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Original Articles

Free vibration analysis of curved lattice sandwich beams

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Pages 343-355 | Received 13 Apr 2022, Accepted 12 Aug 2022, Published online: 25 Aug 2022

References

  • A. A. Khdeir and O. J. Aldraihem, Free vibration of sandwich beams with soft core, Compos. Struct., vol. 154, pp. 179–189, 2016. DOI: 10.1016/j.compstruct.2016.07.045.
  • V. V. Volovoi, D. H. Hodges, C. E. S. Cesnik, and B. Popescu, Assessment of beam modeling methods for rotor blade applications, Math. Comput. Model., vol. 33, no. 10–11, pp. 1099–1112, 2001. DOI: 10.1016/S0895-7177(00)00302-2.
  • A. H. Akbarzadeh, J. W. Fu, L. Liu, Z. T. Chen, and D. Pasini, Electrically conducting sandwich cylinder with a planar lattice core under prescribed eigenstrain and magnetic field, Compos. Struct., vol. 153, pp. 632–644, 2016. DOI: 10.1016/j.compstruct.2016.06.058.
  • J. Xiong, Y. Du, D. Mousanezhad, M. Eydani Asl, J. Norato, and A. Vaziri, Sandwich structures with prismatic and foam cores: A review, Adv. Eng. Mater., vol. 21, no. 1, p. 1800036, 2019. DOI: 10.1002/adem.201800036.
  • E. M. Kerwin, Damping of flexural waves by a constrained viscoelastic layer, J. Acoust. Soc. Am., vol. 31, no. 7, pp. 952–962, 1959. DOI: 10.1121/1.1907821.
  • R. A. DiTaranto, Theory of vibratory bending for elastic and viscoelastic layered finite-length beams, J. Appl. Mech., vol. 32, no. 4, pp. 881–886, 1965. DOI: 10.1115/1.3627330.
  • D. J. Mead and S. Markus, The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions, J. Sound Vib., vol. 10, no. 2, pp. 163–175, 1969. DOI: 10.1016/0022-460X(69)90193-X.
  • D. J. Mead, A comparison of some equations for the flexural vibration of damped sandwich beams, J. Sound Vib., vol. 83, no. 3, pp. 363–377, 1982. DOI: 10.1016/S0022-460X(82)80099-0.
  • Y. Frostig and M. Baruch, Free vibrations of sandwich beams with a transversely flexible core: A high order approach, J. Sound Vib., vol. 176, no. 2, pp. 195–208, 1994. DOI: 10.1006/jsvi.1994.1368.
  • T. Sakiyama, H. Matsuda, and C. Morita, Free vibration analysis of sandwich beam with elastic or viscoelastic core by applying the discrete green function, J. Sound Vib., vol. 191, no. 2, pp. 189–206, 1996. DOI: 10.1006/jsvi.1996.0115.
  • M. G. Sainsbury and Q. J. Zhang, The Galerkin element method applied to the vibration of damped sandwich beams, Comput. Struct., vol. 71, no. 3, pp. 239–256, 1999. DOI: 10.1016/S0045-7949(98)00242-9.
  • J. R. Banerjee, Free vibration of sandwich beams using the dynamic stiffness method, Comput. Struct., vol. 81, no. 18–19, pp. 1915–1922, 2003. DOI: 10.1016/S0045-7949(03)00211-6.
  • R. A. S. Moreira and J. D. Rodrigues, Static and dynamic analysis of soft core sandwich panels with through-thickness deformation, Compos. Struct., vol. 92, no. 2, pp. 201–215, 2010. DOI: 10.1016/j.compstruct.2009.07.015.
  • P. Vidal and O. Polit, Vibration of multilayered beams using sinus finite elements with transverse normal stress, Compos. Struct., vol. 92, no. 6, pp. 1524–1534, 2010. DOI: 10.1016/j.compstruct.2009.10.009.
  • S. M. R. Khalili, N. Nemati, K. Malekzadeh, and A. R. Damanpack, Free vibration analysis of sandwich beams using improved dynamic stiffness method, Compos. Struct., vol. 92, no. 2, pp. 387–394, 2010. DOI: 10.1016/j.compstruct.2009.08.020.
  • A. S. Sayyad and Y. M. Ghugal, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Compos. Struct., vol. 129, pp. 177–201, 2015. DOI: 10.1016/j.compstruct.2015.04.007.
  • Y. Hui, G. Giunta, S. Belouettar, Q. Huang, H. Hu, and E. Carrera, A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements, Compos. B: Eng., vol. 110, pp. 7–19, 2017. DOI: 10.1016/j.compositesb.2016.10.065.
  • Y. Q. Wang and H. L. Zhao, Free vibration analysis of metal foam core sandwich beams on elastic foundation using Chebyshev collocation method, Arch. Appl. Mech., vol. 89, no. 11, pp. 2335–2349, 2019. DOI: 10.1007/s00419-019-01579-0.
  • A. Garg and H. Chalak, Novel higher-order zigzag theory for analysis of laminated sandwich beams, Proc. Inst. Mech. Eng. L, vol. 235, no. 1, pp. 176–194, 2021. DOI: 10.1177/1464420720957045.
  • K. Kohsaka, K. Ushijima, and W. J. Cantwell, Study on vibration characteristics of sandwich beam with BCC lattice core, Mater. Sci. Eng.: B, vol. 264, p. 114986, 2021. DOI: 10.1016/j.mseb.2020.114986.
  • H. Shu, Y. Xu, D. Mu, X. Wang, and Y. Wang, Analysis of vibration characteristics of elastic metamaterial sandwich beam, Int. J. Mod. Phys. B, vol. 35, no. 11, p. 2150160, 2021. DOI: 10.1142/S0217979221501605.
  • A.-J. Wang and D. L. McDowell, In-plane stiffness and yield strength of periodic metal honeycombs, J. Eng. Mater. Technol., vol. 126, no. 2, pp. 137–156, 2004. DOI: 10.1115/1.1646165.
  • L. J. Gibson, Cellular solids, MRS Bull., vol. 28, no. 4, pp. 270–274, 2003. DOI: 10.1557/mrs2003.79.
  • I. G. Masters and K. E. Evans, Models for the elastic deformation of honeycombs, Compos. Struct., vol. 35, no. 4, pp. 403–422, 1996. DOI: 10.1016/S0263-8223(96)00054-2.
  • R. M. Christensen, Mechanics of cellular and other low-density materials, Int. J. Solids Struct., vol. 37, no. 1–2, pp. 93–104, 2000. DOI: 10.1016/S0020-7683(99)00080-3.
  • A. J. Wang and D. L. McDowell, Yield surfaces of various periodic metal honeycombs at intermediate relative density, Int. J. Plast., vol. 21, no. 2, pp. 285–320, 2005. DOI: 10.1016/j.ijplas.2003.12.002.
  • H. Bart-Smith, J. W. Hutchinson, and A. G. Evans, Measurement and analysis of the structural performance of cellular metal sandwich construction, Int. J. Mech. Sci., vol. 43, no. 8, pp. 1945–1963, 2001. DOI: 10.1016/S0020-7403(00)00070-9.
  • S. Arabnejad and D. Pasini, Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods, Int. J. Mech. Sci., vol. 77, pp. 249–262, 2013. DOI: 10.1016/j.ijmecsci.2013.10.003.
  • M. S. A. Elsayed and D. Pasini, Multiscale structural design of columns made of regular octet-truss lattice material, Int. J. Solids Struct., vol. 47, no. 14-15, pp. 1764–1774, 2010. DOI: 10.1016/j.ijsolstr.2010.03.003.
  • Z-j Zhang, B. Han, Q-c Zhang, and F. Jin, Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores, Compos. Struct., vol. 171, pp. 335–344, 2017. DOI: 10.1016/j.compstruct.2017.03.045.
  • J. Lou, B. Wang, L. Ma, and L. Wu, Free vibration analysis of lattice sandwich beams under several typical boundary conditions, Acta Mech. Solida Sin., vol. 26, no. 5, pp. 458–467, 2013. DOI: 10.1016/S0894-9166(13)60041-5.
  • H. Gu, A. D. Shaw, M. Amoozgar, J. Zhang, C. Wang, and M. I. Friswell, Twist morphing of a composite rotor blade using a novel metamaterial, Compos. Struct., vol. 254, p. 112855, 2020. DOI: 10.1016/j.compstruct.2020.112855.
  • C. S. Chang and D. H. Hodges, Vibration characteristics of curved beams, J. Mech. Mater. Struct., vol. 4, no. 4, pp. 675–692, 2009. DOI: 10.2140/jomms.2009.4.675.
  • F. Yang, R. Sedaghati, and E. Esmailzadeh, Free in-plane vibration of curved beam structures: A tutorial and the state of the art, J. Vib. Control, vol. 24, no. 12, pp. 2400–2417, 2018. DOI: 10.1177/1077546317728148.
  • N. M. Auciello and M. A. De Rosa, Free vibrations of circular arches: A review, J. Sound Vib., vol. 176, no. 4, pp. 433–458, 1994. DOI: 10.1006/jsvi.1994.1388.
  • P. Mardanpour, E. Izadpanahi, S. Rastkar, S. A. Fazelzadeh, and D. H. Hodges, Geometrically exact, fully intrinsic analysis of pre-twisted beams under distributed follower forces, AIAA J., vol. 56, no. 2, pp. 836–848, 2018. DOI: 10.2514/1.J055744.
  • Y. Wasserman, The influence of the behaviour of the load on the frequencies and critical loads of arches with flexibly supported ends, J. Sound Vib., vol. 54, no. 4, pp. 515–526, 1977. DOI: 10.1016/0022-460X(77)90609-5.
  • K. J. Kang, C. W. Bert, and A. G. Striz, Vibration and buckling analysis of circular arches using DQM, Comput. Struct., vol. 60, no. 1, pp. 49–57, 1996. DOI: 10.1016/0045-7949(95)00375-4.
  • M. A. De Rosa and C. Franciosi, Exact and approximate dynamic analysis of circular arches using DQM, Int. J. Solids Struct., vol. 37, no. 8, pp. 1103–1117, 2000. DOI: 10.1016/S0020-7683(98)00275-3.
  • B. K. Lee, S. J. Oh, and K. K. Park, Free vibrations of shear deformable circular curved beams resting on elastic foundations, Int. J. Str. Stab. Dyn., vol. 02, no. 01, pp. 77–97, 2002. DOI: 10.1142/S0219455402000440.
  • J.-D. Yau, Vibration of parabolic tied-arch beams due to moving loads, Int. J. Str. Stab. Dyn., vol. 06, no. 02, pp. 193–214, 2006. DOI: 10.1142/S0219455406001915.
  • J.-S. Wu and L.-K. Chiang, Free vibration analysis of arches using curved beam elements, Int. J. Numer. Methods Eng., vol. 58, no. 13, pp. 1907–1936, 2003. DOI: 10.1002/nme.837.
  • F. F. Çalım, Forced vibration of curved beams on two-parameter elastic foundation, Appl. Math. Model., vol. 36, no. 3, pp. 964–973, 2012. DOI: 10.1016/j.apm.2011.07.066.
  • J. S. Wu, F. T. Lin, and H. J. Shaw, Free in-plane vibration analysis of a curved beam (arch) with arbitrary various concentrated elements, Appl. Math. Model., vol. 37, no. 14–15, pp. 7588–7610, 2013. DOI: 10.1016/j.apm.2013.02.029.
  • H. Babaei, Y. Kiani, and M. R. Eslami, Large amplitude free vibration analysis of shear deformable FGM shallow arches on nonlinear elastic foundation, Thin-Walled Struct., vol. 144, p. 106237, 2019. DOI: 10.1016/j.tws.2019.106237.
  • M. Zare, Free in-plane vibration of cracked curved beams: Experimental, analytical, and numerical analyses, Proc. Inst. Mech. Eng. C, vol. 233, no. 3, pp. 928–946, 2019. DOI: 10.1177/0954406218762956.
  • M. R. Amoozgar, A. D. Shaw, and M. I. Friswell, The effect of curved tips on the dynamics of composite rotor blades, Aerosp. Sci. Technol., vol. 106, p. 106197, 2020. DOI: 10.1016/j.ast.2020.106197.
  • M. R. Amoozgar and H. Shahverdi, Aeroelastic stability analysis of curved composite blades in hover using fully intrinsic equations, Int. J. Aeronaut. Space Sci., vol. 20, no. 3, pp. 653–663, 2019. DOI: 10.1007/s42405-019-00161-w.
  • M. R. Amoozgar, S. A. Fazelzadeh, H. Haddad Khodaparast, M. I. Friswell, and J. E. Cooper, Aeroelastic stability analysis of aircraft wings with initial curvature, Aerosp. Sci. Technol., vol. 107, p. 106241, 2020. DOI: 10.1016/j.ast.2020.106241.
  • D. H. Hodges, Geometrically exact, intrinsic theory for dynamics of curved and twisted anisotropic beams, AIAA J., vol. 41, no. 6, pp. 1131–1137, 2003. DOI: 10.2514/2.2054.

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