DOI QR코드

DOI QR Code

Vibro-acoustics of functionally graded porous beams subjected to thermo-mechanical loads

  • Chinnapandi, Lenin Babu Mailan (ESchool of Mechanical Engineering, Vellore Institute of Technology) ;
  • Pitchaimani, Jeyaraj (Advanced Dynamics Lab, Department of Mechanical Engineering, National Institute of Technology Karnataka) ;
  • Eltaher, Mohamed A. (Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University)
  • Received : 2021.11.15
  • Accepted : 2022.11.20
  • Published : 2022.09.25

Abstract

This manuscript work presents a comprehensive continuum model capable to investigate the effect of porosity on vibro-acoustic behaviour of functionally graded (FG) beams resting on an elastic foundation subjected to thermal and mechanical loadings. Effects of uniform temperature rise and edge compressive load on the sound radiation characteristics are studied in a comparative manner. The numerical analysis is carried out by combining finite element method with Rayleigh's integral. Detailed parametric studies are accomplished, and influences of power law index, porosity volume, porosity distribution and boundary conditions on the vibro-acoustic response characteristics are analyzed. It is found that the vibro-acoustic response under mechanical edge compression is entirely different compared to from that under the thermal load. Furthermore, nature of grading of porosity affects the sound radiation behaviour for both the loads. The proposed model can be used to obtain the suppression performance of vibration and noise FG porous beams under thermal and mechanical loads.

Keywords

References

  1. Abo-bakr, H.M., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M. A. (2021a), "Multi-objective shape optimization for axially functionally graded microbeams", Compos. Struct., 258, 113370. https://doi.org/10.1016/j.compstruct.2020.113370.
  2. Abo-Bakr, R.M., Abo-Bakr, H.M., Mohamed, S.A. and Eltaher, M.A. (2021b), "Optimal weight for buckling of FG beam under variable axial load using Pareto optimality", Compos. Struct., 258, 113193. https://doi.org/10.1016/j.compstruct.2020.113193.
  3. Akbas, S.D. (2015), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107.
  4. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. https://doi.org/10.1177/1077546320947302.
  5. Akbas, S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load", Eng. Comput., 1-13. https://doi.org/10.1007/s00366-020-01070-3.
  6. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021b), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. http://dx.doi.org/10.12989/gae.2021.24.1.091.
  7. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A.E. (2021a), "Damped forced vibration analysis of layered functionally graded thick beams with porosity", Smart Struct. Syst., 27(4), 679-689. https://doi.org/10.12989/sss.2021.27.4.679.
  8. Alshabatat, N.T. and Naghshineh, K. (2014), "Optimization of natural frequencies and sound power of beams using functionally graded material", Adv. Acoustic. Vib., 2014. http://dx.doi.org/10.1155/2014/752361.
  9. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Mathem. Modelling, 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006.
  10. Aragh, B.S., Hedayati, H., Farahani, E.B. and Hedayati, M. (2011), "A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels", Europ. J. Mech.-A/Solids, 30(6), 865-883. https://doi.org/10.1016/j.euromechsol.2011.05.002.
  11. Aria, A.I. and Friswell, M.I. (2019), "A nonlocal finite element model for buckling and vibration of functionally graded nanobeams", Compos. Part B: Eng., 166, 233-246. https://doi.org/10.1016/j.compositesb.2018.11.071 .
  12. Aria, A.I. and Friswell, M.I. (2019), "Computational hygrothermal vibration and buckling analysis of functionally graded sandwich microbeams", Compos. Part B: Eng., 165, 785-797. https://doi.org/10.1016/j.compositesb.2019.02.028.
  13. Aria, A.I., Rabczuk, T. and Friswell, M.I. (2019), "A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams", Europ. J. Mech.-A/Solids, 77, 103767. https://doi.org/10.1016/j.euromechsol.2019.04.002.
  14. Arunkumar, M.P., Bhagat, V., Geng, Q., Ning, J. and Li, Y. (2021), "An analytical solution for vibro-acoustic characteristics of sandwich panel with 3DGrF core and FG-CNT reinforced polymer composite face sheets", Aeros. Sci. Technol., 107091. https://doi.org/10.1016/j.ast.2021.107091.
  15. Assie, A., Akbas, S.D., Bashiri, A.H., Abdelrahman, A.A. and Eltaher, M.A. (2021), "Vibration response of perforated thick beam under moving load", Europ. Phys. J. Plus, 136(3), 1-15. https://doi.org/10.1140/epjp/s13360-021-01224-2.
  16. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007.
  17. Berger, R., Kwon, P. and Dharan, C.K.H. (1994), "High speed centrifugal casting of metal matrix composites", In The Fifth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Maui Hawaii.
  18. Choy, K.L. and Felix, E. (2000), "Functionally graded diamondlike carbon coatings on metallic substrates", Mater. Sci. Eng.: A, 278(1-2), 162-169. https://doi.org/10.1016/S0921-5093(99)00569-9.
  19. Darvishgohari, H., Zarastvand, M., Talebitooti, R. and Shahbazi, R. (2021), "Hybrid control technique for vibroacoustic performance analysis of a smart doubly curved sandwich structure considering sensor and actuator layers", J. Sandw. Struct. Mater., 23(5), 1453-1480. https://doi.org/10.1177/1099636219896251.
  20. Deng, T., Sheng, X., Jeong, H. and Thompson, D.J. (2021), "A two-and-half dimensional finite element/boundary element model for predicting the vibro-acoustic behaviour of panels with poro-elastic media", J. Sound Vib., 505, 116147. https://doi.org/10.1016/j.jsv.2021.116147.
  21. Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. http://dx.doi.org/10.12989/sem.2016.59.2.343
  22. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40(3), 1-10. https://doi.org/10.1007/s40430-018-1065-0.
  23. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021a), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17, 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  24. Esen, I., Eltaher, M.A. and Abdelrahman, A.A. (2021b), "Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass", Mech. Based Des. Struct. Machines, 1-25. https://doi.org/10.1080/15397734.2021.1904255.
  25. Esen, I., Daikh, A.A. and Eltaher, M.A. (2021c), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Europ. Phys. J. Plus, 136(4), 1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7.
  26. Esfahani, S.E., Kiani, Y. and Eslami, M.R. (2013), "Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations", Int. Journal of Mechanical Sciences, 69, 10-20. https://doi.org/10.1016/j.ijmecsci.2013.01.007
  27. Esfahani, S.E., Kiani, Y., Komijani, M. and Eslami, M.R. (2014), "Vibration of a temperature-dependent thermally pre/postbuckled FGM beam over a nonlinear hardening elastic foundation", J. Appl. Mech., 81(1). https://doi.org/10.1115/1.4023975.
  28. Fakher, M., Behdad, S. and Hosseini-Hashemi, S. (2020), "Vibration analysis of stress-driven nonlocal integral model of viscoelastic axially FG nanobeams", Europ. Phys. J. Plus, 135(11), 1-21. https://doi.org/10.1140/epjp/s13360-020-00923-6.
  29. Fukui, Y. (1991), "Fundamental investigation of functionally gradient material manufacturing system using centrifugal force", JSME Int. J., Vib. Control Eng., Eng. Ind., 34(1), 144-148. https://doi.org/10.1299/jsmec1988.34.144.
  30. George, N. and Jeyaraj, P. (2018), "Nonuniform heat effects on buckling of laminated composite beam: Experimental investigations", Int. J. Structuct. Stab. Dyn., 18(12), 1850153. https://doi.org/10.1142/S0219455418501535.
  31. George, N., Jeyaraj, P. and Murigendrappa, S.M. (2016), "Buckling of non-uniformly heated isotropic beam: Experimental and theoretical investigations", Thin-Wall. Struct., 108, 245-255. https://doi.org/10.1016/j.tws.2016.08.019.
  32. Gilorkar, A., Murugan, R. and Pitchaimani, J. (2020), "Thermal buckling of sisal and glass hybrid woven composites: Experimental investigation", Compos. Part C, 2, 100012. https://doi.org/10.1016/j.jcomc.2020.100012.
  33. Gunasekaran, V., Pitchaimani, J. and Chinnapandi, L.B.M. (2020), "Analytical investigation on free vibration frequencies of polymer nano composite plate: Effect of graphene grading and non-uniform edge loading", Mater. Today Commun., 24, 100910. https://doi.org/10.1016/j.mtcomm.2020.100910.
  34. Gunasekaran, V., Pitchaimani, J. and Chinnapandi, L.B.M. (2020), "Vibro-acoustics response of an isotropic plate under nonuniform edge loading: An analytical investigation", Aeros. Sci. Technol., 105, 106052. https://doi.org/10.1016/j.ast.2020.106052.
  35. Gunasekaran, V., Pitchaimani, J., Chinnapandi, L.B.M. and Kumar, A. (2020), "Analytical solution for sound radiation characteristics of graphene nanocomposites plate: Effect of porosity and variable edge load", Int. J. Struct. Stab. Dyn., 21(06), 2150087. https://doi.org/10.1142/S0219455421500875.
  36. Hamed, M.A., Abo-Bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 36(4), 1929-1946. https://doi.org/10.1007/s00366-020-01023-w.
  37. Hamed, M.A., Abo-Bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 36(4), 1929-1946. https://doi.org/10.1007/s00366-020-01023-w.
  38. Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 1-11. https://doi.org/10.1007/s00339-016-0324-0.
  39. 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.
  40. Ibnorachid, Z., Boutahar, L., EL Bikri, K. and Benamar, R. (2019), "Buckling temperature and natural frequencies of thick porous functionally graded beams resting on elastic foundation in a thermal environment", Adv. Acoustic. Vib., 2019. https://doi.org/10.1155/2019/7986569.
  41. Jena, S.K., Chakraverty, S. and Malikan, M. (2020), "Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler-Pasternak elastic foundation using a new refined beam theory: an analytical approach", Europ. Phys. J. Plus, 135(2), 1-18. https://doi.org/10.1140/epjp/s13360-020-00176-3.
  42. Kanakannavar, S. and Pitchaimani, J. (2021), "Thermal buckling of braided flax woven polylactic acid composites", J. Reinforce. Plastics Compos., 40(7-8), 261-272. https://doi.org/10.1177/0731684420957740.
  43. Kang, Y.A. and Li, X.F. (2010), "Large deflections of a non-linear cantilever functionally graded beam", J. Reinforced Plastics Compos., 29(12), 1761-1774. https://doi.org/10.1177/0731684409103340.
  44. Khor, K.A. and Gu, Y.W. (2000), "Effects of residual stress on the performance of plasma sprayed functionally graded ZrO2/NiCoCrAlY coatings", Mater. Sci. Eng.: A, 277(1-2), 64-76. https://doi.org/10.1016/S0921-5093(99)00565-1.
  45. Kumar, A., Gunasekaran, V. and Pitchaimani, J. (2020), "Acoustic response behavior of porous 3D graphene foam plate", Appl. Acoustic., 169, 107431. https://doi.org/10.1016/j.apacoust.2020.107431.
  46. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (2013), Functionally Graded Materials: Design, Processing and Applications, Springer Science & Business Media.
  47. Munde, Y.S., Ingle, R.B. and Siva, I. (2019), "Vibration damping and acoustic characteristics of sisal fibre-reinforced polypropylene composite", Noise Vib. Worldwide, 50(1), 13-21. https://doi.org/10.1177/0957456518812784.
  48. Pinnola, F.P., Vaccaro, M.S., Barretta, R. and de Sciarra, F.M. (2021). Random vibrations of stress-driven nonlocal beams with external damping", Meccanica, 56(6), 1329-1344. https://doi.org/10.1007/s11012-020-01181-7.
  49. Pious, D., Jacob, J., George, N., Bhagat, V., Chacko, T. and Jeyaraj, P. (2020), "Vibro-acoustic behaviour of functionally graded graphene reinforced polymer nanocomposites", In AIP Conference Proceeding, AIP Publishing LLC. https://doi.org/10.1063/5.0004109.
  50. Rezaei, A.S., Saidi, A.R., Abrishamdari, M. and Mohammadi, M. P. (2017), "Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach", Thin-Wall. Struct., 120, 366-377. https://doi.org/10.1016/j.tws.2017.08.003.
  51. Robinson, M.T.A. and Adali, S. (2018), "Buckling of nonuniform and axially functionally graded nonlocal Timoshenko nanobeams on Winkler-Pasternak foundation", Compos. Struct., 206, 95-103. https://doi.org/10.1016/j.compstruct.2018.07.046.
  52. Sepehry, N., Ehsani, M., Shamshirsaz, M. and Sadighi, M. (2021), "Modeling of vibro-acoustic modulation induced by non-linear contact in the Euler-Bernoulli beam using the Fourier spectral element", Amirkabir J. Mech. Eng., 53(6), https://doi.org/10.22060/MEJ.2021.18676.6875.
  53. Sharma, N. and Panda, S.K. (2020), "Multiphysical numerical (FE-BE) solution of sound radiation responses of laminated sandwich shell panel including curvature effect", Comput. Mathem. Appl., 80(5), 1221-1239. https://doi.org/10.1016/j.camwa.2020.06.010.
  54. Sharma, N., Mahapatra, T.R., Panda, S.K. and Katariya, P. (2020), "Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel", J. Sandw. Struct. Mater., 22(5), 1357-1385. https://doi.org/10.1177/1099636218784846.
  55. Shen, H.S. (2016), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC press.
  56. Waddar, S., Pitchaimani, J., Doddamani, M. and Barbero, E. (2019), "Buckling and vibration behaviour of syntactic foam core sandwich beam with natural fiber composite facings under axial compressive loads", Compos. Part B: Eng., 175, 107133. https://doi.org/10.1016/j.compositesb.2019.107133.
  57. Wang, D., Geng, Q. and Li, Y. (2018), "Effect of static load on vibro-acoustic behaviour of clamped plates with geometric imperfections", J. Sound Vib., 432, 155-172. https://doi.org/10.1016/j.jsv.2018.06.019.
  58. Yang, Y., Fenemore, C., Kingan, M.J. and Mace, B.R. (2021), "Analysis of the vibroacoustic characteristics of cross laminated timber panels using a wave and finite element method", J. Sound Vib., 494, 115842. https://doi.org/10.1016/j.jsv.2020.115842.
  59. Yayli, M.O. (2015), "Buckling analysis of a rotationally restrained single walled carbon nanotube", Acta Physica Polonica A, 127(3), 678-683. https://doi.org/10.12693/APhysPolA.127.678
  60. Yayli, M.O. (2016), "Buckling analysis of a microbeam embedded in an elastic medium with deformable boundary conditions", Micro Nano Lett., 11, 741-745. https://doi.org/10.1049/mnl.2016.0257.
  61. Yayli, M.O. (2018a), "Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material", Micro Nano Lett., 13 (7), 1031-1035. https://doi.org/10.1049/mnl.2018.0181.
  62. Yayli, M.O. (2018b), "Free vibration analysis of a single-walled carbon nanotube embedded in an elastic matrix under rotational restraints", Micro Nano Lett., 13(2), 202-206. https://doi.org/10.1049/mnl.2017.0463
  63. Yayli, M.O. (2018c), "Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory", Micro Nano Lett., 13(5), 595-599. https://doi.org/10.1049/mnl.2017.0751
  64. Yayli, M.O. (2019), "Effects of rotational restraints on the thermal buckling of carbon nanotube", Micro Nano Lett., 14 (2), 158-162. https://doi.org/1010.1049/mnl.2018.5428.
  65. Yayli, M.O. (2019), "Free vibration analysis of a rotationally restrained (FG) nanotube", Microsyst. Technol., 25(10), 3723-3734. https://doi.org/10.1007/s00542-019-04307-4
  66. Yayli, M.O. (2020), "Axial vibration analysis of a Rayleigh nanorod with deformable boundaries", Microsyst. Technol., 26(8), 2661-2671. https://doi.org/10.1007/s00542-020-04808-7.
  67. Zghal, S. and Dammak, F. (2020), "Vibrational behavior of beams made of functionally graded materials by using a mixed formulation", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234, 3650-3666. https://doi.org/10.1177/0954406220916533
  68. Zghal, S., Ataoui, D. and Dammak, F. (2020), "Static bending analysis of beams made of functionally graded porous materials", Mech. Based Des. Struct. Machines, 50, 1012-1029. https://doi.org/10.1080/15397734.2020.1748053.
  69. Zghal, S., Ataoui, D. and Dammak, F. (2021), "Free vibration analysis of porous beams with gradually varying mechanical properties", Proceedings of the Institute of Mechanical Engineers, Part M: Journal of Engineering for the Marine Environment. https://doi.org/10.1177/14750902211047746.
  70. Zhang, B., Li, Y. and Lu, W.Z. (2016), "Dynamic characteristics of rotating pretwisted clamped-clamped beam under thermal stress", J. Mech. Sci. Technol., 30(9), 4031-4042. https://doi.org/10.1007/s12206-016-0816-z.
  71. Zhang, X.H., Han, J.C., Du, S.Y. and Wood, J.V. (2000), "Microstructure and mechanical properties of TiC-Ni functionally graded materials by simultaneous combustion synthesis and compaction", J. Mater. Sci., 35(8), 1925-1930. https://doi.org/10.1023/A:1004714402128.
  72. Zheng, H. and Cai, C. (2004), "Minimization of sound radiation from baffled beams through optimization of partial constrained layer damping treatment", Appl. Acoustics, 65(5), 501-520. https://doi.org/10.1016/j.apacoust.2003.11.008.