Computers and Concrete

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Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution

  • Yazdani, Raziye (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.08.29
  • Accepted : 2019.10.22
  • Published : 2019.12.25
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Abstract

In this paper, wave propagation of double-bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and carbon nanotube reinforced composite (CNTRC) face sheets are investigated subjected to multi-physical loadings with temperature dependent material properties. The governing equations of motion are derived by Hamilton's principle. Then, the influences of various parameters such as wave number, CNT volume fraction, temperature change, Skempton coefficient, material length scale parameter, porosity coefficient on the phase velocity of double-bonded micro sandwich shell are taken into account. It is seen that by increasing of Skempton coefficient, the phase velocity decreases for higher wave number and the results become approximately the constant. Also, by increasing of the material length scale parameter, the cut of frequency increases, because the stiffness of micro structure increases. The obtained results for this article can be used to detect, locate and quantify crack.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Al-Kamal, M.K. (2019), "Nominal axial and flexural strengths of high-strength concrete columns", Comput. Concrete, 24(1), 85-94. https://doi.org/10.12989/cac.2019.24.1.085.
  2. Ansari, R., Gholami, R. and Sahmani, S. (2011), "Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory", Compos. Struct., 94, 221-228. https://doi.org/10.1016/j.compstruct.2011.06.024.
  3. Arani, A.G., Pourjamshidian, M. and Arefi, M. (2017), "Influence of electro-magneto-thermal environment on the wave propagation analysis of sandwich nano-beam based on nonlocal strain gradient theory and shear deformation theories", Smart Struct. Syst., 20(3), 329-342. https://doi.org/10.12989/sss.2017.20.3.329.
  4. Cong, P.H., Chienc, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermo mechanical 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.
  5. Do, T.V., Nguyen, D.K., Duc, N.D., Doan, D.H. and Bui, T.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.
  6. Doyle, J.F. (1997), Wave Propagation in Structures, New York, USA.
  7. 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.
  8. Duc, N.D. (2016), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 1-28. https://doi.org/10.1177/1099636216653266.
  9. 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.
  10. 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.
  11. Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FGCNTRC double curved shallow shells in thermal environment", Eur. J. Mech., A Solid., 75, 355-366. https://doi.org/10.1016/j.euromechsol.2019.01.024.
  12. Erofeev, V.I. and Mal'khanov, A.O. (2017), "Localized strain waves in a nonlinearly elastic conducting medium interacting with a magnetic field", Mech. Solid., 52(2), 224-231. https://doi.org/10.3103/S0025654417020121.
  13. Farahani, H. and Barati, F. (2015), "Vibration of sumberged functionally graded cylindrical shell based on first order shear deformation theory using wave propagation method", Struct. Eng. Mech., 53(3), 575-587. https://doi.org/10.12989/sem.2015.53.3.575.
  14. Farajpour, A., Hairi Yazdi, MR., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplate", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039.
  15. Frikha, A., Zghal, S. and Dammak, F. (2018), "Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element", Aerosp. Sci. Technol., 78, 438-451. https://doi.org/10.1016/j.ast.2018.04.048.
  16. Ghorbanpour Arani, A., Jalilvand, A. and Haghparast, E. (2018), "Theoretical investigation on wave propagation in embedded DWBNNT conveying ferrofluid via stress and strain-inertia gradient elasticity", Proc. Inst. Mech. Eng., Part L: J. Mater.: Des. Appl., 232(9), 719-732. https://doi.org/10.1177/1464420716644761.
  17. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016), "Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory", Compos. Part B: Eng., 95, 209-224. https://doi.org/10.1016/j.compositesb.2016.03.077.
  18. 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, 10596-10615. https://doi.org/10.1016/j.apm.2016.07.033.
  19. Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Composite Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189.
  20. Ghorbanpour Arani, A.H., Rastgoo, A., Hafizi Bidgoli, A., Kolahchi, R. and Ghorbanpour Arani, A. (2017), "Wave propagation of coupled double-DWBNNTs conveying fluid-systems using different nonlocal surface piezoelasticity theories", Mech. Adv. Mater. Struct., 24(14), 1159-1179. https://doi.org/10.1080/15376494.2016.1227488.
  21. Hossein Hosseini, S.M., Duczek, S. and Gabbert, U. (2013), "Non-reflecting boundary condition for Lamb wave propagation problems in honeycomb and CFRP plates using dashpot elements", Compos. Part B: Eng., 54, 1-10. https://doi.org/10.1016/j.compositesb.2013.04.061.
  22. Hossein Hosseini, S.M., Kharaghani, A., Kirsch, C. and Gabbert, U. (2013), "Numerical simulation of Lamb wave propagation in metallic foam sandwich structures: a parametric study", Compos. Struct., 97, 387-400. https://doi.org/10.1016/j.compstruct.2012.10.039.
  23. Jamali, M., Arani, A.G., Mosayyebi, M., Kolahchi, R. and Esfahani, R.T. (2017), "Wave propagation behavior of coupled viscoelastic FG-CNTRPC micro plates subjected to electro-magnetic fields surrounded by orthotropic visco-Pasternak foundation", Microsyst. Technol., 23(8), 3791-3816. https://doi.org/10.1007/s00542-016-3232-5.
  24. Kakar, R. (2015), "SH-wave propagation in a heterogeneous layer over an inhomogeneous isotropic elastic half-space", Earthq. Struct., 9(2), 305-320. https://doi.org/10.12989/eas.2015.9.2.305.
  25. Ke, L.L., Liu, C.H. and Wang, Y. (2015), "Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions", Physica E, 66, 93-106. https://doi.org/10.1016/j.physe.2014.10.002.
  26. 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.
  27. Li, Y.S. and Pan, E. (2015), "Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory", Int. J. Eng. Sci., 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009.
  28. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. http://dx.doi.org/10.12989/sem.2016.59.3.431.
  29. 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.
  30. Mohammadimehr, M. and Shahedi, S. (2016), "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B, 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040.
  31. Mohammadimehr, M., Farahi, M.J. and Alimirzaei, S. (2016a), "Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory", Appl. Math. Mech. (English Ed.), 37(10), 1375-1392. https://doi.org/10.1007/s10483-016-2138-9.
  32. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016c), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method", Appl. Math. Mech. (English Ed.), 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9.
  33. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2017b), "Dynamic stability of modified strain gradient theory sinusoidal viscoelastic piezoelectric polymeric functionally graded single-walled carbon nanotubes reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Struct., 24(16), 1325-1342. https://doi.org/10.1080/15376494.2016.1227507.
  34. Mohammadimehr, M., Okhravi, S.V. and Akhavan Alavi, S.M. (2018), "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.
  35. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016b), "Bending buckling and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temprature-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. Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2017a), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622.
  37. Mohammadimehr, M., Zarei, H.B., Parakandeh, A. and Arani, A.G. (2017c), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., 64(3), 361-379. https://doi.org/10.12989/sem.2017.64.3.361.
  38. Murmu, T., McCarthy, MA. and Adhikari, S. (2012), "Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nanlocal elasticity approach", J. Sound Vib., 331, 5069-5086. https://doi.org/10.1016/j.jsv.2012.06.005.
  39. Narendar, S. and Gopalakrishnan, S. (2012), "Study of terahertz wave propagation properties in nanoplates with surface and small-scale effects", Int. J. Mech. Sci., 64(1), 221-231. https://doi.org/10.1016/j.ijmecsci.2012.06.012.
  40. Netrebko, A.V. (2013), "Wave propagation in an elastic structure modeling a split Hopkinson pressure bar", Mech. Solid., 48(4), 473-481. https://doi.org/10.3103/S0025654413040158.
  41. Parate, K.N. and Kumar, R. (2019), "Shear strength model for reinforced concrete beam-column joints based on hybrid approach", Comput. Concrete, 23(6), 377-398. https://doi.org/10.12989/cac.2019.23.6.377.
  42. Porokhovs'kyi, V.V. (2009), "Plane problem of interaction between an elastic longitudinal wave and a cylindrical shell with axial cut", J. Math. Sci., 160(4), 443-452. https://doi.org/10.1007/s10958-009-9516-x.
  43. Pourasghar, A. and Kamarian, S. (2016), "Thermoelastic response of CNT reinforced cylindrical panel resting on elastic foundation using theory of elasticity", Mater. Des., 49, 583-590. https://doi.org/10.1016/j.compositesb.2016.06.028.
  44. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.
  45. Rasulova, N.B. and Shamilova, G.R. (2016), "Stress wave propagation in a rectangular bar", Mech. Solid., 51(4), 495-500. https://doi.org/10.1016/0020-7683(69)90020-1.
  46. Rozhkova, E.V. (2018), "To the investigation of plane wave propagation in an elastic anisotropic media by a recursive operator method", Mech. Solid., 53(1), 33-44. https://doi.org/10.3103/S0025654418010041.
  47. Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2019), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B: Eng., 161, 44-54. https://doi.org/10.1016/j.compositesb.2018.10.049.
  48. Saidi, A.R., Bahaadini, R. and Majidi-Mozafari, K. (2019), "On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading", Compos. Part B: Eng., 164, 778-799. https://doi.org/10.1016/j.compositesb.2019.01.074.
  49. Sellappan, P., Wang, E., Espinoza Santos, C.J., On, T. and Kriven, W.M. (2015), "Wave propagation through alumina-porous alumina laminates", J. Eur. Ceram. Soc., 35(1), 197-210. https://doi.org/10.1016/j.jeurceramsoc.2014.08.013.
  50. Shamaev, A.S. and Shumilova, V.V. (2017), "Plane acoustic wave propagation through a composite of elastic and Kelvin-Voigt viscoelastic material layers", Mech. Solid., 52(1), 25-34. https://doi.org/10.3103/S0025654417010046.
  51. Shariyat, M., Jahanshahi, S. and Rahimi, H. (2019) "Nonlinear Hermitian generalized hygrothermoelastic stress and wave propagation analyses of thick FGM spheres exhibiting temperature, moisture, and strain-rate material dependencies", Compos. Struct., 229, 111364. https://doi.org/10.1016/j.compstruct.2019.111364.
  52. Sobhy, M. and Zenkour, A.M. (2018), "Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate", Compos. Part B: Eng., 154, 492-506. https://doi.org/10.1016/j.compositesb.2018.09.011.
  53. Sorokin, S.V. and Grishina, S.V. (2004), "Analysis of wave propagation in sandwich beams with parametric stiffness modulations", J. Sound Vib., 27 (3-5), 1063-1082. https://doi.org/10.1016/j.jsv.2003.03.005.
  54. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  55. Tornabene, F., Fantuzzi, N., Viola, E. and Batra, R.C. (2015), "Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory", Compos. Struct., 119(1), 67-89. https://doi.org/10.1016/j.compstruct.2014.08.005.
  56. Tornabene, F., Liverani, L. and Caligiana, G. (2011), "FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations", Int. J. Mech. Sci., 53(6), 446-470. https://doi.org/10.1016/j.ijmecsci.2011.03.007.
  57. Wu, K., Zhai, J., Xue, J., Xu, F. and Zhao, H. (2019), "Experimental study on shear damage and lateral stiffness of transfer column in SRC-RC hybrid structure", Comput. Concrete, 23(5), 335-349. https://doi.org/10.12989/cac.2019.23.5.335.
  58. Xu, X. and Deng, Z. (2016), "Wave propagation characteristics in thick conventional and auxetic cellular plates", Acta Mechanica Solida Sinica, 29(2), 159-166. https://doi.org/10.1016/S0894-9166(16)30104-5.
  59. Zghal, S., Frikha, A. and Dammak, F. (2018), "Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels", Compos. Part B, 150, 165-183. https://doi.org/10.1016/j.compositesb.2018.05.037.

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