Showing papers by "Shantanu Das published in 2015"

Structure–Property Correlations in Microwave Joining of Inconel 718

Abstract: The butt joining of Inconel 718 plates at 981°C solution treated and aged (981STA) condition was carried out using the microwave hybrid heating technique with Inconel 718 powder as a filler material. The developed joints were free from any microfissures (cracks) and were metallurgically bonded through complete melting of the powder particles. The as-welded joints were subjected to postweld heat treatments, including direct-aged, 981STA and 1080STA. The microstructural features of the welded joints were investigated using a field emission-scanning electron microscope equipped with x-ray elemental analysis. Microhardness and room-temperature tensile properties of the welded joints were evaluated. The postweld heat-treated specimens exhibited higher microhardness and tensile strength than the as-welded specimens due to the formation of strengthening precipitates in the microstructure after postweld heat treatments. The microhardness of the fusion zone of the joint in 1080STA condition was higher than all welded conditions due to the complete dissolution of Laves phase after 1080STA treatment. However, the tensile strength of the welded specimen in 981STA condition was higher than all welded conditions. The tensile strength in 1080STA condition was lower than that in 981STA condition because of the grain coarsening that took place after 1080STA condition. The fractography of the fractured surfaces was carried out to determine the structure–property–fracture correlation.

Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes

Abstract: An optimal trade-off design for fractional order (FO)-PID controller is proposed with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain objectives. A class of delayed FO systems with single non-integer order element, exhibiting both sluggish and oscillatory open loop responses, have been controlled here. The FO time delay processes are handled within a multi-objective optimization (MOO) formalism of LQR based FOPID design. A comparison is made between two contemporary approaches of stabilizing time-delay systems withinLQR. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance and total variation (TV) of the control signal. Tuning rules are formed for the optimal LQR-FOPID controller parameters, using median of the non-dominated Pareto solutions to handle delayed FO processes.

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag-Leffler Function

Abstract: There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

A New Method for Getting Rational Approximation for Fractional Order Differintegrals

Abstract: In this paper a new algorithm is presented to calculate the poles and zeros to approximate a fractional order (FO) differintegral (s±α,α∈(0,1)) by a rational function on a finite frequency band ω∈(ωl,ωh). The constant phase property of the FO differintegral is the basis for development of the algorithm. Interlacing of real poles and zeros is used to achieve the constant phase. The calculations are done using the asymptotic Bode phase plot. A brief investigation is made to get a good approximation for the Bode phase plot. Two design parameters are introduced to keep the average phase close to the desired phase angle and to keep the error within the allowed bounds. A study is done to empirically understand the relationship between the error and the design parameters. The results thus obtained help in the further calculations. The algorithm is computationally simple and inexpensive, and gives a fairly good approximation of fractance frequency response on the specified frequency band.

Analytic Solution of Linear Fractional Differential Equation with Jumarie Derivative in Term of Mittag- Leffler Function

Abstract: There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the linear fractional differential equation composed via Jumarie fractional derivative in terms of Mittag-Leffler function; and show its conjugation with ordinary calculus. In these fractional differential equations the one parameter Mittag-Leffler function plays the role similar as exponential function used in ordinary differential equations.

Solution of System of Linear Fractional Differential Equations with Modified derivative of Jumarie Type

Abstract: Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional differential equations in-terms of Mittag-Leffler function and generalized Sine and Cosine functions, where the fractional derivative operator is of Jumarie type. The use of Jumarie type fractional derivative, which is modified Rieman-Liouvellie fractional derivative, eases the solution to such fractional order systems. The use of this type of Jumarie fractional derivative gives a conjugation with classical methods of solution of system of linear integer order differential equations, by usage of Mittag-Leffler and generalized trigonometric functions. The ease of this method and its conjugation to classical method to solve system of linear fractional differential equation is appealing to researchers in fractional dynamic systems. Here after developing the method, the algorithm is applied in physical system of fractional differential equation. The analytical results obtained are then graphically plotted for several examples for system of linear fractional differential equation.

A simulation approach to material removal in microwave drilling of soda lime glass at 2.45 GHz

Abstract: Material removal during microwave drilling is basically due to thermal ablation of the material in the vicinity of the drilling tool. The microtip of the tool, also termed as concentrator, absorbs microwaves and ionizes the dielectric in its proximity creating a zone of plasma. The plasma takes the shape of a sphere owing to the atmospheric sphere, which acts as the source of thermal energy to be used for processing a material. This mechanism of heating, also called localized microwave heating, was used in the present study to drill holes in 1.2-mm-thick soda lime glass. The mechanism of material removal had been analyzed through simulation of the hot spot region, and the results were attempted to explain through experiment observations. It was realized that the glass being a poor conductor of heat, a low power (90 W in this case) yields better drilling results owing to more localized heat corresponding to a low-volume plasma sphere. The low application time prevents further heat transfer, and a localized concentration of heat becomes possible that primarily causes the material ablation. The plasma sphere appears sustain while the tool moves through the bulk of the glass thickness although its volume gets further shrunk. The process needs careful selection of the parameters. The simulation results show relatively low temperature in the top half (opposite to the tool tip) of the plasma sphere which eventually causes the semimolten viscous glass to collapse into the drill cavity as the tool advances into the bulk and stops the movement of the tool. The continued plasma sphere raises the tip temperature, which makes the tip to melt and gets blunt. The plasma formation ceases owing to larger diameter of the tool, and the tool gets stuck which could be verified through experimental results.

Characterization of non-differentiable points in a function by Fractional derivative of Jumarrie type

Abstract: There are many functions which are continuous everywhere but not differentiable at some points, like in physical systems of ECG, EEG plots, and cracks pattern and for several other phenomena. Using classical calculus those functions cannot be characterized-especially at the non-differentiable points. To characterize those functions the concept of Fractional Derivative is used. From the analysis it is established that though those functions are unreachable at the non-differentiable points, in classical sense but can be characterized using Fractional derivative. In this paper we demonstrate use of modified Riemann-Liouvelli derivative by Jumarrie to calculate the fractional derivatives of the non-differentiable points of a function, which may be one step to characterize and distinguish and compare several non-differentiable points in a system or across the systems. This method we are extending to differentiate various ECG graphs by quantification of non-differentiable points; is useful method in differential diagnostic. Each steps of calculating these fractional derivatives is elaborated.

Solution of System of Linear Fractional Differential Equations with Modified Derivative of Jumarie Type

Abstract: Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional differential equations in-terms of Mittag-Leffler function and generalized Sine and Cosine functions, where the fractional derivative operator is of Jumarie type. The use of Jumarie type fractional derivative, which is modified Rieman-Liouvellie fractional derivative, eases the solution to such fractional order systems. The use of this type of Jumarie fractional derivative gives a conjugation with classical methods of solution of system of linear integer order differential equations, by usage of Mittag-Leffler and generalized trigonometric functions. The ease of this method and its conjugation to classical method to solve system of linear fractional differential equation is appealing to researchers in fractional dynamic systems. Here after developing the method, the algorithm is applied in physical system of fractional differential equation. The analytical results obtained are then graphically plotted for several examples for system of linear fractional differential equation.

Symbolic representation for analog realization of a family of fractional order controller structures via continued fraction expansion.

Abstract: This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO lead–lag compensator. Contemporary researchers have given several formulations for rational approximation of fractional order elements. However, approximation of the controllers studied in this paper, due to having fractional power of a rational transfer function, is not available in analog domain; although its digital realization already exists. This motivates us for applying CFE based analog realization technique for complicated FO controller structures to get equivalent rational transfer functions in terms of the controller tuning parameters. The symbolic expressions for rationalized transfer function in terms of the controller tuning parameters are especially important as ready references, without the need of running CFE algorithm every time and also helps in the synthesis of analog circuits for such FO controllers.

Fractional Weierstrass Function by Application of Jumarie Fractional Trigonometric Functions and Its Analysis

Abstract: The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.

Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals

Abstract: In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type fractional derivative, and describe this method developed by us, to find out particular integrals, for several types of forcing functions. The solutions are obtained in terms of Mittag-Leffler functions, fractional sine and cosine functions. We have used our earlier developed method of finding solution to homogeneous FDE composed via Jumarie fractional derivative, and extended this to non-homogeneous FDE. We have demonstrated these developed methods with few examples of FDE, and also applied in fractional damped forced differential equation. The short cut rules, that are developed here in this paper to replace the operator Da or operator D2a as were used in classical calculus, gives ease in evaluating particular integrals. Therefore this method proposed by us is useful and advantageous as it is having conjugation with the classical methods of solving non-homogeneous linear differential equations, and also useful in understanding physical systems described by FDE.

Solutions of Linear Fractional non-Homogeneous Differential Equations with Jumarie Fractional Derivative and Evaluation of Particular Integrals

Abstract: In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type Fractional Derivative, and describe this method developed by us, to find out Particular Integrals, for several types of forcing functions. The solutions are obtained in terms of Mittag-Leffler functions, fractional sine and cosine functions. We have used our earlier developed method of finding solution to homogeneous FDE composed via Jumarie fractional derivative, and extended this to non-homogeneous FDE. We have demonstrated these developed methods with few examples of FDE, and also applied in fractional damped forced differential equation. This method proposed by us is useful as it is having conjugation with the classical methods of solving non-homogeneous linear differential equations, and also useful in understanding physical systems described by FDE.

Identification of fractional order circuits from frequency response data using seeker optimization algorithm

Abstract: Linear circuits and systems are generally described by traditional differential equations and integer order transfer functions based on the assumption that the dynamics are lumped and time invariant. However, as compared to the conventional integer order calculus, many dynamical systems are better represented by fractional calculus with interaction among the variables modelled by fractional integration and/or fractional differentiation. The present work proposes a generalized approach for the identification of fractional order systems in frequency domain using experimental data. To achieve the same, the system identification task has been framed as an optimization problem and solved using seeker optimization algorithm. The algorithm seeks to attain a set of system parameters for which the deviation between the simulated response of the identified system and experimental data is minimized. The proposed approach has been validated on a set of electrical circuits with varying configuration. The simulation and experimental results reveals that all of the test circuits are better represented by fractional order model, over a wide range of frequency.

Fractional Weierstrass function by application of Jumarie fractional trigonometric functions and its analysis

Abstract: The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we define the fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The Holder exponent and Box dimension of this function are calculated here. It is established that the Holder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function, independent of incorporating the fractional trigonometric function. This is new development in generalizing the classical Weierstrass function by usage of fractional trigonometric function and obtain its character and also of fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, and establishing that roughness index are invariant to this generalization.

Electrical Impedance Response of Gamma Irradiated Gelatin based Solid Polymer Electrolytes Analyzed Using a Generalized Calculus Formalism

Abstract: The electrical impedance response of Gelatin based solid polymer electrolyte to gamma irradiation is investigated by impedance spectroscopy An analysis based on Poisson-Nernst-Plank model, incorporating fractional time derivatives is carried out A detailed derivation for anomalous impedance function is givenThe model involves boundary conditions with convolution of the fractional time derivative of ion density and adsorption desorption relaxation kinetics A fractional diffusion-drift equation is used to solve the bulk behavior of the mobile charges in the electrolyte The complex adsorption-desorption process at the electrode-electrolyte interface produces an anomalous effect in the system The model gives a very good fit for the observed impedance data for this biopolymer based solid electrolyte in wide range of frequencies We have compared different parameters based upon this model for both irradiated and unirradiated samples

Squeeze flow of potato starch gel: effect of loading history on visco-elastic properties

Abstract: In this work gelatinized potato starch is shown to retain the memory of past loading history. It exhibits a visco-elastic response which does not depend solely on instantaneous conditions. A simple squeeze flow experiment is performed, where loading is done in two steps with a time lag $\tau \sim$ seconds between the steps. The effect on the strain, of varying $\tau$ is reproduced by a three element visco-elastic solid model. Non-linearity is introduced through a generalized calculus approach by incorporating a non-integer order time derivative in the viscosity equation. A strain hardening proportional to the time lag between the two loading steps is also incorporated. This model reproduces the three salient features observed in the experiment, namely - the memory effect, slight initial oscillations in the strain as well as the long-time solid-like response. Dynamic visco-elasticity of the sample is also reported.

Analytical solution with tanh-method and fractional sub-equation method for non-linear partial differential equations and corresponding fractional differential equation composed with Jumarie fractional derivative

Abstract: The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.