Natural frequency of Sandwich Beam Structures with Two Dimensional Functionally Graded Porous Layers Based on Novel Formulations

Document Type : Original Article

Authors

Department of Mechanical Engineering, Arak University, Arak, Iran

Abstract

This study presents an analytical solution for free vibration analysis of two-dimensional functionally graded (2D-FG) porous sandwich beams. The equations of motion for the beam were derived using Hamilton's principle, and then the Galerkin method was employed to solve the equations. The material properties of the sandwich beams vary with the thickness and length of each layer according to the power-law function. The mechanical properties gradually changed from aluminum to alumina as the metal and ceramic, respectively. The vibration analysis was investigated based on two new higher-order shear deformation beam theories (NHSDBTs). These two new theories do not need any shear correction factor and have fewer unknown variables than other higher order shear beam theories.  The obtained natural frequencies for the three types of beams were compared with the results of the Timoshenko, first-order , and parabolic shear deformation beam theories. In addition, the effects of porosity, L/h, and FG power indexes along the thickness and length on the non-dimensional frequency of three special types of beams are presented and discussed. Furthermore, the mode shapes of the beam are depicted for various FG power indexes based on these new theories. By comparing the results of the two proposed theories with those of existing studies, the accuracy of the proposed theories was validated. Power-law indexes shifted the node point to the left and resonance will be accrued sooner than the non-FGM beam.

Keywords

Main Subjects

References

  1. Bakhshi Khaniki, H., Hosseini Hashemi, S. and Bakhshi Khaniki, H., "Free vibration analysis of functionally graded materials non-uniform beams", International Journal of Engineering, Transactions C: Aspects, Vol. 29, No. 12, (2016), 1734-1740. doi: 10.5829/idosi.ije.2016.29.12c.12.
  2. Sherafatnia, K., Farrahi, G.H. and Faghidian, S.A., "Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories", International Journal of Engineering, Transactions C: Aspects, Vol. 27, No. 6, (2014), 979-990. doi: 10.5829/idosi.ije.2014.27.06c.17.
  3. El Khouddar, Y., Adri, A., Outassafte, O., Rifai, S. and Benamer, R., "Non-linear forced vibration analysis of piezoelectric functionally graded beams in thermal environment", International Journal of Engineering, Transactions B: Applications, Vol. 34, No. 11, (2021), 2387-2397. doi: 10.5829/ije.2021.34.11b.02.
  4. Amoozgar, M. and Gelman, L., "Vibration analysis of rotating porous functionally graded material beams using exact formulation", Journal of Vibration and Control, (2019), 10775463211027883. doi: 10.1177/10775463211027883.
  5. Hadji, L., Bernard, F., Safa, A. and Tounsi, A., "Bending and free vibration analysis for fgm plates containing various distribution shape of porosity", Advances in Materials Research, Vol. 10, No. 2, (2021), 115-135. doi: 10.12989/AMR.2021.10.2.115.
  6. Celebi, K., Yarimpabuc, D. and Tutuncu, N., "Free vibration analysis of functionally graded beams using complementary functions method", Archive of Applied Mechanics, Vol. 88, No. 5, (2018), 729-739. doi: 10.1007/s00419-017-1338-6.
  7. Lei, J., He, Y., bo, Z., Gan, Z. and Zeng, P., "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", International Journal of Engineering Science, Vol. 72, (2013), 36–52. doi: 10.1016/j.ijengsci.2013.06.012.
  8. Ke, L.-L., Yang, J. and Kitipornchai, S., "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Composite Structures, Vol. 92, (2010), 676-683. doi: 10.1016/j.compstruct.2009.09.024.
  9. Mashat, D.S., Carrera, E., Zenkour, A.M., Al Khateeb, S.A. and Filippi, M., "Free vibration of fgm layered beams by various theories and finite elements", Composites Part B: Engineering, Vol. 59, (2014), 269-278. doi: 10.1016/j.compositesb.2013.12.008.
  10. Faghidian, S.A., "Flexure mechanics of nonlocal modified gradient nano-beams", Journal of Computational Design and Engineering, Vol. 8, No. 3, (2021), 949-959. doi: 10.1093/jcde/qwab027.
  11. Faghidian, S.A., Żur, K.K. and Reddy, J.N., "A mixed variational framework for higher-order unified gradient elasticity", International Journal of Engineering Science, Vol. 170, (2022), 103603. doi: 10.1016/j.ijengsci.2021.103603.
  12. Faghidian, S.A., "Higher order mixture nonlocal gradient theory of wave propagation", Mathematical Methods in the Applied Sciences, (2020). doi: 10.1002/mma.6885.
  13. Faghidian, S.A., "Two-phase local/nonlocal gradient mechanics of elastic torsion", Mathematical Methods in the Applied Sciences, Vol. n/a, No. n/a, (2020). doi: 10.1002/mma.6877.
  14. Shahba, A. and Rajasekaran, S., "Free vibration and stability of tapered euler–bernoulli beams made of axially functionally graded materials", Applied Mathematical Modelling, Vol. 36, No. 7, (2012), 3094-3111. doi: 10.1016/j.apm.2011.09.073.
  15. Wang, Y., Xie, K.-j., Fu, T. and Shi, C., "Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses", Composite Structures, (2019). doi: 10.1016/j.compstruct.2018.11.014.
  16. Xu, J., Yang, Z., Yang, J. and Li, Y., "Free vibration analysis of rotating fg-cnt reinforced composite beams in thermal environments with general boundary conditions", Aerospace Science and Technology, Vol. 118, (2021), 107030. doi: 10.1016/j.ast.2021.107030.
  17. Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M., "Vibration of two-dimensional imperfect functionally graded (2d-fg) porous nano-/micro-beams", Computer Methods in Applied Mechanics and Engineering, Vol. 322, (2017), 615-632. doi: 10.1016/j.cma.2017.05.007.
  18. Kandil, M., Abdelraheem, A., Mahdy, M. and Tahwia, A., "Effect of changing properties of wythes in precast structural sandwich panels", Civil Engineering Journal, Vol. 6, (2020), 1765-1778. doi: 10.28991/cej-2020-03091581.
  19. Singh, V. and Sangle, K., "Analysis of vertically oriented coupled shear wall interconnected with coupling beams", HighTech and Innovation Journal, Vol. 3, No. 2, (2022), 230-242. doi: 10.28991/HIJ-2022-03-02-010.
  20. Mirjavadi, S.S., Mohasel Afshari, B., Shafiei, N., Rabby, S. and Kazemi, M., "Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale timoshenko beam", Journal of Vibration and Control, Vol. 24, No. 18, (2018), 4211-4225. doi: 10.1177/1077546317721871.
  21. Şimşek, M., "Buckling of timoshenko beams composed of two-dimensional functionally graded material (2d-fgm) having different boundary conditions", Composite Structures, Vol. 149, (2016), 304-314. doi: 10.1016/j.compstruct.2016.04.034.
  22. Timoshenko, S.P., "X. On the transverse vibrations of bars of uniform cross-section", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 43, No. 253, (1922), 125-131. doi: 10.1080/14786442208633855.
  23. Aydogdu, M. and Taskin, V., "Free vibration analysis of functionally graded beams with simply supported edges", Materials & Design, Vol. 28, No. 5, (2007), 1651-1656. doi: 10.1016/j.matdes.2006.02.007.
  24. Simsek, M., "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Engineering and Design, Vol. 240, (2010), 697-705. doi: 10.1016/j.nucengdes.2009.12.013.
  25. Elmeiche, A., Megueni, A. and Lousdad, A., "Free vibration analysis of functionally graded nanobeams based on different order beam theories using ritz method", Periodica Polytechnica Mechanical Engineering, Vol. 60, No. 4, (2016), 209-219. doi: 10.3311/PPme.8707.
  26. Khorshidi, K. and Shabani, Y., "Free vibration analysis of sandwich plates with magnetorheological smart fluid core by using modified shear deformation theory", Journal of Science and Technology of Composites, (2022), doi: 10.22068/jstc.2022.552957.1782.
  27. Khorshidi, K., Taheri, M. and Ghasemi, M., "Sensitivity analysis of vibrating laminated composite rec-tangular plates in interaction with inviscid fluid using efast method", Mechanics of Advanced Composite Structures‎, Vol. 7, No. 2, (2020), 219-231. doi: 10.22075/macs.2020.18605.1224.
  28. Khorshidi, K. and Karimi, M., "Analytical approach for thermo-electro-mechanical vibration of piezoelectric nanoplates resting on elastic foundations based on nonlocal theory", Mechanics of Advanced Composite Structures‎, Vol. 6, No. 2, (2019), 117-129. doi: 10.22075/macs.2019.15518.1156.
  29. Ghayesh, M.H., Amabili, M. and Farokhi, H., "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", International Journal of Engineering Science, Vol. 63,  (2013), 52-60. doi: 10.1016/j.ijengsci.2012.12.001.
  30. Shabani, Y. and Khorshidi, K., "Free vibration analysis of rectangular doubly curved auxetic-core sandwich panels integrated with cnt-reinforced composite layers using galerkin method", Journal of Science and Technology of Composites, Vol. 8, No. 3, (2022), 1686-1677. doi:  10.22068/jstc.2022.545477.1762.
  31. Khorshidi, K. and Fallah, A., "Free vibration analysis of size-dependent, functionally graded, rectangular nano/micro-plates based on modified nonlinear couple stress shear deformation plate theories", Mechanics of Advanced Composite Structures, Vol. 4, No. 2, (2017), doi: 10.22075/MACS.2017.1800.1094.
  32. Mohamed, B., Elmeiche, A., Elhennani, A., Kebir, T., El, Z. and zine el abidine, H., "Exact solution for free vibration analysis of fgm beams", Revue des Composites et des Matériaux Avancés, Vol. 30, (2020). doi: 10.18280/rcma.300201.
  33. Reddy, J.N. and Robbins, D.H., Jr, "Theories and computational models for composite laminates", Applied Mechanics Reviews, Vol. 47, No. 6, (1994), 147-169. doi: 10.1115/1.3111076.
International Journal of Engineering
Volume 35, Issue 11
TRANSACTIONS B: Applications
November 2022
Pages 2092-2101

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