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  • Open Access


    Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

    Dumitru Baleanu1,2, Behzad Ghanbari3, Jihad H. Asad4,*, Amin Jajarmi5, Hassan Mohammadi Pirouz5

    CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 953-968, 2020, DOI:10.32604/cmes.2020.010236

    Abstract In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative. More >

  • Open Access


    An Atomistic Study of Elliptic Cross-Sectional Nanosprings

    I-L. Chang1, M.-S. Yeh1

    CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 95-106, 2009, DOI:10.3970/cmes.2009.041.095

    Abstract One-dimensional copper nanospring with elliptic cross section was studied using molecular statics method based on minimum energy consideration. Various geometric sizes (wire semi-axis length, radius, pitch) and crystal orientations of nanosprings were systematically modeled to investigate the size dependence of elastic properties for both normal and binormal nanosprings. It was observed that as the wire semi-axis increases, and the radius and pitch decrease, the nanospring stiffness would increase irrespective to the crystal orientations. Moreover, it was noticed that the normal nanosprings always behave stiffer than the binormal ones for the same radius, pitch and cross-sectional geometry in our study. More >

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