Search results for: Dual fuzzy polynomial equations

Authors: Mostafa Raki, Mahdi Hamzehei

Abstract:

Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.

Keywords: Stability of plate, thermal buckling, rectangularplate, functionally graded material, first order shear deformationtheory.

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Authors: Dmitry V. Fomichev, Vladimir I. Solonin

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This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown.

An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics.

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Authors: Rawya Rizk, Rehab Abdel-Kader, Rabab Ramadan

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Unlike the best effort service provided by the internet today, next-generation wireless networks will support real-time applications. This paper proposes an adaptive early packet discard (AEPD) policy to improve the performance of the real time TCP traffic over ATM networks and avoid the fragmentation problem. Three main aspects are incorporated in the proposed policy. First, providing quality-of-service (QoS) guaranteed for real-time applications by implementing a priority scheduling. Second, resolving the partially corrupted packets problem by differentiating the buffered cells of one packet from another. Third, adapting a threshold dynamically using Fuzzy logic based on the traffic behavior to maintain a high throughput under a variety of load conditions. The simulation is run for two priority classes of the input traffic: real time and non-real time classes. Simulation results show that the proposed AEPD policy improves throughput and fairness over that using static threshold under the same traffic conditions.

Keywords: Early packet discard, Fuzzy logic, packet dropping policies, quality-of-service (QoS), TCP over ATM

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Authors: Kaltima Phichai, Pornchanoke Pragrobpondee, Thaweesak Khumpart, Samorn Hirunpraditkoon

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The paper provides biomasses characteristics by proximate analysis (volatile matter, fixed carbon and ash) and ultimate analysis (carbon, hydrogen, nitrogen and oxygen) for the prediction of the heating value equations. The heating value estimation of various biomasses can be used as an energy evaluation. Thirteen types of biomass were studied. Proximate analysis was investigated by mass loss method and infrared moisture analyzer. Ultimate analysis was analyzed by CHNO analyzer. The heating values varied from 15 to 22.4MJ kg-1. Correlations of the calculated heating value with proximate and ultimate analyses were undertaken using multiple regression analysis and summarized into three and two equations, respectively. Correlations based on proximate analysis illustrated that deviation of calculated heating values from experimental heating values was higher than the correlations based on ultimate analysis.

Keywords: Heating value equation, Proximate analysis, Ultimate analysis.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

Abstract:

As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Keywords: periodic solution, neutral Rayleigh equation, variable sign, Deviating argument, p-Laplacian, Mawhin’s continuation.

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Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

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This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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Authors: T. P. Athira, Gibin Chacko George

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This paper proposes a dual tree complex wavelet transform (DT-CWT) based directional interpolation scheme for noisy images. The problems of denoising and interpolation are modelled as to estimate the noiseless and missing samples under the same framework of optimal estimation. Initially, DT-CWT is used to decompose an input low-resolution noisy image into low and high frequency subbands. The high-frequency subband images are interpolated by linear minimum mean square estimation (LMMSE) based interpolation, which preserves the edges of the interpolated images. For each noisy LR image sample, we compute multiple estimates of it along different directions and then fuse those directional estimates for a more accurate denoised LR image. The estimation parameters calculated in the denoising processing can be readily used to interpolate the missing samples. The inverse DT-CWT is applied on the denoised input and interpolated high frequency subband images to obtain the high resolution image. Compared with the conventional schemes that perform denoising and interpolation in tandem, the proposed DT-CWT based noisy image interpolation method can reduce many noise-caused interpolation artifacts and preserve well the image edge structures. The visual and quantitative results show that the proposed technique outperforms many of the existing denoising and interpolation methods.

Keywords: Dual-tree complex wavelet transform (DT-CWT), denoising, interpolation, optimal estimation, super resolution.

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: Axisymmetric problem, compressible Navier- Stokes equations, continuous finite elements, swirling flow.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

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Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler-s known method that was developed under the guidance of the famous scientists Adams, Runge and Kutta is the most popular one among these methods. Recently the scientists began to construct the methods preserving some properties of Adams and Runge-Kutta methods and called them hybrid methods. The constructions of such methods are investigated from the middle of the XX century. Here we investigate one generalization of multistep and hybrid methods and on their base we construct specific methods of accuracy order p = 5 and p = 6 for k = 1 ( k is the order of the difference method).

Keywords: Multistep and hybrid methods, initial value problem, degree and stability of hybrid methods

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Authors: Xin Luo, Jin Huang, Pan Cheng

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By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

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Authors: Safaa Al-Ali, Ahmad Shahin, Fadi Chakik

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Image coding based on clustering provides immediate access to targeted features of interest in a high quality decoded image. This approach is useful for intelligent devices, as well as for multimedia content-based description standards. The result of image clustering cannot be precise in some positions especially on pixels with edge information which produce ambiguity among the clusters. Even with a good enhancement operator based on PDE, the quality of the decoded image will highly depend on the clustering process. In this paper, we introduce an ambiguity cluster in image coding to represent pixels with vagueness properties. The presence of such cluster allows preserving some details inherent to edges as well for uncertain pixels. It will also be very useful during the decoding phase in which an anisotropic diffusion operator, such as Perona-Malik, enhances the quality of the restored image. This work also offers a comparative study to demonstrate the effectiveness of a fuzzy clustering technique in detecting the ambiguity cluster without losing lot of the essential image information. Several experiments have been carried out to demonstrate the usefulness of ambiguity concept in image compression. The coding results and the performance of the proposed algorithms are discussed in terms of the peak signal-tonoise ratio and the quantity of ambiguous pixels.

Keywords: Ambiguity Cluster, Anisotropic Diffusion, Fuzzy Clustering, Image Compression.

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

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Authors: F.Saadi, A.Aboudi Asl

Abstract:

In this paper, the dynamic analysis of fuel storage tanks has been studied and some equations are presented for the created fluid waves due to storage tank motions. Also, the equations for finite elements of fluid and structure interactions, and boundary conditions dominant on structure and fluid, were researched. In this paper, a numerical simulation is performed for the dynamic analysis of a storage tank contained a fluid. This simulation has carried out by ANSYS software, using FSI solver (Fluid and Structure Interaction solver), and by considering the simulated fluid dynamic motions due to earthquake loading, based on velocities and movements of structure and fluid according to all boundary conditions dominant on structure and fluid.

Keywords: fluid and structure interactions, finite elementmethod, ANSYS – FSI

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Authors: Salem Alsanusi, Loubna Bentaher

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Response Surface Methods (RSM) provide statistically validated predictive models that can then be manipulated for finding optimal process configurations. Variation transmitted to responses from poorly controlled process factors can be accounted for by the mathematical technique of propagation of error (POE), which facilitates ‘finding the flats’ on the surfaces generated by RSM. The dual response approach to RSM captures the standard deviation of the output as well as the average. It accounts for unknown sources of variation. Dual response plus propagation of error (POE) provides a more useful model of overall response variation. In our case, we implemented this technique in predicting compressive strength of concrete of 28 days in age. Since 28 days is quite time consuming, while it is important to ensure the quality control process. This paper investigates the potential of using design of experiments (DOE-RSM) to predict the compressive strength of concrete at 28th day. Data used for this study was carried out from experiment schemes at university of Benghazi, civil engineering department. A total of 114 sets of data were implemented. ACI mix design method was utilized for the mix design. No admixtures were used, only the main concrete mix constituents such as cement, coarseaggregate, fine aggregate and water were utilized in all mixes. Different mix proportions of the ingredients and different water cement ratio were used. The proposed mathematical models are capable of predicting the required concrete compressive strength of concrete from early ages.

Keywords: Mix proportioning, response surface methodology, compressive strength, optimal design.

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We then discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, Nonuniform fiber, Nonlinear pulse.

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Authors: Dilavar Khan, Z. Ahmad

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Riprap is mostly used to prevent erosion by flows down the steep slopes in river engineering. A total of 53 stability tests performed on angular riprap with a median stone size ranging from 15 to 278 mm and slope ranging from 1 to 40% are used in this study. The existing equations for the prediction of medium size of angular stones are checked for their accuracy using the available data. Predictions of median size using these equations are not satisfactory and results show deviation by more than ±20% from the observed values. A multivariable power regression analysis is performed to propose a new equation relating the median size with unit discharge, bed slope, riprap thickness and coefficient of uniformity. The proposed relationship satisfactorily predicts the median angular stone size with ±20% error. Further, the required size of the rounded stone is more than the angular stone for the same unit discharge and the ratio increases with unit discharge and also with embankment slope of the riprap.

Keywords: Angularity, Gradation, Riprap, Stabilization

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Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian

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In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.

Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.

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Authors: Ding Guo-hao, Li Hua, Wang Wen-long

Abstract:

A parallel computational fluid dynamics code has been developed for the study of aerodynamic heating problem in hypersonic flows. The code employs the 3D Navier-Stokes equations as the basic governing equations to simulate the laminar hypersonic flow. The cell centered finite volume method based on structured grid is applied for spatial discretization. The AUSMPW+ scheme is used for the inviscid fluxes, and the MUSCL approach is used for higher order spatial accuracy. The implicit LU-SGS scheme is applied for time integration to accelerate the convergence of computations in steady flows. A parallel programming method based on MPI is employed to shorten the computing time. The validity of the code is demonstrated by comparing the numerical calculation result with the experimental data of a hypersonic flow field around a blunt body.

Keywords: Aerodynamic Heating, AUSMPW+, MPI, ParallelComputation

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper presents a differential evolution algorithm to design a robust PI and PID controllers for Load Frequency Control (LFC) of nonlinear interconnected power systems considering the boiler dynamics, Governor Dead Band (GDB), Generation Rate Constraint (GRC). Differential evolution algorithm is employed to search for the optimal controller parameters. The proposed method easily copes of with nonlinear constraints. Further the proposed controller is simple, effective and can ensure the desirable overall system performance. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic controller for the same power systems. The comparison is done using various performance measures like overshoot, settling time and standard error criteria of frequency and tie-line power deviation following a 1% step load perturbation in hydro area. It is noticed that, the dynamic performance of proposed controller is better than fuzzy logic controller. Furthermore, it is also seen that the proposed system is robust and is not affected by change in the system parameters.

Keywords: Automatic Generation control (AGC), Generation Rate Constraint (GRC), Governor Dead Band (GDB), Differential Evolution (DE)

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Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

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These days, the field of tissue engineering is getting serious attention due to its usefulness. Bone tissue engineering helps to address and sort-out the critical sized and non-healing orthopedic problems by the creation of manmade bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature “parametric sweep”, with which we will be able to predict the oxygen, glucose and cell density dynamics, more accurately. We will fix these problems by modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes and by transient analysis.

Keywords: Bone tissue engineering, Transient Analysis, Scaffolds, fabrication techniques.

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Authors: Shiuh-Jer Huang, Yu-Chi Liu, Su-Hai Hsiang

Abstract:

A novel low-cost impedance control structure is proposed for monitoring the contact force between end-effector and environment without installing an expensive force/torque sensor. Theoretically, the end-effector contact force can be estimated from the superposition of each joint control torque. There have a nonlinear matrix mapping function between each joint motor control input and end-effector actuating force/torques vector. This new force control structure can be implemented based on this estimated mapping matrix. First, the robot end-effector is manipulated to specified positions, then the force controller is actuated based on the hall sensor current feedback of each joint motor. The model-free fuzzy sliding mode control (FSMC) strategy is employed to design the position and force controllers, respectively. All the hardware circuits and software control programs are designed on an Altera Nios II embedded development kit to constitute an embedded system structure for a retrofitted Mitsubishi 5 DOF robot. Experimental results show that PI and FSMC force control algorithms can achieve reasonable contact force monitoring objective based on this hardware control structure.

Keywords: Robot, impedance control, fuzzy sliding mode control, contact force estimator.

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Authors: Kuang-Hsiung Tan, Chih-Chan Hu, Chien-Wu Lan, Shih-Sung Lin, Te-Jen Chang

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An active islanding detection method using disturbance signal injection with intelligent controller is proposed in this study. First, a DC\AC power inverter is emulated in the distributed generator (DG) system to implement the tracking control of active power, reactive power outputs and the islanding detection. The proposed active islanding detection method is based on injecting a disturbance signal into the power inverter system through the d-axis current which leads to a frequency deviation at the terminal of the RLC load when the utility power is disconnected. Moreover, in order to improve the transient and steady-state responses of the active power and reactive power outputs of the power inverter, and to further improve the performance of the islanding detection method, two probabilistic fuzzy neural networks (PFNN) are adopted to replace the traditional proportional-integral (PI) controllers for the tracking control and the islanding detection. Furthermore, the network structure and the online learning algorithm of the PFNN are introduced in detail. Finally, the feasibility and effectiveness of the tracking control and the proposed active islanding detection method are verified with experimental results.

Keywords: Distributed generators, probabilistic fuzzy neural network, islanding detection, non-detection zone.

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Authors: Ch. Surawut, D. Sukawat

Abstract:

In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. This equation provides downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: Dynamic Equation, Downscaling, Inverse distance weight interpolation.

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

Abstract:

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic.

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Authors: Cheng-Chi Yu, Chi-Shiun Chiou

Abstract:

This study developed a plug-in hybrid powertrain system which consisted of two continuous variable transmissions. By matching between the engine, motor, generator, and dual continuous variable transmissions, this integrated power system can take advantages of the components. The hybrid vehicle can be driven by the internal combustion engine, or electric motor alone, or by these two power sources together when the vehicle is driven in hard acceleration or high load. The energy management of this integrated hybrid system controls the power systems based on rule-based control strategy to achieve better fuel economy. When the vehicle driving power demand is low, the internal combustion engine is operating in the low efficiency region, so the internal combustion engine is shut down, and the vehicle is driven by motor only. When the vehicle driving power demand is high, internal combustion engine would operate in the high efficiency region; then the vehicle could be driven by internal combustion engine. This strategy would operate internal combustion engine only in optimal efficiency region to improve the fuel economy. In this research, the vehicle simulation model was built in MATLAB/ Simulink environment. The analysis results showed that the power coupled efficiency of the hybrid powertrain system with dual continuous variable transmissions was better than that of the Honda hybrid system on the market.

Keywords: Plug-in hybrid power system, fuel economy, performance, continuous variable transmission.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

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This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: Faruk Fırat Çalım, Nurullah Karaca, Hakan Tacettin Türker

Abstract:

In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: Circular rod, Out-of-plane free vibration analysis, Transfer Matrix Method.

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Authors: Madhu Aneja, Sapna Sharma

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The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: Bioconvection, inclined stretching sheet, Gyrotactic micro-organisms, Brownian motion, thermophoresis, finite element method.

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Authors: Atilla Akpinar, Basri Çelik

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In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We introduce two new collineations of M(A).

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation.

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