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Vibration of a composite elastic beam on an inhomogeneous elastic foundation

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Języki publikacji
EN
Abstrakty
EN
The lowest vibration modes of a composite beam resting on an inhomogeneous elastic foundation in the case of a clamped-free boundary condition are investigated. It is observed that the relation between the frequency and foundation constant has an effect on the valid solution of the problem. An asymptotic procedure is employed to derive the eigenfrequencies as well as the eigenforms revealing that only under certain conditions on the ratios of material parameters. Numerical illustrations are presented to confirm that the obtained asymptotic frequencies agree well with the exact frequencies in the lowest frequency range. Comparisons of asymptotic and exact displacements are also presented and a remarkable agreement is observed for high-contrast beam components.
Rocznik
Strony
107--119
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
autor
  • Faculty of Arts and Sciences, Department of Mathematics, Giresun University, Giresun, Turkey
Bibliografia
  • [1] Aßmus, M., Naumenko, K., & Altenbach, H. (2017). Mechanical behaviour of photovoltaic composite structures: Influence of geometric dimensions and material properties on the eigenfrequencies of mechanical vibrations. Composites Communications, 6, 59-62.
  • [2] Qin, Y., Wang, X., & Wang, Z.L. (2008). Microfibre-nanowire hybrid structure for energy scavenging. Nature, 451(7180):809.
  • [3] Schulze, S.H., Pander, M., Naumenko, K., & Altenbach, H. (2012). Analysis of laminated glass beams for photovoltaic applications. Int. J. Solids Struct., 49(15), 2027-2036.
  • [4] Martin, T.P., Layman, C.N., Moore, K.M., & Orris, G.J. (2012). Elastic shells with high-contrast material properties as acoustic metamaterial components. Physical Review B, 85(16), 161103.
  • [5] Brunet, T., Leng, J., & Mondain-Monval, O. (2013). Soft acoustic metamaterials. Science, 342(6156), 323-324.
  • [6] Rus, D., & Tolley, M.T. (2015). Design, fabrication and control of soft robots. Nature, 521(7553), 467-475.
  • [7] Majidi, C. (2014). Soft robotics: a perspective-current trends and prospects for the future. Soft Robot, 1(1), 5-11.
  • [8] Manna, S., & Anjali, T.C. (2020). Rayleigh type wave dispersion in an incompressible functionally graded orthotropic half-space loaded by a thin fluid-saturated aeolotropic porous layer. Applied Mathematical Modelling, 83, July, 590-613.
  • [9] Kudaibergenov, A., Nobili, A., & Prikazchikova L. (2016). On low-frequency vibrations of a composite string with contrast properties for energy scavenging fabric devices. J. Mech. Mater. Struct., 11, 3, 231-243.
  • [10] Kaplunov, J., Prikazchikov, D., & Sergushova O. (2016). Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. J. Sound Vib., 366, 264-276.
  • [11] Kaplunov, J., Prikazchikov, D., Prikazchikova, L.A., & Sergushova O. (2019). The lowest vibration spectra of multi-component structures with contrast material properties. J. Sound Vib., 445, 132-147.
  • [12] S¸ ahin, O. (2019). The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams. Journal of Mechanics of Materials and Structures, 14(4), 569-585.
  • [13] S¸ ahin, O., Erbas¸, B., Kaplunov, J., & Savˇsek T. (2019). The lowest vibration modes of an elastic beam composed of alternating stiff and soft components. Archive of Applied Mechanics, 1-14, DOI: 10.1007/s00419-019-01612-2.
  • [14] Hetenyi, M. (1955). Beams on Elastic Foundation. 4th printing. Ann Arbor, Michigan: University of Michigan Press.
  • [15] Mead, D.J. (1970). Free wave propagation in periodically supported, infinite beams. Journal of Sound and Vibration, 11(2), 181-197.
  • [16] Yu, D., Wen J., Shen H., Xiao Y., Wen X. (2012). Propagation of flexural wave in periodic beam on elastic foundations. Physics Letters A, 376(4), 626-630.
  • [17] Zhou, D. (1993). A general solution to vibrations of beams on variable Winkler elastic foundation. Computers and Structures, 47(1), 83-90.
  • [18] Doyle, P.F., & Pavlovic M.N. (1982). Vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10(5), 663-674.
  • [19] Wang, J. (1991). Vibration of stepped beams on elastic foundations. Journal of Sound and Vibration, 149(2), 315-322.
  • [20] Cos¸kun, I., & Engin H. (1999). Non-linear vibrations of a beam on an elastic foundation. Journal of Sound and Vibration, 223, 335-354.
  • [21] Cos¸kun, I. (2000). Non-linear vibrations of a beam resting on a tensionless Winkler foundation. Journal of Sound and Vibration, 236(3), 401-411.
  • [22] Karahan, M.F., & Pakdemirli, M. (2017). Vibration analysis of a beam on a nonlinear elastic foundation. Structural Engineering and Mechanics, 62(2), 171-178.
  • [23] Kural, S., & O¨ zkaya, E. (2017). Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation. Journal of Vibration and Control, 23(7), 1106-1114.
  • [24] Mahmoudpour, E., Hosseini-Hashemi, S.H., & Faghidian, S.A. (2018). Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model. Applied Mathematical Modelling, 57, 302-315.
  • [25] Elishakoff, I., Ajenjo, A., & Livshits, D. (2020). Generalization of Eringen’s result for random response of a beam on elastic foundation. European Journal of Mechanics-A/Solids, 81, 103931
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b628a09e-763c-41c1-8bbf-fd8b4f4267e4
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