Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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Transient response of 2D functionally graded beam structure

  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Akbas, Seref D. (Deparment of Civil Engineering, Bursa Technical University)
  • Received : 2019.10.24
  • Accepted : 2020.02.21
  • Published : 2020.08.10
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Abstract

The objective of this article is investigation of dynamic response of thick multilayer functionally graded (FG) beam under generalized dynamic forces. The plane stress problem is exploited to describe the constitutive equation of thick FG beam to get realistic and accurate response. Applied dynamic forces are assumed to be sinusoidal harmonic, sinusoidal pulse or triangle in time domain and point load. Equations of motion of deep FG beam are derived based on the Hamilton principle from kinematic relations and constitutive equations of plane stress problem. The numerical finite element procedure is adopted to discretize the space domain of structure and transform partial differential equations of motion to ordinary differential equations in time domain. Numerical time integration method is used to solve the system of equations in time domain and find the time responses. Numerical parametric studies are performed to illustrate effects of force type, graduation parameter, geometrical and stacking sequence of layers on the time response of deep multilayer FG beams.

Keywords

References

  1. Abdalrahmaan, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M., and Hendi, A.A. (2019), "Free and Forced Analysis of Perforated Beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  2. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Sturct. Syst., 18(6), 1125-1143. http://dx.doi.org/10.12989/sss.2016.18.6.1125
  3. Akbas, S. D. (2017), "Forced vibration analysis of functionally graded nanobeams", J. Appl. Mech., 9(07), 1750100. https://doi.org/10.1142/S1758825117501009
  4. Akbas, S. D. (2018a), "Forced vibration analysis of cracked nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40(8), 392. https://doi.org/10.1007/s40430-018-1315-1
  5. Akbas, S. D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039
  6. Akbas, S. D. (2018c), "Investigation on Free and Forced Vibration of a Bi-Material Composite Beam", Journal of Polytechnic-Politeknik Dergisi, 21(1), 65-73.
  7. Akbas, S. D. (2019a), "Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam", J. Appl. Comput. Mech., 5(2), 477-485. https://doi.org/10.22055/JACM.2018.26819.1360
  8. Akbas, S. D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259
  9. Albino, J. C. R., Almeida, C. A., Menezes, I. F. M. and Paulino, G. H. (2018), "Co-rotational 3D beam element for nonlinear dynamic analysis of risers manufactured with functionally graded materials (FGMs)", Eng. Struct., 173, 283-299. https://doi.org/10.1016/j.engstruct.2018.05.092
  10. Almitani, K.H., Abdalrahmaan, A.A., Eltaher, M.A., (2019), "On Forced and Free Vibrations of Cutout Squared Beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643
  11. Alshorbagy, A. E., Eltaher, M. A. and Mahmoud, F. F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Modell., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  12. Andrianov, I. V., Awrejcewicz, J. and Diskovsky, A. A. (2018), "Design optimization of FGM beam in stability problem", Eng. Comput., 36(1), 248-270. https://doi.org/10.1108/EC-03-2018-0108
  13. Assie, A. E., Eltaher, M. A. and Mahmoud, F. F. (2011), "Behavior of a viscoelastic composite plates under transient load", J. Mech. Sci. Technol., 25(5), 1129. https://doi.org/10.1007/s12206-011-0302-6
  14. Attia, M. A., Eltaher, M. A., Soliman, A., Abdelrahman, A. A. and Alshorbagy, A. E. (2018), "Thermoelastic Crack Analysis in Functionally Graded Pipelines Conveying Natural Gas by an FEM", J. Appl. Mech., 10(04), 1850036. https://doi.org/10.1142/S1758825118500369
  15. Chen, Y., Jin, G., Zhang, C., Ye, T. and Xue, Y. (2018), "Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory", Compos. Part B Eng., 153, 376-386. https://doi.org/10.1016/j.compositesb.2018.08.111
  16. Doroushi, A., Eslami, M. R. and Komeili, A. (2011), "Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory", J. Intelligent Mater. Syst. Struct., 22(3), 231-243. https://doi.org/10.1177/1045389X11398162
  17. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039
  18. Eltaher, M. A., A. A. Abdelrahman, A. Al-Nabawy, M. Khater, and A. Mansour, (2014), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028
  19. Eltaher, M. A., Attia, M. A., Soliman, A. E. and Alshorbagy, A. E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097
  20. Eltaher, M. A., Abdraboh, A. M. and Almitani, K. H. (2018b), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6
  21. Eltaher, M. A., Mohamed, N., Mohamed, S. A. and Seddek, L. F. (2019a), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Math. Modell., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026
  22. Eltaher, M. A., Omar, F. A., Abdalla, W. S. and Gad, E. H. (2019b), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Waves in Random and Complex Media, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693
  23. Eltaher, M.A., Mohamed, S.A., (2020), "Buckling and Stability Analysis of Sandwich Beams subjected to Varying Axial Loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241
  24. Emam, S., Eltaher, M., Khater, M. and Abdalla, W. (2018), "Postbuckling and Free Vibration of Multilayer Imperfect Nanobeams under a Pre-Stress Load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238
  25. Esen, I. (2019), "Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass", J. Mech. Sci., 153, 21-35. https://doi.org/10.1016/j.ijmecsci.2019.01.033
  26. Hamed, M. A., Sadoun, A. M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089
  27. Hamed M.A., Mohamed, S.A., Eltaher, M.A., (2020), "Buckling Analysis of Sandwich Beam Rested on Elastic Foundation and Subjected to Varying Axial In-Plane Loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075
  28. He, X. Q., Ng, T. Y., Sivashanker, S. and Liew, K. M. (2001), "Active control of FGM plates with integrated piezoelectric sensors and actuators", J. Solids Struct., 38(9), 1641-1655. https://doi.org/10.1016/S0020-7683(00)00050-0
  29. Huang, Y., Wang, T., Zhao, Y. and Wang, P. (2018), "Effect of axially functionally graded material on whirling frequencies and critical speeds of a spinning Timoshenko beam", Compos. Struct., 192, 355-367. https://doi.org/10.1016/j.compstruct.2018.02.039
  30. Li, L., Liao, W. H., Zhang, D. and Zhang, Y. (2019), "Vibration control and analysis of a rotating flexible FGM beam with a lumped mass in temperature field", Compos. Struct., 208, 244-260. https://doi.org/10.1016/j.compstruct.2018.09.070
  31. Malekzadeh, P. and Monajjemzadeh, S.M. (2013), "Dynamic response of functionally graded plates in thermal environment under moving load", Compos. Part B Eng., 45(1), 1521-1533. https://doi.org/10.1016/j.compositesb.2012.09.022
  32. Malekzadeh, P. and Monajjemzadeh, S. M. (2015), "Nonlinear response of functionally graded plates under moving load", Thin-Wall. Struct., 96, 120-129. https://doi.org/10.1016/j.tws.2015.07.017
  33. Mohamed, N., Eltaher, M.A., Mohamed, S. and Seddek, L.F. (2019), "Energy Equivalent Model in Analysis of Postbuckling of Imperfect Carbon Nanotubes Resting on Nonlinear Elastic Foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737
  34. Rajasekaran, S. and Khaniki, H. B. (2019), "Size-dependent forced vibration of non-uniform bi-directional functionally graded beams embedded in variable elastic environment carrying a moving harmonic mass", Appl. Math. Modell., 72, 129-154. https://doi.org/10.1016/j.apm.2019.03.021
  35. Shooshtari, A. and Rafiee, M. (2011), "Nonlinear forced vibration analysis of clamped functionally graded beams", Acta Mechanica, 221(1-2), 23. https://doi.org/10.1007/s00707-011-0491-1
  36. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  37. Simsek, M. (2010), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  38. Su, Z., Jin, G. and Ye, T. (2016), "Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions", Smart Mater. Struct., 25(6), 065003. https://doi.org/10.1088/0964-1726/25/6/065003
  39. Wang, Y. and Wu, D. (2016), "Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load", Acta Astronautica, 127, 171-181. https://doi.org/10.1016/j.actaastro.2016.05.030
  40. Wang, Y., Xie, K., Fu, T. and Shi, C. (2019), "Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses", Compos. Struct., 209, 928-939. https://doi.org/10.1016/j.compstruct.2018.11.014
  41. Xiang, H. J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Compos. Part B Eng., 39(2), 292-303. https://doi.org/10.1016/j.compositesb.2007.01.005
  42. Yang, J., Chen, Y., Xiang, Y. and Jia, X. L. (2008), "Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load", J. Sound Vib., 312(1-2), 166-181. https://doi.org/10.1016/j.jsv.2007.10.034

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