Smart Structures and Systems

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Active vibration control of nonlinear stiffened FG cylindrical shell under periodic loads

  • Ahmadi, Habib (Faculty of Mechanical Engineering, Shahrood University of Technology) ;
  • Foroutan, Kamran (Faculty of Mechanical Engineering, Shahrood University of Technology)
  • Received : 2019.02.07
  • Accepted : 2020.02.04
  • Published : 2020.06.25
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Abstract

Active control of nonlinear vibration of stiffened functionally graded (SFG) cylindrical shell is studied in this paper. The system is subjected to axial and transverse periodic loads in the presence of thermal uncertainty. The material composition is considered to be continuously graded in the thickness direction, also these properties depend on temperature. The relations of strain-displacement are derived based on the classical shell theory and the von Kármán equations. For modeling the stiffeners on the cylindrical shell surface, the smeared stiffener technique is used. The Galerkin method is used to discretize the partial differential equations of motion. Some comparisons are made to validate the SFG model. For suppression of the nonlinear vibration, the linear and nonlinear control strategies are applied. For control objectives, the piezoelectric actuator is attached to the external surface of the shell and the thin ring piezoelectric sensor is attached to the middle internal surface of shell. The effect of PID, feedback linearization and sliding mode control on the suppression of vibration for SFG cylindrical shell is presented.

Keywords

References

  1. Ahmadi, H. and Foroutan, K. (2019), "Nonlinear primary resonance of spiral stiffened functionally graded cylindrical shells with damping force using the method of multiple scales", Thin-Wall Struct., 135, 33-44. https://doi.org/10.1016/j.tws.2018.10.028
  2. Bailey, T. and Hubbard, J.E. (1985), "Distributed piezoelectric-polymer active vibration control of a cantilever beam", J. Guidance Control Dyn., 8(5), 605-611. https://doi.org/10.2514/3.20029
  3. Baillargeon, B.P. and Vel, S.S. (2005), "Active vibration suppression of sandwich beams using piezoelectric shear actuators: Experiments and numerical simulations", J. Intell. Mater. Syst. Struct., 16(6), 517-530. https://doi.org/10.1177/1045389X05053154
  4. Bich, D.H., Van Dung, D., Nam, V.H. and Phuong, N.T. (2013), "Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression", Int. J. Mech. Sci., 74, 190-200. https://doi.org/10.1016/j.ijmecsci.2013.06.002
  5. Biglar, M., Mirdamadi, H.R. and Danesh, M. (2014), "Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired rayleigh-ritz modes using genetic algorithm", J. Sound Vib., 333(5), 1224-1244. https://doi.org/10.1016/j.jsv.2013.10.025
  6. Boukhelf, F., Bouiadjra, M.B., Bouremana, M. and Tounsi, A. (2018), "Hygro-thermo-mechanical bending analysis of FGM plates using a new HSDT", Smart Struct. Syst., Int. J., 21(1), 75-97. https://doi.org/10.12989/sss.2018.21.1.075
  7. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill New York, NY, USA.
  8. Chen, Y.Z. (2018), "Transfer matrix method for solution of FGMs thick-walled cylinder with arbitrary inhomogeneous elastic response", Smart Struct. Syst., Int. J., 21(4), 469-477. https://doi.org/10.12989/sss.2018.21.4.469
  9. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020
  10. Correia, I.P., Soares, C.M.M., Soares, C.A.M. and Herskovits, J. (2002), "Active control of axisymmetric shells with piezoelectric layers: A mixed laminated theory with a high order displacement field", Comput. Struct., 80(27-30), 2265-2275. https://doi.org/10.1016/S0045-7949(02)00239-0
  11. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017
  12. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. A-Solid., 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004
  13. Duc, N.D. (2018), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266
  14. Duc, N.D. and Cong, P.H. (2018), "Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson's ratio in auxetic honeycombs", J. Sandw. Struct. Mater., 20(6), 692-717. https://doi.org/10.1177/1099636216674729
  15. Dung, D. and Nam, V.H. (2014), "Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium", Eur. J. Mech. A-Solid., 46, 42-53. https://doi.org/10.1016/j.euromechsol.2014.02.008
  16. Duc, N.D. and Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened s-fgm circular cylindrical shells surrounded on elastic foundations", Aerosp. Sci. Technol., 40, 115-127. https://doi.org/10.1016/j.ast.2014.11.005
  17. Duc, N.D., Anh, V.T.T. and Cong, P.H. (2014), "Nonlinear axisymmetric response of FGM shallow spherical shells on elastic foundations under uniform external pressure and temperature", Eur. J. Mech. A-Solid., 45, 80-89. https://doi.org/10.1016/j.euromechsol.2013.11.008
  18. Duc, N.D., Cong, P.H., Anh, V.M., Quang, V.D., Tran, P., Tuan, N.D. and Thinh, N.H. (2015), "Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment", Compos. Struct., 132, 597-609. https://doi.org/10.1016/j.compstruct.2015.05.072
  19. Duc, N.D., Bich, D.H. and Cong, P.H. (2016), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Therm. Stress., 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194
  20. Duc, N.D., Lee, J., Nguyen-Thoi, T. and Thang, P.T. (2017a), "Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations", Aerosp. Sci. Technol., 68, 391-402. https://doi.org/10.1016/j.ast.2017.05.032
  21. Duc, N.D., Nguyen, P.D. and Khoa, N.D. (2017b), "Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin Wall Struct., 117, 178-189. https://doi.org/10.1016/j.tws.2017.04.013
  22. Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018a), "Nonlinear dynamic response of functionally graded porous porous plates on elastic foundation subjected to thermal and mechanical loads using the first order shear deformation theory", J. Appl. Comput. Mech., 4(4), 245-259. https://doi.org/10.22055/JACM.2018.23219.1151
  23. Duc, N.D., Khoa, N.D. and Thiem, H.T. (2018b), "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 25(13), 1156-1167. https://doi.org/10.1080/15376494.2017.1341581
  24. Duc, N.D., Kim, S.E. and Chan, D.Q. (2018c), "Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT", J Therm. Stress., 41(3), 331-365. https://doi.org/10.1080/01495739.2017.1398623
  25. Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment", Eur. J. Mech. A-Solid., 75, 355-366. https://doi.org/10.1016/j.compstruct.2015.05.072
  26. Foroutan, K., Shaterzadeh, A. and Ahmadi, H. (2018), "Nonlinear dynamic analysis of spiral stiffened functionally graded cylindrical shells with damping and nonlinear elastic foundation under axial compression", Struct. Eng. Mech., Int. J., 66(3), 295-303. https://doi.org/10.12989/sem.2018.66.3.295
  27. Fuller, C.C., Elliott, S. and Nelson, P.A. (1996), Active Control of Vibration, Academic Press.
  28. Ghiasian, S., Kiani, Y. and Eslami, M. (2013), "Dynamic buckling of suddenly heated or compressed fgm beams resting on nonlinear elastic foundation", Compos. Struct., 106, 225-234. https://doi.org/10.1016/j.compstruct.2013.06.001
  29. Hasheminejad, S.M. and Oveisi, A. (2016), "Active vibration control of an arbitrary thick smart cylindrical panel with optimally placed piezoelectric sensor/actuator pairs", Int. J. Mech. Mater. Des., 12(1), 1-16. https://doi.org/10.1007/s10999-015-9293-2
  30. Hong, S.Y. (1993), "Active vibration control of adaptive flexible structures using piezoelectric smart sensors and actuators", J. Acoust. Soc. Am., 93(2), 1205-1205. https://doi.org/10.1121/1.405523
  31. Jha, A. and Inman, D. (2002), "Piezoelectric actuator and sensor models for an inflated toroidal shell", Mech. Syst. Signal Pr., 16(1), 97-122. https://doi.org/10.1006/mssp.2001.1442
  32. Khoa, N.D., Thiem, H.T. and Duc, N.D. (2019), "Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 26(3), 248-259. https://doi.org/10.1080/15376494.2017.1341583
  33. Kiani, Y., Sadighi, M. and Eslami, M. (2013), "Dynamic analysis and active control of smart doubly curved FGM panels", Compos. Struct., 102, 205-216. https://doi.org/10.1016/j.compstruct.2013.02.031
  34. Kim, S.J., Hwang, J.S., Mok, J. and Ko, H.M. (2001), "Active vibration control of composite shell structure using modal sensor/actuator system", Smart. Struct. Integr. Syst., 4327, 688-697. https://doi.org/10.1117/12.436576
  35. Kumar, R.S. and Ray, M. (2013), "Active control of geometrically nonlinear vibrations of doubly curved smart sandwich shells using 1-3 piezoelectric composites", Compos. struct., 105, 173-187. https://doi.org/10.1016/j.compstruct.2013.03.010
  36. Kwak, M.K. and Yang, D.-H. (2013), "Active vibration control of a ring-stiffened cylindrical shell in contact with unbounded external fluid and subjected to harmonic disturbance by piezoelectric sensor and actuator", J. Sound Vib., 332(20), 4775-4797. https://doi.org/10.1016/j.jsv.2013.04.014
  37. Kwak, M.K., Heo, S. and Jeong, M. (2009), "Dynamic modelling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators", J. Sound Vib., 321(3-5), 510-524. https://doi.org/10.1016/j.jsv.2008.09.051
  38. Kwak, M.K., Yang, D.-H. and Lee, J.-H. (2012), "Active vibration control of a submerged cylindrical shell by piezoelectric sensors and actuatorsed", Int. Soc. Optics Photon., 8341, 83412F. https://doi.org/10.1117/12.916032
  39. Loghmani, A., Danesh, M., Kwak, M.K. and Keshmiri, M. (2017), "Vibration suppression of a piezo-equipped cylindrical shell in a broad-band frequency domain", J. Sound Vib., 411, 260-277. https://doi.org/10.1016/j.jsv.2017.08.051
  40. Ma, X., Jin, G. and Liu, Z. (2014), "Active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system", Int. J. Mech. Sci., 79, 182-194. https://doi.org/10.1016/j.ijmecsci.2013.12.010
  41. Moita, J.M.S., Correia, V.M.F., Martins, P.G., Soares, C.M.M. and Soares, C.A.M. (2006), "Optimal design in vibration control of adaptive structures using a simulated annealing algorithm", Compos. Struct., 75(1-4), 79-87. https://doi.org/10.1016/j.compstruct.2006.04.062
  42. Ogata, K. and Yang, Y. (2002), Modern Control Engineering, Prentice Hall, India.
  43. Pan, X. and Hansen, C. (1997), "Active control of vibration transmission in a cylindrical shell", J. Sound Vib., 203(3), 409-434. https://doi.org/10.1006/jsvi.1996.9987
  44. Pellicano, F. (2007), "Vibrations of circular cylindrical shells: Theory and experiments", J. Sound Vib., 303(1-2), 154-170. https://doi.org/10.1016/j.jsv.2007.01.022
  45. Plattenburg, J., Dreyer, J.T. and Singh, R. (2017), "Vibration control of a cylindrical shell with concurrent active piezoelectric patches and passive cardboard liner", Mech. Syst. Signal Pr., 91, 422-437. https://doi.org/10.1016/j.ymssp.2016.11.008
  46. Qin, Z., Chu, F. and Zu, J. (2017), "Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study", Int. J. Mech. Sci., 133, 91-99. https://doi.org/10.1016/j.ijmecsci.2017.08.012
  47. Roy, T. and Chakraborty, D. (2009), "Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm", J. Sound Vib., 319(1-2), 15-40. https://doi.org/10.1016/j.jsv.2008.05.037
  48. Sewall, J.L. and Naumann, E.C. (1968), "An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners", NASA TN D-4705.
  49. Sewall, J.L., Clary, R.R. and Leadbetter, S.A. (1964), "An experimental and analytical vibration study of a ring-stiffened cylindrical shell structure with various support conditions", NASA TN D-2398.
  50. Sheng, G. and Wang, X. (2009), "Active control of functionally graded laminated cylindrical shells", Compos. Struct., 90(4), 448-457. https://doi.org/10.1016/j.compstruct.2010.06.007
  51. Sheng, G. and Wang, X. (2010), "Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings", Compos. Struct., 93(1), 132-141. https://doi.org/10.1016/j.compstruct.2010.06.007
  52. Sohn, J.W., Jeon, J. and Choi, S.-B. (2014), "Active vibration control of ring-stiffened cylindrical shell structure using macro fiber composite actuators", J. Nanosci. Nanotechno., 14(10), 7526-7532. https://doi.org/10.1166/jnn.2014.9748
  53. Song, Z., Zhang, L. and Liew, K. (2016), "Active vibration control of cnt-reinforced composite cylindrical shells via piezoelectric patches", Compos. Struct., 158, 92-100. https://doi.org/10.1016/j.compstruct.2016.09.031
  54. Tan, X. and Vu-Quoc, L. (2005), "Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control", Int. J. Numer. Meth. Eng., 64(15), 1981-2013. https://doi.org/10.1002/nme.1433
  55. Thom, D.V., Kien, N.D., Duc, N.D., Duc, D.H. and Tinh, B.Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin-Wall. Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022
  56. Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  57. Volmir, A.S. (1972), Non-linear Dynamics of Plates and Shells, Science Edition M, USSR.
  58. Wrona, S. and Pawelczyk, M. (2013), "Controllability-oriented placement of actuators for active noise-vibration control of rectangular plates using a memetic algorithm", Arch. Acoust., 38(4), 529-536. https://doi.org/10.2478/aoa-2013-0062
  59. Yue, H., Lu, Y., Deng, Z. and Tzou, H. (2017), "Experiments on vibration control of a piezoelectric laminated paraboloidal shell", Mech. Syst. Signal Pr., 82, 279-295. https://doi.org/10.1016/j.ymssp.2016.05.023

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