Nonlinear dynamic analysis of axially moving porous FG plate subjected to local force with kinetic dynamic relaxation method

Nonlinear dynamic analysis of axially moving porous FG plate subjected to local force with kinetic dynamic relaxation method

Mostafa Esmaeilzadeh1, Mehran Kadkhodayan2

1Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

2Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.



In some engineering applications like moving ships and production of paper and textiles the axially moving structures have to be investigated. In this paper, the nonlinear response and stability of axially moving porous FGM plate under local concentrated load are studied. The plate is made of materials which properties are assumed to be graded in thickness direction. To take the effect of porosity into account, the modified rule of mixture is chosen to calculate the effective material properties. The kinetic dynamic relaxation method along with the implicit Newmark integration are used to solve the nonlinear dynamic equations. Finally, the effect of material gradient index, porosity volume fraction and boundary conditions on dynamic deflection and instability of plate are discussed.   

Cite as:

Esmaeilzadeh , M., Kadkhodayan, M. (2018). Nonlinear dynamic analysis of axially moving porous FG plate subjected to local force with kinetic dynamic relaxation method. Computer Methods in Materials Science, 18(1), 18 – 28.

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Akay, H., 1979, Dynamic large deflection analysis of platesusing mixed finite elements, Comput. Struct., 11, 1-11.

Alamatian, J., 2012, A new formulation for fictitious massof the dynamic relxation method with kinetic damping,Comput. Struct, 90-91, 42-54.

Alic, V., Persson, K., 2016, Form finding with dynamicrelaxation and isogeometric membrane, Comput.Methods Appl. Mech. Engrg., 300, 734-747.

Atmane, H., Tounsi, A., Bernard, F., 2015, Effect of thicknessstretching and porosity on mechanical responseof a functionally graded beams resting on elasticfoundations, Int. J. Mech. Mater. Des., 1-14.

Banichuk, N., Jeronen, J., Neittaanmaki, P., Tuovinen, T.,2010, On the instability of an axially moving elasticplate, Int. J. Solids Struct., 47, 91-99.

Biot, M., 1964, Theory of buckling of a porous slab and itsthermoelastic analogy, J. Appl. Mech., 31, 194-198.

Chen, A., Jian, S., 2011, Dynamic response of clampedaxially moving beam: integral transform, Appl. Math.Comput., 218, 249-256.

Chen, D., Yang, J., Kitipornchai, S., 2015, Elastic bucklingand static bending of shear deformable functionallygraded porous beam, Compos. Struct., 133, 54-61.

Chen, L.-Q., Yang, X.-D., 2007, Nonlinear free transversevibration of an axially moving beam: comparison oftwo models, J. Sound. Vib., 299, 348-354.

Clough, R., J.Penzien, 1993, Dynamic of Structures, s.l.:McGraw-Hill.Ebrahimi, F., Ghasemi, A., Salari, E., 2016, Investigatingthermal effects on vibration behavior of temperaturedependentcompositionally graded euler beams withporosities, Meccanica, 51, 223-249.

Ebrahimi, F., Zia, M., 2015, Large amplitude nonlinearvibration analysis of functionally graded Timoshenkobeams with porosities, Acta Astronaut., 116, 117-125.

Eftekhari, S., 2014, A Differential quadrature procedurewith regularization of dirac – delta – function for numericalsolution of moving load problem, Lat. Am. J.Solids Struct., 12, 1241-1265.

Fallah, A., Aghdam, M., 2012, Thermo-mechanical bucklingand nonlinear free vibration analysis of functionallygraded beams on nonlinear elastic foundation,Compos B., 43, 1523-1530.

Golmakani, M., Kadkhodayan, M., 2013, Large deflectionthermoelastic analysis of functionally graded stiffenedannular sector plates, Int. J. Mech. Sci., 69, 94-106.

Hatami, S., Ronagh, H., Azhari, M., 2008, Exact free vibrationanalysis of axially moving viscoelastic plates,Comput. Struct., 86, 1738–1746.

Ishak, A., Azizah Yacob, N., Bachok, N., 2011, Radiationeffects on the thermal boundary layer flow over amoving plate with convective boundary condition,Meccanica, 46, 795–801.

Jabbari, M., Joubaneh, E., Khorshidvand, A., Eslami, M.,2013, Buckling analysis of porous circular plate withpiezoelectric actuator layers under uniform radialcompression, Int. J. Mech. Sci., 70, 50-56.

Joubaneh, E., Mojahedin, A., Khorshidvand, A., Jabbari,M., 2014, Thermal buckling analysis of porous circularplate with piezoelectric sensor–actuator layers underuniform thermal load, J. Sandwich. Struct. Mater.,17, 3-25.

Kieback, B., Neubrand, A., Riedel, A., 2003, Processingtechniques for functionally graded materials, Mater.Sci. Eng., A, 362, 81-106.

Lee, K. S., Han, S. E., Park, T., 2011, A simple explicit arclengthmethod using the dynamic relaxation method,Comput. Struct., 89, 216-233.

Marynowski, K., and Kapitaniak, T., 2002, Kelvin-Voigtversus Burgers internal damping in modeling of axiallymoving viscoelastic web, Int. J. Non-Linear Mech.,37, 1147-1161.

Rezaiee-Pajand, M., Alamatian, J., 2008, Nonlinear dynamicanalysis by dynamic relaxation method, J.Struct. Eng. Mech., 28, 549-570.

Shin, C., Chung, J., Kim, W., 2005, Dynamic characteristicsof the out-of-plane vibration for an axially movingmembrane, J. Sound Vib., 286, 1019-1031.

Swope, R., Ames, W., 1963, Vibration of moving threadline,J. Franklin Inst., 275, 36-55.

Taheri, M., Ting, E., 1989, Dynamic response of plate tomoving loads: structural impedance method, Comp.Struct., 33, 1379-1390.

Topping, B., Ivanyi, P., 2007, Computer aided design ofcable-membrane structures, s.l.: Saxe-Coburg Publicationson Computational Engineering.Ulsoy, A, Mote Jr., C., 1982, Vibrations of wide band saw blades, ASME, 104, 71-78.

Wang, Y.Q., Zu, J.W., 2017, Vibration characteristics of moving sigmoid functionally graded plates containing porosities, Int. J. Mech. Mater. Des., 1-17.

Wattanasakulpong, N., Gangadhara Prusty, B., Kelly, D.W., Hoffman, M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Mater. Des. 36, 182-190.

Wattanasakulpong, N., Chaikittiratana, A., 2015, Flexural Vibration of imperfect functionally graded beams based on timoshenko beam theory: Chebyshev collo-cation method, Meccanica, 50, 1331-1342.

Wattanasakulpong, N., Ungbhakorn, V., 2014, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerosp. Sci. Tech., 1, 111-120.

Yang, X., Zhang, W., Chen, L., Yao, M., 2012, Dynamical analysis of axially moving plate by finite difference method, Nonlinear Dyn., 67, 997-1006.

Yao, G., Zhang, Y.-M., 2016, Dynamics and stability of an axially moving plate interacting with surrounding air-flow, Meccanica, 51, 2111-2119.