Steel and Composite Structures

  • 제39권5호
  • /
  • Pages.615-630
  • /
  • 2021
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Flutter phenomenon in composite sandwich beams with flexible core under follower force

  • 투고 : 2020.07.09
  • 심사 : 2020.04.09
  • 발행 : 2021.06.10
⟨ 이전 논문 다음 논문 ⟩

초록

The main purpose of the present work was to study the dynamic instability of a three-layered, thick composite sandwich beam with the functionally graded (FG) flexible core subjected to an axial compressive follower force. Flutter instability of a sandwich cantilever beam was analyzed using the high-order theory of sandwich beams, for the first time. The governing equations in general for sandwich beams with an FG core were extracted and could be used for all types of sandwich beams with any types of face sheets and cores. A polynomial function is considered for the vertical distribution of the displacement field in the core layer along the thickness, based on the results of the first Frosting's higher order model. The governing partial differential equations and the equations of boundary conditions of the dynamic system are derived using Hamilton's principle. By applying the boundary conditions and numerical solution methods of squares quadrature, the beam flutter phenomenon is studied. In addition, the effects of different geometrical and material parameters on the flutter threshold were investigated. The results showed that the responses of the dynamic instability of the system were influenced by the follower force, the coefficients of FGs and the geometrical parameters like the core thickness. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory. The results showed that the follower force of the flutter phenomenon threshold for long beams tends to the corresponding results in the Timoshenko beam.

키워드

참고문헌

  1. Alidoost, H. and Rezaeepazhand, J. (2017), "Instability of a delaminated composite beam subjected to a concentrated follower force", Thin-Wall. Struct., 120, 191-202. https://doi.org/10.1016/j.tws.2017.08.032.
  2. Alkhaldi, H.S., Alshaikh, I.A., Mallouh, R.A. and Ghazal, O. (2014), "Closed-form solution of large deflection of a springhinged beam subjected to non-conservative force and tip end moment", Eur. J. Mech. - A/Solids, 47, 271-279. https://doi.org/10.1016/j.euromechsol.2014.02.019.
  3. Asgari, GH., Payganeh, GH. and Malekzadeh Fard, K. (2019), "Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations", Struct. Eng. Mech., 72(4), 525-540. https://doi.org/10.12989/sem.2019.72.4.525.
  4. Beck, M. (1952), "Die Knicklast des einseitig eingespannten, tangential gedruckten Stabes (The buckling load of the cantilever column subjected to tangential force)", Zeitsehrift fur angexvandte Malliematik und Physik ZAMP, 3, 225-228. https://doi.org/10.1007/BF02008828.
  5. Behdinan, K., Moradi-Dastjerdi, R., Safaei, B., Qin, Z., Chu, F. and Hui, D. (2020) "Graphene and CNT impact on heat transfer response of nanocomposite cylinders", Nanotech. Rev., 9(1), 41-52. https://doi.org/10.1515/ntrev-2020-0004.
  6. Chang, S. (2012), Differential quadrature and its application in engineering, Springer Science & Business Media.
  7. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech., 68(6), 721-733. http://doi.org/10.12989/sem.2018.68.6.721.
  8. Delale, F. and Erdogan, F. (1993), "The crack problem for a nonhomogeneous plane," J. Appl. Mech., 50(3), 609-614. http://doi.org/10.1115/1.3167098.
  9. Deng, H.Q., Li, T.J, Xue, B.J and Wang, Z.W. (2015), "Analysis of thermally induced vibration of cable-beam structures", Constr. Steel Res., 53(3), 443-453. https://doi.org/10.12989/sem.2015.53.3.443.
  10. Du, H., Lim, M.K. and Lim, R.M. (1994) "Application of generalized differential quadrature method to structural problems", Numer. Method. Eng., 37, 1881-1896. https://doi.org/10.1002/nme.1620371107.
  11. Dwivedy, S.K., Sahu, K.C. and Babu. SK. (2007), "Parametric instability regions of three layered soft-cored sandwich beam using higher order theory", J. Sound Vib., 304(1-2), 326-344. https://doi.org/10.1016/j.jsv.2007.03.016.
  12. Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.
  13. Fattahi, A.M., Safaei, B. And Ahmed, N.A. (2019a), "A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets", Eur. Phys. J. Plus, 134(11), 555. https://doi.org/10.1140/epjp/i2019-12912-7.
  14. Fattahi, A.M., Safaei, B. and Moaddab, E. (2019b), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., 32(2), 281-292. http://dx.doi.org/10.12989/scs.2019.32.2.281.
  15. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Jorge, R.M.N. (2006), "Natural frequencies of functionally graded plates by a meshless method", Compos. Struct., 75(1-4), 593-600. https://doi.org/10.1016/j.compstruct.2006.04.018.
  16. Foroutan, M., Moradi-Dastjerdi, R. and Sotoodeh-Bahreini, R. (2012), "Static analysis of FGM cylinders by a mesh-free method", Steel Compos. Struct., 12(1), 1-11. https://doi.org/10.12989/scs.2012.12.1.001.
  17. Frostig, Y. and Thomsen, O.T. (2004), "High-order free vibrations of sandwich panels with a flexible core", Int. J. Solid. Struct., 41(5-6), 1697-1724. https://doi.org/10.1016/j.ijsolstr.2003.09.051.
  18. Ganapathi, M. and Varadan, T.K. (1995), "Supersonic flutter of laminated curved panels", Defence Sci. J., 45(2), 147-159. https://doi.org/10.14429/dsj.45.4114.
  19. Gao, W., Qin, Z. and Chu, F. (2020) "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerosp. Sci. Technol., 102, 105860. https://doi.org/10.1016/j.ast.2020.105860.
  20. Ghanati, P. and Safaei, B. (2019), "Elastic buckling analysis of polygonal thin sheets under compression", Indian J. Phys., 93(1), 47-52. https://doi.org/10.1007/s12648-018-1254-9.
  21. Goyala, V.K. and Kapania, R.K. (2008), "Dynamic stability of laminated beams subjected to non-conservative loading", Thin-Wall. Struct., 46(12), 1359-1369. https://doi.org/10.1016/j.tws.2008.03.014.
  22. Kahya, V. and Turan, M. (2018) "Vibration and buckling of laminated beams by a multi-layer finite element model", Steel Compos. Struct., 28(4), 415-426. https://doi.org/10.12989/scs.2018.28.4.415.
  23. Kar, R.C. and Hauger, W. (1982), "Stability of a pretwisted tapered cantilever beam subjected to dissipative and follower forces", J. Sound Vib., 81(4), 565-573. https://doi.org/10.1016/0022-460X(82)90297-8.
  24. Katariya, P.V. and Panda, S.K. (2019) "Frequency and Deflection Responses of Shear Deformable Skew Sandwich Curved Shell Panel: A Finite Element Approach", Arabian J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0.
  25. Katariya, P.V. and Panda, S.K. (2020) "Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect", Steel Compos. Struct., 34(2), 279-288. https://doi.org/10.12989/scs.2020.34.2.279.
  26. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017) "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595.
  27. Katariya, P.V., Hirwani, C.k. and Panda, S.K. (2019) "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35, 467-485. https://doi.org/10.1007/s00366-018-0609-3.
  28. Katariya, P.V., Panda, S.K. and Thakare, O. (2018) "Bending and vibration analysis of skew sandwich plate", Aircraft Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087.
  29. Khalili, S.M.R., Tafazoli, S. and Malekzadeh Fard, K. (2011), "Free vibrations of laminated composite shells with uniformly distributed attached mass using higher order shell theory including stiffness effect", J. Sound Vib., 330(26), 6355-6371. https://doi.org/ 10.1016/j.jsv.2011.07.004.
  30. Kheirikhah, M.M., Khalili, S.M.R. and Malekzadeh Fard, K. (2012), "Analytical solution for bending analysis of soft-core composite sandwich plates using improved high-order theory", Struct. Eng. Mech., 44(1), 15-34. https://doi.org/10.12989/sem.2012.44.1.015.
  31. Kim, N.I. and Lee, J. (2014), "Divergence and flutter behavior of Beck's type of laminated box beam", Int. J. Mech. Sci., 84, 91-101. https://doi.org/10.1016/j.ijmecsci.2014.04.014.
  32. Leipholz, H.H.E. (1972), "On the sufficiency of the energy criterion for the stability of certain nonconservative systems of the follower-load type", J. Appl. Mech., 39(3), 717-722. https://doi.org/10.1115/1.3422778.
  33. Li, H., Wu, T., Gao, Z., Wang, X., Ma, H., Han, Q. and Qin, Z. (2020), "An iterative method for identification of temperature and amplitude dependent material parameters of fiber-reinforced polymer composites", Int. J. Mech. Sci., 184, 105818. DOI: https://doi.org/10.1016/j.ijmecsci.2020.105818.
  34. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  35. Li, Q.S. (2008), "Stability of non-uniform columns under the combined action of concentrated follower forces and variably distributed loads", J. Constr. Steel Res., 64(3), 367-376. https://doi.org/10.1016/j.jcsr.2007.07.006.
  36. Ma, R., Wei, J.Z., Tan, H.F. and Yang, Z.H. (2018), "Modal analysis of inflated membrane cone considering pressure follower force effect", Thin-Wall. Struct., 132, 596-603. https://doi.org/10.1016/j.tws.2018.09.007.
  37. Malekzadeh Fard, K. (2014), "Higher order free vibration of sandwich curved beams with a functionally graded core", Struct. Eng. Mech., 49(5), 537-554. https://doi.org/10.12989/sem.2014.49.5.537.
  38. Malekzadeh Fard, K., Livani, M., veisi, A. and Gholami, M. (2014), "Improved high-order bending analysis of double curved sandwich panels subjected to multiple loading conditions", Latin Am. J. Solid. Struct., 11(9), 1591-1614. https://doi.org/10.1590/S1679-78252014000900006.
  39. Malekzadeh, K., Khalili, M.R. and Mittal, R.K. (2005), "Local and global damped vibrations of plates with a viscoelastic soft flexible core: An improved high-order approach", J. Sandwich Struct. Mater., 7(5), 431-456. https://doi.org/10.1177/1099636205053748.
  40. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019) "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002.
  41. Meunier, M. and Shenoi, R.A. (1999), "Free vibration analysis of composite sandwich plates", J. Mech. Eng. Sci., 213(7), 715-727. https://doi.org/10.1177/095440629921300707.
  42. Moradi-Dastjerdi, R. and Behdinan, K. (2019) "Thermoelastic static and vibrational behaviors of nanocomposite thick cylinders reinforced with graphene", Steel Compos. Struct., 31(5), 529-539. https://doi.org/10.12989/scs.2019.31.5.529.
  43. Moradi-Dastjerdi, R. and Behdinan, k. (2020), "Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers", Int. J. Mech. Sci., 167, 105283. https://doi.org/10.1016/j.ijmecsci.2019.105283.
  44. Moradi-Dastjerdi, R., Behdinan, k., Safaei, B. and Qin, Z. (2020a), "Buckling behavior of porous CNT-reinforced plates integrated between active piezoelectric layers", Eng. Struct., 222, 111141. https://doi.org/10.1016/j.engstruct.2020.111141.
  45. Moradi-Dastjerdi, R., Behdinan, k., Safaei, B. and Qin, Z. (2020b), "Static performance of agglomerated CNT-reinforced porous plates bonded with piezoceramic faces", Int. J. Mech. Sci., 188, 105966. https://doi.org/10.1016/j.ijmecsci.2020.105966.
  46. Nayak, B., Sastri, J.B.S., Dwivedy, S.K. and Murthy, K.S.R.K. (2012), "A Comparative Study of The Classical and Higher Order Theory for Free Vibration Analysis of MRE Cored Sandwich Beam with Composite Skins Using Finite Element method", Proceedings of the IEEE-International Conference on Advances in Engineering, Nagapattinam, Tamil Nadu, India, March.
  47. Nikolai, E. L. (1928), On the Stability of the Rectilinear Form of Equilibrium of a Bar in Compression and Torsion, Leningrad Polytekhn: Inv.
  48. Noor, A.K., Peters, J.M. and Burton, W.S. (1994), "Three-dimensional solutions for initially stressed structural sandwiches", J. Eng. Mech. - ASCE, 120(2), 284-303. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:2(284).
  49. Park, w.t., Han, S.CH., Jung, W.H. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  50. Phan, Duc.H. and Kobayshi, H. (2013), "Analytical and experimental study on aerodynamic control of flutter and buffeting of bridge deck by using mechanically driven flaps", Struct. Eng. Mech., 46(4), 549-569. https://doi.org/10.12989/sem.2013.46.4.549.
  51. Pourasghar, A. and Kamarian, S. (2015), "Dynamic stability analysis of functionally graded nanocomposite non-uniform column reinforced by carbon nanotube", J. Vib. Control, 21(13), 2499-2508. https://doi.org/10.1177/1077546313513625.
  52. 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.
  53. Qin, Z., Safaei, B., Pang, X. and Chu, F. (2019a) "Traveling wave analysis of rotating functionally graded graphene platelet reinforced nanocomposite cylindrical shells with general boundary conditions", Results in Phys., 15, 102752. https://doi.org/10.1016/j.rinp.2019.102752.
  54. Qin, Z., Yang, Z., Zu, J. and Chu, F. (2018) "Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates", Int. J. Mech. Sci., 142-143, 127-139. https://doi.org/10.1016/j.ijmecsci.2018.04.044.
  55. Qin, Z., Zhao, S., Pang, X., Safaei, B. and Chu, F. (2019b) "Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions", Compos. Struct., 220, 847-860. https://doi.org/10.1016/j.compstruct.2019.04.046.
  56. Qin, Z., Zhao, S., Pang, X., Safaei, B. and Chu, F. (2020) "A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions", Int. J. Mech. Sci., 170, 105341. https://doi.org/10.1016/j.ijmecsci.2019.105341.
  57. Ramteke, P.M., Mehar, K., Sharma, N. and Panda, S.K. (2020), "Numerical Prediction of Deflection and Stress Responses of Functionally Graded Structure for Grading Patterns (Power-Law, Sigmoid and Exponential) and Variable Porosity (Even and Uneven)", Scientia Iranica. http://dx.doi.org/10.24200/sci.2020.55581.4290.
  58. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. http://dx.doi.org/10.12989/scs.2019.33.6.865.
  59. Reddy, J.N. (1998), Thermomechanical behavior of functionally graded materials, A&M University, College Station, Texas, USA.
  60. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells Theory and Analysis, (2nd Edition), CRC Press, New York, NY, USA.
  61. Safaei, B. (2020) "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct., 35(5), 659-670. https://doi.org/10.12989/scs.2020.35.5.659.
  62. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019a), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv. Nano Res., 7(4), 265-275. http://dx.doi.org/10.12989/anr.2019.7.4.265.
  63. Safaei, B., Moradi-Dastjerdi, R., Qin, Z., Behdinan, K. and Chu, F. (2019b) "Determination of thermoelastic stress wave propagation in nanocomposite sandwich plates reinforced by clusters of carbon nanotubes", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636219848282.
  64. Sahmani, S. and Safaei, B. (2021), "Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect", Appl. Math. Model., 89, 1792-1813. https://doi.org/10.1016/j.apm.2020.08.039.
  65. Sahoo, R. and Singh, B.N. (2015), "Dynamic Instabilit of laminated-Composite and sandwich plate using a new inverse Trigonometric Zigzag Theory", J. Vib. Acoust., 137(6), 061001. https://doi.org/10.1115/1.4030716.
  66. Sarath Babu, C. and Kant, T. (1999), "Two shear deformable finite element models for buckling analysis of skew fiber-reinforced composite and sandwich panels", Compos. Struct., 46(2), 115-124. https://doi.org/10.1016/S0263-8223(99)00039-2.
  67. Sawyer, J.W. (1977), "Flutter and buckling of general laminated plates", J. Aircraft, 14(4), 387-393. https://doi.org/10.2514/3.58789.
  68. Sharma, N., Mahapatra, T.R., Panda, S.K. and Mehar, K. (2018), "Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model", Steel Compos. Struct., 28(5), 629-639. DOI: http://dx.doi.org/10.12989/scs.2018.28.5.629.
  69. Shen, H.S. and Li, S.R. (2008), "Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties", Compos. Part B: Eng., 39(2), 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004.
  70. Shen, H.S. and Xia, X.K. (2008), "Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment", J. Sound Vib., 314(1-2), 254-274. https://doi.org/10.1016/j.jsv.2008.01.019.
  71. Simitses, G.J. and Hodges, D.H. (2006), Fundamentals of Structural Stability, Butterworth-Heinemann Limited, Oxford, UK, England.
  72. Smyczynski, M.J. and Magnucka-Blandzi, E. (2015), "Static and dynamic stability of an axially compressed five-layer sandwich beam", Thin-Wall. Struct., 90, 23-30. https://doi.org/10.1016/j.tws.2015.01.005.
  73. Sun, W., Ding, ZH., Qin, ZH., Chu, F. and Han, Q. (2020), "Wind energy harvesting based on fluttering double-flag type triboelectric nanogenerators", Nano Energy, 70, 104526. https://doi.org/10.1016/j.nanoen.2020.104526.
  74. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B: Eng., 67, 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012.
  75. Trahair, N.S. (2014), "Bending and buckling of tapered steel beam structures", Eng. Struct., 59, 229-237. https://doi.org/10.1016/j.engstruct.2013.10.031.
  76. Wang, Q. (2003), "On complex flutter and buckling analysis of a beam structure subjected to static follower force", Struct. Eng. Mech., 16(5), 533-556. https://doi.org/10.12989/sem.2003.16.5.533.
  77. Wang, X. and Wang, Y. (2004) "Free vibration analyses of thin sector plates by the new version of differential quadrature method", Comput. Method. Appl. M., 193(36-38), 3957-3971. https://doi.org/10.1016/j.cma.2004.02.010.
  78. Xiao, Q.X, Zou, J., Lee, K.Y and Li, X.F. (2017), "Surface effects on flutter instability of nanorod under generalized follower force", Struct. Eng. Mech., 64(6), 723-730. https://doi.org/10.12989/sem.2017.64.6.723.
  79. Xu, K., Yuan, Y. and Li, M. (2019), "Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets", Steel Composite Structures, 32(5), 633-642. https://doi.org/10.12989/scs.2019.32.5.633.
  80. Yas, M.H., Kamarian, S. and Pourasghar, A. (2017), "Free vibration analysis of functionally graded beams resting on variable elastic foundations using a generalized power-law distribution and GDQ method", Annals of Solid and Structural Mechanics volume, 9(6), 1-11. https://doi.org/10.1007/s12356-017-0046-9