Multi objective optimization of the vibration analysis of composite natural gas pipelines in nonlinear thermal and humidity environment under non-uniform magnetic field

Document Type : Research Paper

Authors

1 Department of Mechanical, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

2 Department of Mechanical engineering, Abadan Branch, Islamic Azad University, Abadan , Iran

3 Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

The fluid-conveying pipe is a fundamental dynamical problem in the field of fluid– structure interactions. In recent years considerable attention has been given to the lateral vibrations of pipes containing by a moving fluid. In this paper, the vibration analysis of composite natural gas pipeline in the thermal and humidity environment is studied. The effect of the non-uniform magnetic field is investigated. By applying the Hamilton’s principle, the equation of motion is derived for the pipe with the effects of both linear and non-linear stress temperature cases. The differential quadrature method (DQM) has been utilized in computing the results for the pipe conveying fluid. The Bees algorithm and Genetic algorithm NSGA II for multi-objective optimization of a pipe model are used. Sample results are presented for several cases with varying values of the system parameter. Results are demonstrated for the dependence of natural frequencies on the flow velocity as well as temperature change and humidity percent. The influence of temperature change on the critical flow velocity at which buckling instability occurs is investigated. It is concluded that the effect of temperature change on the instability of conveyed fluid pipe is significant.

Keywords

Main Subjects

[1]          M. H. Ghayesh, M. Amabili, Post-buckling bifurcations and stability of high-speed axially moving beams, International Journal of Mechanical Sciences, Vol. 68, pp. 76-91, 2013.
[2]          A. Arani, M. Maboudi, A. G. Arani, S. Amir, 2D-magnetic field and biaxiall in-plane pre-load effects on the vibration of double bonded orthotropic graphene sheets, J Solid Mech, Vol. 5, No. 2, pp. 193-205, 2013.
[3]          S. Narendar, S. Gupta, S. Gopalakrishnan, Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modelling, Vol. 36, No. 9, pp. 4529-4538, 2012.
[4]          K. Bubke, H. Gnewuch, M. Hempstead, J. Hammer, M. L. Green, Optical anisotropy of dispersed carbon nanotubes induced by an electric field, Applied physics letters, Vol. 71, No. 14, pp. 1906-1908, 1997.
[5]          X. Liu, J. L. Spencer, A. B. Kaiser, W. M. Arnold, Electric-field oriented carbon nanotubes in different dielectric solvents, Current Applied Physics, Vol. 4, No. 2, pp. 125-128, 2004.
[6]          E. Camponeschi, R. Vance, M. Al-Haik, H. Garmestani, R. Tannenbaum, Properties of carbon nanotube–polymer composites aligned in a magnetic field, Carbon, Vol. 45, No. 10, pp. 2037-2046, 2007.
[7]          P. Lu, L. He, H. Lee, C. Lu, Thin plate theory including surface effects, International Journal of Solids and Structures, Vol. 43, No. 16, pp. 4631-4647, 2006.
[8]          K. Kiani, Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models, Physica E: Low-dimensional Systems and Nanostructures, Vol. 45, pp. 86-96, 2012.
[9]          T. Murmu, M. McCarthy, S. Adhikari, In-plane magnetic field affected transverse vibration of embedded single-layer graphene sheets using equivalent nonlocal elasticity approach, Composite Structures, Vol. 96, pp. 57-63, 2013.
[10]        K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, in Proceeding of, Springer, pp. 849-858.
[11]        D. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim, M. Zaidi, The bees algorithm-A novel tool for complex optimisation, in Proceeding of, sn, pp.
[12]        D. Pham, A. Ghanbarzadeh, Multi-objective optimisation using the bees algorithm, in Proceeding of.
[13]        G. Zou, N. Cheraghi, F. Taheri, Fluid-induced vibration of composite natural gas pipelines, International journal of solids and structures, Vol. 42, No. 3, pp. 1253-1268, 2005.
[14]        T. Je¸ kot, Nonlinear problems of thermal postbuckling of a beam, Journal of Thermal Stresses, Vol. 19, No. 4, pp. 359-367, 1996.
[15]        M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.
[16]        M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, 2012.
[17]        M. Mohammadi, A. Farajpour, M. Goodarzi, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014.
[18]        H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.
[19]        S. Asemi, A. Farajpour, H. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[20]        M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, No. 4, pp. 659-682, 2014.
[21]        M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.
[22]        M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version differential quadrature method, Journal of solid mechanics in engineering, Vol. 3, No. 2, pp. 47-56, 2011.
[23]        M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, Journal of Solid Mechanics, Vol. 7, No. 3, pp. 299-311, 2015.
[24]        A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, No. 7, pp. 1849-1867, 2016.
[25]        M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, No. 8, pp. 2207-2232, 2016.
[26]        M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.
[27]        S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.
[28]        M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature effect on vibration analysis of annular graphene sheet embedded on visco-pasternak foundation, J. Solid Mech, Vol. 5, pp. 305-323, 2013.
[29]        M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-Mechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the Visco-Pasternak Foundation, Journal of Solid Mechanics Vol, Vol. 8, No. 4, pp. 788-805, 2016.
[30]        M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[31]        A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, 2017.
[32]        J. D. Schaffer, Multiple objective optimization with vector evaluated genetic algorithms, in Proceeding of, LawrenceErlbaumAssociates, Inc., Publishers, pp.
[33]        C. M. Fonseca, P. J. Fleming, Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization, in Proceeding of, Citeseer, pp. 416-423.
[34]        J. Horn, N. Nafpliotis, D. E. Goldberg, A niched Pareto genetic algorithm for multiobjective optimization, in Proceeding of, Ieee, pp. 82-87.
[35]        J. Knowles, D. Corne, The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation, in Proceeding of, IEEE, pp. 98-105.
[36]        E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach, IEEE transactions on Evolutionary Computation, Vol. 3, No. 4, pp. 257-271, 1999.
[37]        K. Deb, J. Sundar, Reference point based multi-objective optimization using evolutionary algorithms, in Proceeding of, ACM, pp. 635-642.
[38]        Moradi A, Shirazi KH, Keshavarz M, Falehi AD, Moradi M. Smart piezoelectric patch in non-linear beam: design, vibration control and optimal location. Transactions of the Institute of Measurement and Control. 2014 Feb;36(1):131-44.
Volume 48, Issue 1
June 2017
Pages 53-64
  • Receive Date: 08 May 2017
  • Revise Date: 09 June 2017
  • Accept Date: 15 June 2017