Size-dependent coupled bending-torsional vibration of functionally graded carbon nanotube reinforced composite Timoshenko microbeams

• Autorzy: Dehkordi Hamid Reza Balali , Beni Yaghoub Tadi

Identyfikatory

DOI

10.1007/s43452-023-00725-4

• Języki publikacji: EN

Abstrakty

EN

This paper investigates the free vibration of a carbon nanotube-reinforced composite Timoshenko microbeam considering the effect of axial load and bending-torsion coupling. The microbeam properties are developed based on the micromechanical model concerning the extended rule of mixtures. The governing equations of motion are derived using the modified couple stress theory and Hamilton’s principle. The uniform nanotube distribution and three functionally graded distributions are considered for the carbon nanotube-reinforced composite microbeam. The generalized differential quadrature method is applied to the governing equations for deriving the natural frequency under different boundary conditions. Next, the effects of different parameters, including nanotube distribution, geometric characteristics of microbeam, material length scale, and nanotube volume fraction, on the natural frequency are demonstrated through different tables and diagrams. Among obtained results is the significant effect of the carbon nanotube volume fraction on the natural frequency of the microbeam. Also, the nonconformity between the mass and elastic axes leads to the natural frequency reduction. The comparison between obtained results and results of other credible papers confirms the validity of obtained results.

Słowa kluczowe

EN

coupled bending and torsional vibration; functionally graded carbon nanotube reinforced composite; Timoshenko beam theory; modified coupled stress theory; generalized differential quadrature method

PL

sprzęgło; belka zespolona; nanorurka węglowa

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2023
• Tom: Vol. 23, no. 3
• Strony: art. no. e186, 2023
• Opis fizyczny: Bibliogr. 27 poz., rys., wykr.

Twórcy

autor

Dehkordi Hamid Reza Balali

• Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran

autor

Beni Yaghoub Tadi

• Faculty of Engineering, Shahrekord University, Shahrekord, Iran
• Nanotechnology Research Institute, Shahrekord University, Shahrekord, Iran

• https://orcid.org/0000-0002-1645-6403

Bibliografia

• 1. Takawa T, Fukuda T, Takada T. Flexural-torsion coupling vibration control of fiber composite cantilevered beam by using piezoceramic actuators. Smart Mater Struct. 1997;6(4):477.
• 2. Eslimy-Isfahany SHR, Banerjee JR. Use of generalized mass in the interpretation of dynamic response of bending–torsion coupled beams. J Sound Vib. 2000;238(2):295–308.
• 3. Banerjee JR, Williams FW. Coupled bending-torsional dynamic stiffness matrix for Timoshenko beam elements. Comput Struct. 1992;42(3):301–10.
• 4. Banerjee JR, Williams FW. Coupled bending-torsional dynamic stiffness matrix of an axially loaded Timoshenko beam element. Int J Solids Struct. 1994;31(6):749–62.
• 5. Li J, Shen R, Hua H, Jin X. Bending–torsional coupled dynamic response of axially loaded composite Timosenko thin-walled beam with closed cross-section. Compos Struct. 2004;64(1):23–35.
• 6. Sari MES, Al-Kouz WG, Al-Waked R. Bending–torsional- coupled vibrations and buckling characteristics of single and double composite Timoshenko beams. Adv Mech Eng. 2019;11(3):1687814019834452.
• 7. Esawi AM, Farag MM. Carbon nanotube reinforced composites: potential and current challenges. Mater Des. 2007;28(9):2394–401.
• 8. Mohammadimehr M, Monajemi AA, Afshari H. Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams. Microsyst Technol. 2020;26(10):3085–99.
• 9. Arshid E, Arshid H, Amir S, Mousavi SB. Free vibration and buckling analyses of FG porous sandwich curved microbeams in thermal environment under magnetic field based on modified couple stress theory. Arch Civ Mech Eng. 2021;21(1):1–23.
• 10. Rokni H, Milani AS, Seethaler RJ. Size-dependent vibration behavior of functionally graded CNT-reinforced polymer micro- cantilevers: modeling and optimization. Eur J Mech-A/Solids. 2015;49:26–34.
• 11. Ahmadi M, Ansari R, Rouhi H. On the free vibrations of piezo- electric carbon nanotube-reinforced microbeams: a multiscale finite element approach. Iran J Sci Technol Trans Mech Eng. 2019;43(1):285–94.
• 12. Rostami R, Mohammadimehr M, Ghannad M, Jalali A. Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties. Theor Appl Mech Lett. 2018;8(2):97–108.
• 13. Borjalilou V, Taati E, Ahmadian MT. Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions. SN Appl Sci. 2019;1(11):1–15.
• 14. Glabisz W, Jarczewska K, Holubowski R. Stability of Timoshenko beams with frequency and initial stress dependent nonlocal parameters. Arch Civ Mech Eng. 2019;19:1116–26.
• 15. Arshid E, Arshid H, Amir S, Mousavi SB. Free vibration and buckling analyses of FG porous sandwich curved microbeams in thermal environment under magnetic field based on modified couple stress theory. Arch Civ Mech Eng. 2021;21:1–23.
• 16. Yue XG, Sahmani S, Luo H, Safaei B. Nonlocal strain gradient-based quasi-3D nonlinear dynamical stability behavior of agglomerated nanocomposite microbeams. Arch Civ Mech Eng. 2022;23(1):21.
• 17. Panahi R, Asghari M, Borjalilou V. Nonlinear forced vibration analysis of micro-rotating shaft–disk systems through a formulation based on the nonlocal strain gradient theory. Arch Civ Mech Eng. 2023;23(2):85.
• 18. Shen HS. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Com- pos Struct. 2009;91(1):9–19.
• 19. Lee U, Jang I. Spectral element model for axially loaded bend- ing–shear–torsion coupled composite Timoshenko beams. Compos Struct. 2010;92(12):2860–70.
• 20. Ng CHW, Zhao YB, Xiang Y, Wei GW. On the accuracy and stability of a variety of differential quadrature formulations for the vibration analysis of beams. Int J Eng Appl Sci. 2009;1(4):1–25.
• 21. Tornabene F, Fantuzzi N, Bacciocchi M. Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: conver- gence and accuracy. Eng Anal Boundary Elem. 2018;92:3–37.
• 22. Fantuzzi N, Tornabene F, Bacciocchi M, Neves AM, Ferreira AJ. Stability and accuracy of three Fourier expansion-based strong form finite elements for the free vibration analysis of laminated composite plates. Int J Numer Meth Eng. 2017;111(4):354–82.
• 23. Tornabene F, Fantuzzi N, Ubertini F, Viola E. Strong formulation finite element method based on differential quadrature: a survey. Appl Mech Rev DOI. 2015;10(1115/1):4028859.
• 24. Balali Dehkordi HR, Tadi Beni Y. Size-dependent coupled bend- ing–torsional vibration of Timoshenko microbeams. Arch Civ Mech Eng. 2022;22(3):1–15.
• 25. Yas MH, Samadi N. Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation. Int J Press Vessels Pip. 2012;98:119–28.
• 26. Griebel M, Hamaekers J. Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites. Comput Methods Appl Mech Eng. 2004;193(17–20):1773–88.
• 27. Han Y, Elliott J. Molecular dynamics simulations of the elas- tic properties of polymer/carbon nanotube composites. Comput Mater Sci. 2007;39(2):315–23.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024)