Contact

Phone: 470-578-4992

Email: smashay1@kennesaw.edu

Office Location: MS 242

Office Hours:
TR 8:30 AM - 9:30 AM

Journal Papers

  • 2017 - 2018
    • Fractional Viscoelasticity in Fractal Media: Theory, Experimental Validation, and Uncertainty Analysis
               S.Mashayekhi,P.Miles, M.Yousuff Hussaini and W.Oates
               Journal of the Mechanics and Physics of Solids,Volume 111, February 2018, Pages 134-156
    • In this paper, fractional and non-fractional viscoelastic models for elastomeric materials......
      Abstract
      In this paper, fractional and non-fractional viscoelastic models for elastomeric materials are derived and analyzed in comparison to experimental results. The viscoelastic models are derived by expanding thermodynamic balance equations for both fractal and non-fractal media. The order of the fractional time derivative is shown to strongly affect the accuracy of the viscoelastic constitutive predictions. Model validation uses experimental data describing viscoelasticity of the dielectric elastomer Very High Bond (VHB) 4910. Since these materials are known for their broad applications in smart structures, it is important to characterize and accurately predict their behavior across a large range of time scales. Whereas integer order viscoelastic models can yield reasonable agreement with data, the model parameters often lack robustness in prediction at different deformation rates. Alternatively, fractional order models of viscoelasticity provide an alternative framework to more accurately quantify complex rate-dependent behavior. Prior research that has considered fractional order viscoelasticity lacks experimental validation and contains limited links between viscoelastic theory and fractional order derivatives. To address these issues, we use fractional order operators to experimentally validate fractional and non-fractional viscoelastic models in elastomeric solids using Bayesian uncertainty quantification. The fractional order model is found to be advantageous as predictions are significantly more accurate than integer order viscoelastic models for deformation rates spanning four orders of magnitude.
    • Population divergence estimation using individual lineage label switching
              P. Beerli,S. Mashayekhi,H. Ashki, , and M. Palczewski
              https://www.biorxiv.org/content/10.1101/587832v1.abstract
    • Divergence time estimation from multilocus genetic data has become......
      Abstract
      Divergence time estimation from multilocus genetic data has become common in population genetics and phylogenetics. We present a new Bayes inference method that treats the divergence time as a random variable. The divergence time is calculated from an assembly of splitting events on individual lineages in a genealogy. The waiting time for such a splitting event is drawn from a hazard function of the truncated normal distribution. This allows easy integration into the standard coalescence framework used in programs such as MIGRATE. We explore the accuracy of the new inference method with simulated population splittings over a wide range of divergence time values and with a dataset of the Zika virus; the geographic analyses of the expansion of the pathogen follows a trajectory from Africa to Asia to America, corroborating analyses based only on the dates of incidences. Evaluations of simple divergence models show high accuracy, whereas the accuracy of the results of isolation with migration (IM) models depend on the magnitude of the immigration rate and potentially on the number of samples. High immigration rates lead to a time of the most recent common ancestor of the sample that predates the divergence time, thus loses any potential signal of the divergence event in the sample data. This reduced accuracy with high immigration rates is problematic for all IM methods, including ours.
    •  Numerical solutions of fractional differential equations by using fractional Taylor basis
                V.S. Krishnasamy, S. Mashayekhi, M.Razzaghi
                IEEE/CAA Journal of Automatica Sinica,Volume: 4 , Issue: 1 ,Jan.2017
    • In this paper, a new numerical method for solving fractional......
      Abstract
      In this paper, a new numerical method for solving fractional differential equations (FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.

     

  • 2015 - 2016
    • An approximate method for solving fractional optimal control problems by hybrid functions
              S. Mashayekhi, M.Razzaghi
              Journal of Vibration and Control,Volume 24,Issue 9,August 2016 , Pages 1621-1631
    • In this paper, a new numerical method for solving fractional optimal control......
      Abstract
      In this paper, a new numerical method for solving fractional optimal control problems by using hybrid functions is presented. The Riemann–Liouville fractional integral operator for hybrid functions is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. The method is computationally very attractive and gives very accurate results.
    • Numerical solution of distributed order fractional differential equations by hybrid functions
              S. Mashayekhi, M.Razzaghi
             Journal of Computational Physics, Volume 315, June 2016, Pages 169-181
    • In this paper, a new numerical method for solving the Duffing equation......
      Abstract 
      In this paper, a new numerical method for solving the Duffing equation is presented. We consider this equation in two forms, with integral boundary conditions and involving both integral and non-integral forcing terms. The method is based on a hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is given. This matrix is then utilized to reduce the solution of the Duffing equation to a nonlinear equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.


    • In this paper, a new numerical method for solving the distributed fractional differential......
      Abstract
      In this paper, a new numerical method for solving the distributed fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann–Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the distributed fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
    • Numerical solution of the fractional Bagley‐Torvik equation by using hybrid functions approximation
          S. Mashayekhi, M.Razzaghi
        Journal of Mathematical Methods in the Applied Sciences, Volume39, Issue3,February 2016,Pages 353-365
    • In this paper, a new numerical method for solving the fractional Bagley‐Torvik......
      Abstract
      In this paper, a new numerical method for solving the fractional Bagley‐Torvik equation is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block‐pulse functions and Bernoulli polynomials are presented. The Riemann‐Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the initial and boundary value problems for the fractional Bagley‐Torvik differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
    • Solution of Lane–Emden type equations using rational Bernoulli functions
              Velinda Calvert,S. Mashayekhi, M.Razzaghi
              Journal of Differential Equations and Dynamical Systems, Volume24, Issue1,January 2016,Pages 1-20
    • In this paper, a new numerical method for solving multi-delay and piecewise......
      Abstract
      In this paper, a new numerical method for solving multi-delay and piecewise constant delay systems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration, product and delay are given. These matrices are then utilized to reduce the solution of multi-delay systems and the piecewise constant delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
    • Numerical solution of nonlinear fractional integro-differential equations by hybrid functions
              S. Mashayekhi, M.Razzaghi
            Journal of Engineering Analysis with Boundary Elements, Volume 56, July 2015, Pages 81-89
    • In this paper, a new numerical method for solving the optimal control of......
      Abstract
      In this paper, a new numerical method for solving the optimal control of a class of systems described by integro-differential equations with quadratic performance index is presented. This optimization problem plays an important role in describing the dynamics of an elastic aircraft with allowance for non-steady flow past its profile. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the solution of optimization problem to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.
  • 2013 - 2014
    • Hybrid functions approach for optimal control of systems described by integro-differential equations
               S. Mashayekhi, Y Ordokhani, M Razzaghi
              Journal of Applied Mathematical Modelling, Volume 37,Issue 5, March 2013, Pages 3355-3368
    • In this paper, a new numerical method for solving the optimal control of......
      Abstract
      In this paper, a new numerical method for solving the optimal control of a class of systems described by integro-differential equations with quadratic performance index is presented. This optimization problem plays an important role in describing the dynamics of an elastic aircraft with allowance for non-steady flow past its profile. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the solution of optimization problem to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.
    • A hybrid functions approach for the Duffing equation
              S. Mashayekhi, Y Ordokhani, M Razzaghi
             Journal of Physica Scripta, Volume 88,Issue 2,July 2013, 025002
    • In this paper, a new numerical method for solving the Duffing equation......
      Abstract
      In this paper, a new numerical method for solving the Duffing equation is presented. We consider this equation in two forms, with integral boundary conditions and involving both integral and non-integral forcing terms. The method is based on a hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is given. This matrix is then utilized to reduce the solution of the Duffing equation to a nonlinear equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.


  • 2012
    • Hybrid functions approach for nonlinear constrained optimal control problems
               S. Mashayekhi, Y Ordokhani, M Razzaghi
              Journal of Communications in Nonlinear Science and Numerical Simulation, Volume 17,Issue 4 , April 2012, Pages 1831-1843
    • In this paper, a new numerical method for solving the nonlinear constrained optimal control......
      Abstract 
      In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is introduced. This matrix is then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.


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