, the static behavior of super elliptical Winkler plate is analyzed by applying the double side approach method. The lack of information about super elliptical Winkler plates is the motivation of this study and we use the double side approach method to solve this problem because of its superior ability on efficiently treating problems with complex boundary shape. The double side approach method has the advantages of high accuracy, easy calculation procedure and less calculation load required. Most important of all, it can give the error bound of the approximate solution. The numerical results not only show that the double side approach method works well on this problem but also provide us the knowledge of static behavior of super elliptical Winkler plate in practical use.

Keywords: Super elliptical Winkler Plate, double side approach method, error bound.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: S. Kahvecioglu, A. Karamancioglu, A. Yazici

Abstract:

In this paper, a nonlinear model predictive swing-up and stabilizing sliding controller is proposed for an inverted pendulum-cart system. In the swing up phase, the nonlinear model predictive control is formulated as a nonlinear programming problem with energy based objective function. By solving this problem at each sampling instant, a sequence of control inputs that optimize the nonlinear objective function subject to various constraints over a finite horizon are obtained. Then, this control drives the pendulum to a predefined neighborhood of the upper equilibrium point, at where sliding mode based model predictive control is used to stabilize the systems with the specified constraints. It is shown by the simulations that, due to the way of formulating the problem, short horizon lengths are sufficient for attaining the swing up goal.

Keywords: Inverted pendulum, model predictive control, swingup, stabilization.

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Authors: Zeinab Galavani, Reza Rezaei-Nasirabad, Rasoul Sadighi-Bonabi

Abstract:

Using a force balanced translational-radial dynamics, phase space of the moving single bubble sonoluminescence (m- SBSL) in 85% wt sulfuric acid has been numerically calculated. This phase space is compared with that of single bubble sonoluminescence (SBSL) in pure water which has been calculated by using the mere radial dynamics. It is shown that in 85% wt sulfuric acid, in a general agreement with experiment, the bubble-s positional instability threshold lays under the shape instability threshold. At the onset of spatial instability of moving sonoluminescing (SL) bubble in 85% wt sulfuric acid, temporal effects of the hydrodynamic force on the bubble translational-radial dynamics have been investigated. The appearance of non-zero history force on the moving SL bubble is because of proper condition which was produced by high viscosity of acid. Around the moving bubble collapse due to the rapid contraction of the bubble wall, the inertial based added mass force overcomes the viscous based history force and induces acceleration on the bubble translational motion.

Keywords: Bjerknes force, History force, Reynolds number, Sonoluminescence.

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

Abstract:

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear identification, NNARX.

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Authors: Ola Elfmark, Lars M. Bardal, Luca Oggiano, H˚avard Myklebust

Abstract:

Team pursuit is a relatively new event in international long track speed skating. For a single speed skater the aerodynamic drag will account for up to 80% of the braking force, thus reducing the drag can greatly improve the performance. In a team pursuit the interactions between athletes in near proximity will also be essential, but is not well studied. In this study, systematic measurements of the aerodynamic drag, body posture and relative positioning of speed skaters have been performed in the low speed wind tunnel at the Norwegian University of Science and Technology, in order to investigate the aerodynamic interaction between two speed skaters. Drag measurements of static speed skaters drafting, leading, side-by-side, and dynamic drag measurements in a synchronized and unsynchronized movement at different distances, were performed. The projected frontal area was measured for all postures and movements and a blockage correction was performed, as the blockage ratio ranged from 5-15% in the different setups. The static drag measurements where performed on two test subjects in two different postures, a low posture and a high posture, and two different distances between the test subjects 1.5T and 3T where T being the length of the torso (T=0.63m). A drag reduction was observed for all distances and configurations, from 39% to 11.4%, for the drafting test subject. The drag of the leading test subject was only influenced at -1.5T, with the biggest drag reduction of 5.6%. An increase in drag was seen for all side-by-side measurements, the biggest increase was observed to be 25.7%, at the closest distance between the test subjects, and the lowest at 2.7% with ∼ 0.7 m between the test subjects. A clear aerodynamic interaction between the test subjects and their postures was observed for most measurements during static measurements, with results corresponding well to recent studies. For the dynamic measurements, the leading test subject had a drag reduction of 3% even at -3T. The drafting showed a drag reduction of 15% when being in a synchronized (sync) motion with the leading test subject at 4.5T. The maximal drag reduction for both the leading and the drafting test subject were observed when being as close as possible in sync, with a drag reduction of 8.5% and 25.7% respectively. This study emphasize the importance of keeping a synchronized movement by showing that the maximal gain for the leading and drafting dropped to 3.2% and 3.3% respectively when the skaters are in opposite phase. Individual differences in technique also appear to influence the drag of the other test subject.

Keywords: Aerodynamic interaction, drag cycle, drag force, frontal area, speed skating.

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Authors: Fashad Amini, Lin Li

Abstract:

High performance turf reinforcement mat (HPTRM) is one of the most advanced flexible armoring technologies for severe erosion challenges. The effect of turbulence on the slope stability of an earthen levee strengthened by high performance turf reinforcement mat (HPTRM) is investigated in this study for combined storm surge and wave overtopping conditions. The results show that turbulence has strong influence on the slope stability during the combined storm surge and wave overtopping conditions. Among the surge height, peak wave force and turbulent force. The turbulent force has the ability to stabilize the earthen levee at the large wave force the turbulent force has strongest effect on the FS. The surge storm acts as an independent force on the slope stability of the earthen levee. It just adds to the effects of the turbulent force and wave force on the slope stability of HPTRM strengthened levee.

Keywords: Slope stability, strength reduction method, HPTRM, levee, overtopping.

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Authors: Olga Tkacheva, Pavel Arkhipov, Alexey Rudenko, Yurii Zaikov

Abstract:

The aluminum electrolysis process in the conventional cryolite-alumina electrolyte with cryolite ratio of 2.7 was carried out at an initial temperature of 970 °C and the anode current density of 0.5 A/cm² in a 15A lab-scale cell in order to study the formation of the side ledge during electrolysis and the alumina distribution between electrolyte and side ledge. The alumina contained 35.97% α-phase and 64.03% γ-phase with the particles size in the range of 10-120 μm. The cryolite ratio and the alumina concentration were determined in molten electrolyte during electrolysis and in frozen bath after electrolysis. The side ledge in the electrolysis cell was formed only by the 13^th hour of electrolysis. With a slight temperature decrease a significant increase in the side ledge thickness was observed. The basic components of the side ledge obtained by the XRD phase analysis were Na₃AlF₆, Na₅Al₃F₁₄, Al₂O₃, and NaF^.5CaF₂^.AlF₃. As in the industrial cell, the increased alumina concentration in the side ledge formed on the cell walls and at the ledge-electrolyte-aluminum three-phase boundary during aluminum electrolysis in the lab cell was found (FTP No 05.604.21.0239, IN RFMEFI60419X0239).

Keywords: Alumina, alumina distribution, aluminum electrolyzer, cryolite-alumina electrolyte, side ledge.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

Abstract:

In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: M.V Rajesh, Archana R, A Unnikrishnan, R Gopikakumari, Jeevamma Jacob

Abstract:

The System Identification problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a performance function based on error between the given process output and identified process output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems. The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5]. The work reported here is an attempt to implement few of the well known algorithms in the context of modeling of nonlinear systems, and to make a performance comparison to establish the relative merits and demerits.

Keywords: Multilayer neural networks, Radial Basis Functions, Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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Authors: Hamza Nejib, Okba Taouali

Abstract:

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

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

Abstract:

This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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Authors: Şaban Çetin, Özgür Demir

Abstract:

In this study, Fuzzy PID Control scheme is designed for an active suspension system. The main goal of an active suspension system for using in a vehicle model is reducing body deflections and handling high comfort for a passenger car. The present system was modelled as a two-degree-of-freedom (2-DOF) nonlinear vehicle model.

Keywords: Active suspension system, Fuzzy PID controller, a nonlinear quarter car model.

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Authors: Abdulrahman Abdulrahman

Abstract:

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: Analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile.

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