Steel and Composite Structures

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Vibration analysis and control of micro porous beam integrated with FG-CNT distributed piezoelectric sensor and actuator

  • Akhavan Alavi, S.M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Ejtahed, S.H. (Department of Control, Faculty of Computer and Electrical Engineering, University of Kashan)
  • Received : 2019.05.22
  • Accepted : 2021.10.21
  • Published : 2021.11.25
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Abstract

In this study, the active control and vibration analysis of a micro sandwich beam based on modified couple stress theory (MCST) are investigated. The core of sandwich structure is porous and the face sheets are made from piezoelectric material and reinforced by carbon nanotubes. The generalized rule of mixture is employed to predict the mechanical and electrical properties of a micro sandwich composite beam. Based on Hamilton's principle, the governing equations of motion for a micro Reddy beam are derived and active control is considered by the state space representation of the system. The results of this research show that the porosity coefficient, porosity distributions, carbon nanotubes (CNTs) volume fraction, CNTs distributions, the material length scale parameter and different face sheet and core thicknesses effect on the natural frequencies, the resonance phenomenon, settling time and deflection response of system. This research can provide a valuable background for further experimental studies as a basic investigation for applications of a micro sandwich beams in the field of micro robots. Also the results are potentially useful for active control, preventing the resonance phenomenon, design and optimization of micro sandwich beams.

Keywords

Acknowledgement

The authors would like to thank the referees for their valuable comments. This work was supported by the Iranian Nanotechnology Development Committee and the University of Kashan under Grant No. 682561/9.

References

  1. Akbas, S.D. (2018), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
  2. Akhavan Alavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech. A/Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  3. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. http://dx.doi.org/10.12989/scs.2015.18.3.659.
  4. Arefi, M., Karroubi, R. and Irani-Rahaghi, M. (2016), "Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer", Appl. Math. Mech., 37(7), 821-834. https://doi.org/10.1007/s10483-016-2098-9.
  5. Arefi, M., Pourjamshidian, M., Ghorbanpour Arani, A. (2018), "Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass", J. Sandw. Struct. Mater., 20(4), 462-492. https://doi.org/10.1177/1099636216658895.
  6. Chuaqui, T.R.C. and Roque, C.M.C. (2017), "Analysis of functionally graded piezoelectric Timoshenko smart beams using a multiquadric radial basis function method", Compos. Struct., 176, 640-653. https://doi.org/10.1016/j.compstruct.2017.05.062.
  7. Ebrahimi, F. and Barati, M.R. (2017), "Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory", Compos. Struct., 166, 256-267. https://doi.org/10.1016/j.compstruct.2017.01.036.
  8. Ghayesh, M.H. (2018), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004.
  9. Ghorbanpour Arani, A., Haghparast, E., Heidari Rarani, M. and Khoddami Maraghi, Z. (2015a), "Strain gradient shell model for nonlinear vibration analysis of visco-elastically coupled boron nitride nano-tube reinforced composite micro-tubes conveying viscous fluid", Comput. Mater. Sci., 96, 448-458. https://doi.org/10.1016/j.commatsci.2014.06.013.
  10. Ghorbanpour Arani, A., Haghparast, E., Khoddami Maraghi, Z. and Amir, S. (2015b), "Static stress analysis of carbon nanotube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo mechanical loads and uniform electromagnetic fields", Compos.: Part B, 68, 136-145. https://doi.org/10.1016/j.compositesb.2014.08.036.
  11. Ghorbanpour Arani, A., Khani Arani, H. and Khoddami Maraghi, Z. (2016), "Vibration analysis of sandwich composite micro-plate under electro-magneto-mechanical loadings", Appl. Math. Model., 40(23-24), 10596-10615. https://doi.org/10.1016/j.apm.2016.07.033.
  12. Ghorbanpour Arani, A., Rahnama Mobarakeh, M., Shams, S.H. and Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magneto electro mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26, 2565-2572. https://doi.org/10.1007/s12206-012-0639-5.
  13. Jamalpoor, A., Ahmadi-Savadkoohi, A. and Hosseini-Hashemi, S.H. (2016), "Free vibration and biaxial buckling analysis of magneto-electro-elastic microplate resting on visco-Pasternak substrate via modified strain gradient theory", Smart Mater. Struct., 25, 105035. https://doi.org/10.1088/0964-1726/25/10/105035
  14. Jin, G., Yang, C. and Liu, Z. (2016), "Vibration and damping analysis of sandwich viscoelastic-core beam using Reddy's higher-order", Compos. Struct., 140, 390-409. https://doi.org/10.1016/j.compstruct.2016.01.017.
  15. Jooybar, N., Malekzadeh, P. and Fiouz, A. (2016), "Vibration of functionally graded carbon nanotubes reinforced composite truncated conical panels with elastically restrained against rotation edges in thermal environment", Compos. Part B, 106, 242-261. https://doi.org/10.1016/j.compositesb.2016.09.030.
  16. Jun, L., Xiang, H. and Xiaobin, L. (2016), "Free vibration analyses of axially loaded laminated composite beams using a unified higher-order shear deformation theory and dynamic stiffness method", Compos. Struct., 158, 308-322. https://doi.org/10.1016/j.compstruct.2016.09.012.
  17. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beam reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  18. Kolahdouzan, F., Ghorbanpour Arani, A. and Abdollahian, M. (2018), "Buckling and free vibration analysis of FG-CNTRC-micro sandwich plate", Steel Compos. Struct., 26(3), 273-287. https://doi.org/10.12989/scs.2018.26.3.273.
  19. Koochaki, G.R. (2011), "Free vibration analysis of functionally graded beams", Int. J. Mech. Aerosp. Industrial, Mechatron. Manufact. Eng., 5, 514-517.
  20. Kumar, R., Mishra, B.K. and Jain, S.C. (2008), "Static and dynamic analysis of smart cylindrical shell", Finite Elem. Anal. Des., 45(1), 13-24. https://doi.org/10.1016/j.finel.2008.07.005.
  21. Kumar, S., Mitra, A. and Roy, H. (2017), "Forced vibration response of axially functionally graded non-uniform plates considering geometric nonlinearity", Int. J. Mech. Sci., 128-129, 194-205. https://doi.org/10.1016/j.ijmecsci.2017.04.022.
  22. Lee, J.W. and Lee, J.Y. (2017), "Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression", Int. J. Mech. Sci., 122, 1-17. https://doi.org/10.1016/j.ijmecsci.2017.01.011.
  23. Li, X., Li, L., Hu, Y., Ding, Z. and Deng, W. (2017), "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory", Compos. Struct., 165, 250-265. https://doi.org/10.1016/j.compstruct.2017.01.032.
  24. Mahapatra, T.R., Kar, V.R., Panda, S.K. and Mehar K. (2017), "Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stresses, 40(9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788.
  25. Mehar, K., Panda S.K. and Mahapatra T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech. - A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005
  26. Mehar, K., Panda, S.K., Tinh, Q.B. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stresses, 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.
  27. Mohammadimehr, M., Akhavan Alavi, S.M., Okhravi, S.V. and Edjtahed, S.H. (2018a), "Free vibration analysis of micro magneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube-reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory", J. Intel. Mat. Syst. Str., 29(5), 863-882. https://doi.org/10.1177/1045389X17721048.
  28. Mohammadimehr, M., Emdadi, M. and Rousta Navi, B. (2018b), "Dynamic stability analysis of microcomposite annular sandwich plate with carbon nanotube reinforced composite facesheets based on modified strain gradient theory", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636218782770.
  29. Mohammadimehr, M. and Mehrabi, M. (2018), "Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow", Appl. Math. Model., 60, 255-272. https://doi.org/10.1016/j.apm.2018.03.008.
  30. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Akhavan Alavi, S.M., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018c), "Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., 29(3), 405-422. https://doi.org/10.12989/scs.2018.29.3.405.
  31. Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B, 94, 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030.
  32. Mohammadimehr, M., Okhravi, S.V. and Akhavan Alavi, S.M. (2018d), "Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT", J. Vib. Control, 24(8), 1551-1569. https://doi.org/10.1177/1077546316664022.
  33. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Free vibration of viscoelastic double bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077.
  34. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007.
  35. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016a), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055.
  36. Nayak, A.K., Moy, S.S.J. and Shenoi, R.A. (2002), "Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory", Compos. Part B: Eng., 33, 505-519. https://doi.org/10.1016/S1359-8368(02)00035-5.
  37. Panda, R.K., Nayak, B. and Sarangi, S.K. (2016), "Active vibration control of smart functionally graded beams", Procedia Eng., 144, 551-559. https://doi.org/10.1016/j.proeng.2016.05.041.
  38. Phung-Van, P., De Lorenzis, L., Thai, C.H., Abdel-Wahab, M. and Nguyen-Xuan, H. (2015), "Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements", Comput. Mater. Sci., 96, 495-505. https://doi.org/10.1016/j.commatsci.2014.04.068.
  39. Poikselka, K., Leinonen, M., Palosaari, J., Vallivaara, I., Roning, J. and Juuti, J. (2017), "Novel genetically optimised high-displacement piezoelectric actuator with efficient use of active material", Smart Mater. Struct., 26, 095022. https://doi.org/10.1088/0964-1726/26/9/095022
  40. Rahmani, O., Khalili, S.M.R. and Thomsen, O. (2012), "A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads", Compos. Struct., 94(7), 2129-2142. https://doi.org/10.1016/j.compstruct.2012.02.002.
  41. Shabanlou, Gh., Hosseini, S.A.A. and Zamanian, M. (2018), "Vibration analysis of FG spinning beam using higher-order shear deformation beam theory in thermal environment", Appl. Math. Model., 56, 325-341. https://doi.org/10.1016/j.apm.2017.11.021.
  42. Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Method. Appl. M., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  43. Shao, D., Hu, S., Wang, Q. and Pang, F. (2017), "Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions", Compos. Part B: Eng., 108, 75-90. https://doi.org/10.1016/j.compositesb.2016.09.093.
  44. Sharif Zarei, M., Hajmohammad, M.H., Mostafavifar, M. and Mohammadimehr, M. (2017), "Influence of temperature change and humidity condition on free vibration analysis of a nano composite sandwich plate resting on orthotropic Pasternak foundation by considering agglomeration effect", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636217735118.
  45. Shen, H.S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube- reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010.
  46. Shen, H.S. and Zhu, Z.H. (2012), "Postbuckling of sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations", Eur. J. Mech. A/Solids, 35, 10-21. https://doi.org/10.1016/j.euromechsol.2012.01.005.
  47. Shojaeian, M. and Zeighampour, H. (2016), "Size dependent pull-in behavior of functionally graded sandwich nanobridges using higher order shear deformation theory", Compos. Struct., 143, 117-129. https://doi.org/10.1016/j.compstruct.2016.02.008.
  48. Shooshtari, A. and Razavi, S. (2015), "Nonlinear vibration analysis of rectangular magneto-electro-elastic thin plates", IJE Transactions A, 28, 136-144. https://doi.org/10.5829/idosi.ije.2015.28.01a.18.
  49. Singh,V.K, Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mehar, K. (2019), "Numerical and experimental nonlinear dynamic response reduction of smart composite curved structure using collocation and non-collocation configuration", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 233(5), 1601-1619. https://doi.org/10.1177/0954406218774362.
  50. Singh,V.K, Mahapatra, T.R. and Panda, S.K. (2016a), "Nonlinear flexural analysis of single/doubly curved smart composite shell panels integrated with PFRC actuator", Eur. J. Mech. - A/Solids, 60, 300-314. https://doi.org/10.1016/j.euromechsol.2016.08.006.
  51. Singh,V.K, Mahapatra, T.R. and Panda, S.K. (2016b), "Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator", Compos. Struct., 157, 121-130. https://doi.org/10.1016/j.compstruct.2016.08.020.
  52. Thai, C.H., Ferreira, A.J.M. and Nguyen-Xuan, H. (2018), "Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory", Compos. Struct., 192, 274-288. https://doi.org/10.1016/j.compstruct.2018.02.060.
  53. Wu, H., Kitipornchai, S. and Yang, J. (2016), "Thermo-electromechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections", Smart Mater. Struct., 25, 095022. https://doi.org/10.1088/0964-1726/25/9/095022
  54. Wu, H.L., Yang, J. and Kitipornchai, S. (2016), "Nonlinear vibration of functionally graded carbon nanotube reinforced composite beams with geometric imperfections", Compos. Part B: Eng., 90, 86-96. https://doi.org/10.1016/j.compositesb.2015.12.007.
  55. Xiang, S., Jiang, S.X., Bi, Z.Y., Jin, Y.X. and Yang, M.S. (2011), "A nth-order meshless generalization of Reddy's third-order shear deformation theory for the free vibration on laminated composite plates", Compos. Struct., 93(2), 299-307. https://doi.org/10.1016/j.compstruct.2010.09.015.
  56. Xin, L. and Hu, Z. (2016), "Free vibration of simply supported and multilayered magneto-electro-elastic plates", Compos. Struct., 121, 344-350. https://doi.org/10.1016/j.compstruct.2014.11.030.
  57. Zhang, Z.J., Han, B., Zhang, Q.C. and Jin, F. (2017), "Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores", Compos. Struct., 171, 335-344. https://doi.org/10.1016/j.compstruct.2017.03.045.