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Vibration and buckling analyses of nanobeams embedded in an elastic medium

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Chinese Physics B 2015年第9期24卷 489-496页

作者： s chakraverty Laxmi Behera Department of Mathematics National Institute of Technology Rourkela

Boundary characteristic orthogonal polynomials are used as shape functions in the Rayleigh–Ritz method to investigate vibration and buckling of nanobeams embedded in an elastic medium. The present formulation is based on the nonlocal Euler–Bernoulli beam theory. The eigen value equation is developed for the buckling and vibration analyses. The orthogonal property of these polynomials makes the computation easier with less computational effort. It is observed that the frequency and critical buckling load parameters are dependent on the temperature, elastic medium, small scale coefficient,and length-to-diameter ratio. These observations are useful in the mechanical design of devices that use carbon nanotubes.

关键词： Rayleigh–Ritz method boundary characteristic orthogonal polynomials nonlocal elasticity theory Euler–Bernoulli beam theory

Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

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Chinese Physics B 2014年第12期23卷 14-20页

作者： s.chakraverty smita Tapaswini Department of Mathematics National Institute of Technology RourkelaOdisha–769 008 India

The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method（ADM） symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.

关键词： double parametric form of fuzzy number fuzzy fractional diffusion equation ADM

Numerical solution of the imprecisely defined inverse heat conduction problem

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Chinese Physics B 2015年第5期24卷 153-162页

作者： smita Tapaswini s.chakraverty Diptiranjan Behera Department of Mathematics National Institute of Technology Rourkela

This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method （VIM）. This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. sci. （2008） 178 1917] along with homotopy perturbation method （HPM） and [Int. Commun. Heat Mass Transfer （2012） 39 30] in the special cases to demonstrate the validity and applicability.

关键词： triangular fuzzy number double parametric form of fuzzy numbers uncertain inverse heat con-duction variational iteration method (VIM)

Dynamic Response and Oscillating Behaviour of Fractionally Damped Beam

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Computer Modeling in Engineering & sciences 2015年第3期104卷 211-225页

作者： Diptiranjan Behera s.chakraverty Corresponding Author.school of Mechatronics Engineering University of Electronic Science and Technology of ChinaNo.2006Xiyuan AvenueWest Hi-Tech ZoneChengduSichuan 611731P.R.China Department of Mathematics National Institute of Technology RourkelaOdisha-769008India

This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary *** Perturbation Method(HPM)is used to obtain the dynamic response with respect to unit impulse *** results are depicted in term of *** are made with the analytic solutions obtained by Zu-feng and Xiao-yan(2007)to show the effectiveness and validation of the present method.

关键词： Viscoelastic beam Fractional derivative Impulse response function Homotopy Perturbation Method(HPM)

solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped spring-Mass structural systems Using Novel Fuzzy-Affine Approach

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Computer Modeling in Engineering & sciences 2019年第12期121卷 947-980页

作者： s.Rout s.chakraverty Department of Mathematics National Institute of Technology RourkelaOdishaIndia

The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact *** in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy *** article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers *** and *** on the parametric form,fuzzy numbers have been transformed into family of standard *** due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been *** the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine *** application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed ***,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership *** comparisons are also demonstrated to show the reliability and efficacy of the present approach.

关键词： Fuzzy nonlinear eigenvalue problem fuzzy set theory affine arithmetic interval overestimation problem triangular fuzzy number trapezoidal fuzzy number fuzzy-affine approach

Effect of Coriolis constant on Geophysical Korteweg-de Vries equation

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Journal of Ocean Engineering and science 2019年第2期4卷 113-121页

作者： P.Karunakar s.chakraverty Department of Mathematics National Institute of Technology RourkelaRourkela 769008 OdishaIndia

The present article investigates the effect of Coriolis constant on the solution of the Geophysical Korteweg-de Vries(gKdV)*** such,the Homotopy Perturbation Method(HPM)has been applied here for solving the nonlinear gKdV *** results are compared with existing results that are available in the literature and they are found to be in good *** the Coriolis term has been considered in terms of the interval to form interval Geophysical Korteweg-de Vries(IgKdV)*** equation has been solved by HPM to analyse the effect of *** this analysis,it has been concluded that the constant of Coriolis is directly proportional to wave height and inversely proportional to *** presence of the Coriolis term in gKdV equation has a remarkable change in the shape of the solution.

关键词： Geophysical Korteweg-de Vries Equation Coriolis constant HPM Interval gKdV.

Development of a mathematical model to evaluate the rate of aggregate risk of invasive alien plant species： Fuzzy risk assessment approach

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International Journal of Biomathematics 2018年第4期11卷 77-93页

作者： H. O. W. Peiris s. s. N. Perera s. chakraverty s. M. W. Ranwala Department of Mathematics The Open University of Sri Lanka Nawala Nugegoda Sri Lanka Research and Development Centre for Mathematical Modeling Faculty of science University of Colombo 94 Cumaratunga Munidasa Mw Colombo 03 Sri Lanka Department of MathematicsNational Institute of Technology Rourkela Ronrkela India Department of Plant sciences University of Colombo94 Cumaratunga Munidasa Mw Colombo 03 Sri Lanka

This study presents a novel approach to evaluate the rate of aggregate risk of Invasive Alien Plant species. Using risk values and grade of importance of weights of risk factors which may reflect invasiveness of plant species are considered. We use Linguistic Ordered Weighted Averaging operator to evaluate the grade of important of weights. since the risk values and important weights are identified from two different linguistic term sets, fuzzy set theory techniques were used to combine the two sets. The rates obtained from the model were compared with NRA risk levels and the model was validated with data from known and non-invasive species. The model is improved by weighting the risk values of risk factors. The improved model produced significant results and resulted a better tracking system for identifying potential invaders than the conventional risk assessment.

关键词： Invasive alien plant species invasive attributes fuzzy set theory operators linguistic ordered weighted averaging operator.

AVAILABILITY MODEL FOR sELF TEsT AND REPAIR IN FAULT TOLERANT FPGA-BAsED sYsTEMs

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Journal of Electronics(China) 2014年第4期31卷 271-283页

作者： shampa chakraverty Anubhav Agarwal Broteen Kundu Anil Kumar Division of Computer Engineering Netaji Subhas Institute of Technology

Dynamically reconfigurable Field Programmable Gate Array(dr-FPGA) based electronic systems on board mission-critical systems are highly susceptible to radiation induced hazards that may lead to faults in the logic or in the configuration memory. The aim of our research is to characterize self-test and repair processes in Fault Tolerant(FT) dr-FPGA systems in the presence of environmental faults and explore their interrelationships. We develop a Continuous Time Markov Chain(CTMC) model that captures the high level fail-repair processes on a dr-FPGA with periodic online Built-In self-Test(BIsT) and scrubbing to detect and repair faults with minimum latency. simulation results reveal that given an average fault interval of 36 s, an optimum self-test interval of 48.3 s drives the system to spend 13% of its time in self-tests, remain in safe working states for 76% of its time and face risky fault-prone states for only 7% of its time. Further, we demonstrate that a well-tuned repair strategy boosts overall system availability, minimizes the occurrence of unsafe states, and accommodates a larger range of fault rates within which the system availability remains stable within 10% of its maximum level.

关键词： Dynamically reconfigurable Field Programmable Gate Array (dr-FPGA) Built-In self-Test (BIsT) Fault Tolerance (FT) single Event Effects (sEEs) Continuous Time Markov Chain (CTMC) scrubbingCLC number:TN47