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Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions

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  • Silambarasan, Rathinavel
  • Baskonus, Haci Mehmet
  • Vijay Anand, R.
  • Dinakaran, M.
  • Balusamy, Balamurugan
  • Gao, Wei

Abstract

The axisymmetric longitudinal waves propagating in the long infinite cylindrical rod composed of material and structural constants, combinedly called as general incompressible materials, are derived using the perturbation reduction method as the far-field equation in the form of KdV equation in Dai and Huo (2002). In this work, the F expansion method is applied to the far-field equation and the properties of longitudinal strain waves travelling in the cylindrical rod are studied. The behaviour of the strain waves is analysed with the material and structural constants. To support the study, the graphs are drawn in the two and three dimensional surfaces. The obtained longitudinal strain waves are in the form of Jacobi elliptic function and necessary condition for the existence of each wave is provided.

Suggested Citation

  • Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Vijay Anand, R. & Dinakaran, M. & Balusamy, Balamurugan & Gao, Wei, 2021. "Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 566-602.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:566-602
    DOI: 10.1016/j.matcom.2020.11.011
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    References listed on IDEAS

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    1. Gao, Wei & Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Anand, R. Vijay & Rezazadeh, Hadi, 2020. "Periodic waves of the non dissipative double dispersive micro strain wave in the micro structured solids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Vitanov, Kaloyan N., 2015. "Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 363-378.
    4. Çulha Ünal, Sevil & Daşcıoğlu, Ayşegül & Varol Bayram, Dilek, 2020. "New exact solutions of space and time fractional modified Kawahara equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
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    1. Silambarasan, Rathinavel & Nisar, Kottakkaran Sooppy, 2023. "Doubly periodic solutions and non-topological solitons of 2+1− dimension Wazwaz Kaur Boussinesq equation employing Jacobi elliptic function method," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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