Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Numerical analysis of beams with damping subjected to dynamic loading

  • A.A. Mosallaie Barzoki (Department of Mechanical Engineering, Kashan University) ;
  • M. Saadantia (Department of Mechanical Engineering, University of Sydney) ;
  • Hamed Karami (Department of Civil Engineering, Jasb Branch, Islamic Azad University)
  • Received : 2019.12.12
  • Accepted : 2022.10.24
  • Published : 2023.02.25
⟨ Previous Next ⟩

Abstract

In this article, the vibration response of elastic nanocomposite beams with enhanced damping by nanoparticles is presented based on the mathematical model. Damp construction is considered by spring and damper elements based on the Kelvin model. Exponential shear deformation beam theory (ESDBT) has been used to model the structure. The mixed model model is used to obtain the effective properties of the structure including compaction effects. Using the energy method and Hamilton's principle, the equations of motion are calculated. The beam frequency is obtained by analytical method. The purpose of this work is to investigate the effect of volume percentage of nanoparticles and density, length and thickness of the beam on the frequency of the structure. The results show that the frequency increases with the increase in volume percentage of nanoparticles.

Keywords

References

  1. Al-Furjan, M., Farrokhian, A., Keshtegar, B., Kolahchi, R. and Trung, N.T. (2021c), "Dynamic stability control of viscoelastic nanocomposite piezoelectric sandwich beams resting on Kerr foundation based on exponential piezoelasticity theory", Eur. J. Mech. A/Solid., 86, 104169. https://doi.org/10.1016/j.euromechsol.2020.104169.
  2. Al-Furjan, M., Farrokhian, A., Keshtegar, B., Kolahchi, R. and Trung, N.T. (2020), "Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones", Aerosp. Sci. Technol., 107, 106259. https://doi.org/10.1016/j.ast.2020.106259.
  3. Al-Furjan, M.S.H., Farrokhian, A., Mahmoud, S.R. and Kolahchi, R. (2021a), "Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact", Thin Wall. Struct., 163, 107706. https://doi.org/10.1016/j.tws.2021.107706.
  4. Al-Furjan, M.S.H., Hajmohammad, M.H., Shen, X., Rajak, D.K. and Kolahchi, R. (2021b), "Evaluation of tensile strength and elastic modulus of 7075-T6 aluminum alloy by adding SiC reinforcing particles using vortex casting method", J. Alloys Compd., 886, 161261. https://doi.org/10.1016/j.jallcom.2021.161261.
  5. Al-Furjan, M.S.H., Shan, L., Shen, X., Kolahchi, R. and Rajak, D.K. (2022e), "Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories", Thin Wall. Struct., 178, 109495. https://doi.org/10.1016/j.tws.2022.109495.
  6. Al-Furjan, M.S.H., Shan, L., Shen, X., Zarei, M.S., Hajmohammad, M.H. and Kolahchi, R. (2022d), "A review on fabrication techniques and tensile properties of glass, carbon, and kevlar fiber reinforced polymer composites", J. Mater. Res. Technol., 19, 2930-2959. https://doi.org/10.1016/j.jmrt.2022.06.008.
  7. Al-Furjan, M.S.H., Xu, M.X., Farrokhian, A., Jafari, G.S., Shen, X. and Kolahchi, R. (2022a), "On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories", Waves Random Complex Media, 2022, 1-25. https://doi.org/10.1080/17455030.2022.2030499.
  8. Al-Furjan, M.S.H., Yang, Y., Farrokhian, G.S., Shen, X., Kolahchi, R. and Rajak, D.K. (2022b), "Dynamic instability of nanocomposite piezoelectric-leptadenia pyrotechnica rheological elastomer-porous functionally graded materials micro viscoelastic beams at various strain gradient higher-order theories", Polym. Compos., 43(1), 282-298. https://doi.org/10.1002/pc.26373.
  9. Al-Furjan, M.S.H., Yin, C., Shen, X., Kolahchi, R., Zarei, M.S. and Hajmohammad, M.H. (2022c), "Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate", Mech. Syst. Signal Pr., 178, 109269. https://doi.org/10.1016/j.ymssp.2022.109269.
  10. Al-Furjan, M.S.H., Kong, X.S., Shan, L., Soleimani Jafari, G., Farrokhian, A., Kolahchi, R. and Rajak, D.K. (2022f), "Influence of LPRE on the size-dependent phase velocity of sandwich beam including FG porous and smart nanocomposite layers", Polym. Compos., 43(10), 7390-7402. https://doi.org/10.1002/pc.26820.
  11. Amoli, A., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory", Earthq. Struct., 15(3), 285-294. https://doi.org/10.12989/eas.2018.15.3.285.
  12. Arbabi, A., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Concrete columns reinforced with Zinc Oxide nanoparticles subjected to electric field: Buckling analysis", Wind Struct., 24(5), 431-446. https://doi.org/10.12989/was.2017.24.5.431.
  13. Azmi, M., Kolahchi, R. and Rabani Bidgoli, M. (2019), "Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load", Adv. Concrete Constr., 7(1), 51-63. https://doi.org/10.12989/acc.2019.7.1.051.
  14. Bakhshande Amnieh, H., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140.
  15. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036.
  16. Faramoushjan, S.G., Jalalifar, H. and Kolahchi, R. (2021), "Mathematical modelling and numerical study for buckling study in concrete beams containing carbon nanotubes", Adv. Concrete Constr., 11(6), 521-529. https://doi.org/10.12989/acc.2021.11.6.521.
  17. Farokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.
  18. Golabchi, H., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431.
  19. Hajmohammad, M.H., Azizkhani, M.B. and Kolahchi, R. (2018a), "Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis", Int. J. Mech. Sci., 137, 205-213. https://doi.org/10.1016/j.ijmecsci.2018.01.026.
  20. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2021), "Dynamic analysis in beam element of wave-piercing Catamarans undergoing slamming load based on mathematical modelling", Ocean Eng., 234, 109269. https://doi.org/10.1016/j.oceaneng.2021.109269.
  21. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018c), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002.
  22. Hajmohammad, M.H., Nouri, A.H., Zarei, M.S. and Kolahchi, R. (2019a), "A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal", Eng. Comput., 35(4), 1141-1157. https://doi.org/10.1007/s00366-018-0655-x.
  23. Hajmohammad, M.H., Sharif Zarei, M., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 2017, 1099636217720373. https://doi.org/10.1177/1099636217720373.
  24. Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018b), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., 6(4), 299-321. https://doi.org/10.12989/anr.2018.6.4.299.
  25. Hajmohammad, M.H., Zarei, M.S., Kolahchi, R. and Karami, H. (2019b), "Visco-piezoelasticity-zigzag theories for blast response of porous beams covered by graphene platelet-reinforced piezoelectric layers", J. Sandw. Struct. Mater., 2019, 1099636219839175. https://doi.org/10.1177/1099636219839175.
  26. Heidarzadeh, A., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Concrete pipes reinforced with AL2O3 nanoparticles considering agglomeration: Magneto-thermo-mechanical stress analysis", Int. J. Civil Eng., 16(3), 315-322. https://doi.org/10.1007/s40999-016-0130-2.
  27. Jafari Natanzi, A., Soleimani Jafari, G. and Kolahchi, R. (2018), "Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation", Comput. Concrete, 21(5), 569-582. https://doi.org/10.12989/cac.2018.21.5.569.
  28. Jafarian Arani, A. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567.
  29. Jamali, M., Shojaee, T., Kolahchi, R. and Mohammadi, B. (2016), "Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials", Steel Compos. Struct., 22(3), 691-712. https://doi.org/10.12989/scs.2016.22.3.691.
  30. Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.
  31. Jassas, M.R., Rabani Bidgoli, M. and Kolahchi, R. (2019), "Forced vibration analysis of concrete plates reinforced by agglomerated SiO2 nanoparticles based on numerical methods", Constr. Build. Mater., 211, 796-806. https://doi.org/10.1016/j.conbuildmat.2019.03.263.
  32. Javani, R., Rabani Bidgoli, M. and Kolahchi, R. (2019), "Buckling analysis of plates reinforced by Graphene platelet based on Halpin-Tsai and Reddy theories", Steel Compos. Struct., 31(4), 419-426. https://doi.org/10.12989/scs.2019.31.4.419.
  33. Keshtegar, B. and Kolahchi, R. (2018), "Reliability analysis-based conjugate map of beams reinforced by ZnO nanoparticles using sinusoidal shear deformation theory", Steel Compos. Struct., 28(2), 195-207. https://doi.org/10.12989/scs.2018.28.2.195.
  34. Keshtegar, B., Farrokhian, A., Kolahchi, R. and Trung, N.T. (2020b), "Dynamic stability response of truncated nanocomposite conical shell with magnetostrictive face sheets utilizing higher order theory of sandwich panels", Eur. J. Mech. A/Solid., 82, 104010. https://doi.org/10.1016/j.euromechsol.2020.104010.
  35. Keshtegar, B., Motezaker, M., Kolahchi, R. and Trung, N.T. (2020a), "Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping", Thin Wall. Struct., 154, 106820. https://doi.org/10.1016/j.tws.2020.106820.
  36. Keshtegar, B., Tabatabaei, J., Kolahchi, R. and Trung, N.T. (2020c), "Dynamic stress response in the nanocomposite concrete pipes with internal fluid under the ground motion load", Adv. Concrete Constr., 9(3), 327-335. https://doi.org/10.12989/acc.2020.9.3.327.
  37. Kolahchi, R. (2017a), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016.
  38. Kolahchi, R. and Kolahdouzan, F. (2021), "A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Appl. Math. Model., 91, 458-475. https://doi.org/10.1016/j.apm.2020.09.060.
  39. Kolahchi, R., Arbabi, A. and Rabani Bidgoli, M. (2020b), "Experimental study for ZnO nanofibers effect on the smart and mechanical properties of concrete", Smart Struct. Syst., 25(1), 97-104. https://doi.org/10.12989/sss.2020.25.1.097.
  40. Kolahchi, R., Hosseini, H., Fakhar, M.H., Taherifar, R. and Mahmoudi, M. (2018), "A numerical method for magnetohygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Comput. Math. Appl., 78(6), 2018-2034. https://doi.org/10.1016/j.camwa.2019.03.042.
  41. Kolahchi, R., Keshtegar, B. and Trung, N.T. (2022), "Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions", Int. J. Sandw. Struct., 24, 643-662. https://doi.org/10.1177/10996362211020388.
  42. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. ttps://doi.org/10.1016/j.compstruct.2016.05.023.
  43. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A.H. (2017b), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.
  44. Kolahchi, R., Zhu, S.P., Keshtegar, B. and Trung, N.T. (2020a), "Dynamic buckling optimization of laminated aircraft conical shells with hybrid nanocomposite martial", Aerosp. Sci. Technol., 98, 105656. https://doi.org/10.1016/j.ast.2019.105656.
  45. Kolahdouzan, F., Mosayyebi, M., Ghasemi, F.A., Kolahchi, R. and Mousavi Panah, S.M. (2020), "Free vibration and buckling analysis of elastically restrained FG-CNTRC sandwich annular nanoplates", Adv. Nano Res., 9(4), 237-250. https://doi.org/10.12989/anr.2020.9.4.237.
  46. Mosharrafian, F. and Kolahchi, R. (2016), "Nanotechnology, smartness and orthotropic nonhomogeneous elastic medium effects on buckling of piezoelectric pipes", Struct. Eng. Mech., 58(5), 931-947. https://doi.org/10.12989/sem.2016.58.5.931.
  47. Motezaker, M. and Kolahchi, R. (2017a), "Seismic response of concrete columns with nanofiber reinforced polymer layer", Comput. Concrete, 20(3), 361-368. https://doi.org/10.12989/cac.2017.20.3.361.
  48. Motezaker, M. and Kolahchi, R. (2017a), "Seismic response of SiO2 nanoparticles-reinforced concrete pipes based on DQ and newmark methods", Comput. Concrete, 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745.
  49. Motezaker, M., Kolahchi, R., Kumar Rajak, D. and Mahmoud, S. R. (2021), "Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load", Polym. Compos., 42(8), 4073-4081. https://doi.org/10.1002/pc.26118.
  50. Naseri Taheri, M., Sabet, S.A. and Kolahchi, R. (2020), "Experimental investigation of self-healing concrete after crack using nano-capsules including polymeric shell and nanoparticles core", Smart Struct. Syst., 25(3), 337-343. https://doi.org/10.12989/sss.2020.25.3.337.
  51. Seo, Y.S., Jeong, W.B., Yoo, W.S. and Jeong, H.K. (2015), "Frequency response analysis of cylindrical shells conveying fluid using finite element method", J. Mech. Sci. Techol., 19, 625-633. https://doi.org/10.1007/BF02916184.
  52. Taherifar, R., Zareei, S.A., Rabani Bidgoli, M. and Kolahchi, R. (2020), "Seismic analysis in pad concrete foundation reinforced by nanoparticles covered by smart layer utilizing plate higher order theory", Steel Compos. Struct., 37(1), 99-115. https://doi.org/10.12989/scs.2020.37.1.099.
  53. Taherifar, R., Zareei, S.A., Rabani Bidgoli, M. and Kolahchi, R. (2021), "Application of differential quadrature and Newmark methods for dynamic response in pad concrete foundation covered by piezoelectric layer", J. Comput. Appl. Math., 382, 113075. https://doi.org/10.1016/j.cam.2020.113075.
  54. Tan, P. and Tong, L. (2001), "Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials", Compos. Sci. Technol., 61, 759-769. https://doi.org/10.1016/S0266-3538(01)00014-8.
  55. Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009.
  56. Yang, Y. and Li, H. (2020), "Experimental study on shear behaviors of partial precast steel reinforced concrete beams", Steel Compos. Struct., 37, 605-620, http://doi.org/10.12989/scs.2020.37.5.605.
  57. Zamani, A., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concrete, 20(6), 671-682. https://doi.org/10.12989/cac.2017.20.6.671.
  58. Zamanian, M., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nanoparticles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043.
  59. Zarei, M.S., Azizkhani, M.B., Hajmohammad, M.H. and Kolahchi, R. (2017), "Dynamic buckling of polymer-carbon nanotube-fiber multiphase nanocomposite viscoelastic laminated conical shells in hygrothermal environments", J. Sandw. Struct. Mater., 2017, 1099636217743288. https://doi.org/10.1177/1099636217743288.
  60. Zheng, W., Chen, W.G., Feng, T., Li, W.Q., Liu, X.T., Dong, L.L. and Fu, Y.Q. (2019), "Enhancing chloride ion penetration resistance into concrete by using graphene oxide reinforced waterborne epoxy coating", Prog. Org. Coat., 138, 105389. https://doi.org/10.1016/j.porgcoat.2019.105389.