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Articles

Dynamic response of fractionally damped two-layered viscoelastic plate

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Pages 36-53 | Received 20 Aug 2021, Accepted 13 Jun 2022, Published online: 07 Jul 2022

References

  • Abdoun, F., L. Azrar, E. M. Daya, and M. Potier-Ferry. 2009. Forced harmonic response of viscoelastic structures by an asymptotic numerical method. Computers & Structures 87 (1-2):91–100. doi:10.1016/j.compstruc.2008.08.006.
  • Atanackovic, T. M. 2002. A modified Zener model of a viscoelastic body. Continuum Mechanics and Thermodynamics 14 (2):137–48. doi:10.1007/s001610100056.
  • Bagley, R. L., and P. J. Torvik. 1985. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA Journal 23 (6):918–25. doi:10.2514/3.9007.
  • Bagley, R. L., and P. J. Torvik. 1986. On the fractional calculus model of viscoelastic behavior. Journal of Rheology 30 (1):133–55. doi:10.1122/1.549887.
  • Caputo, M. 1967. Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International 13 (5):529–39. doi:10.1111/j.1365-246X.1967.tb02303.x.
  • Caputo, M., and F. Mainardi. 1971. A new dissipation model based on memory mechanism. Pure and Applied Geophysics 91 (1):134–47. doi:10.1007/BF00879562.
  • Chang, T.-S., and M. P. Singh. 2009. Mechanical model parameters for viscoelastic dampers. Journal of Engineering Mechanics 135 (6):581–4. doi:10.1061/(ASCE)0733-9399(2009)135:6(581).
  • Civalek, Ö. 2008. Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method. Finite Elements in Analysis and Design 44 (12-13):725–31. Ö doi:10.1016/j.finel.2008.04.001.
  • Civalek, Ö., and M. Avcar. 2022. Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method. Engineering with Computers 38 (S1):489–33. doi:10.1007/s00366-020-01168-8.
  • Civalek, Ö., S. Dastjerdi, and B. Akgöz. 2022. Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates. Mechanics Based Design of Structures and Machines 50 (6):1914–18. doi:10.1080/15397734.2020.1766494.
  • Cortés, F., and M. J. Elejabarrieta. 2007. Viscoelastic materials characterisation using the seismic response. Materials & Design 28 (7):2054–62. doi:10.1016/j.matdes.2006.05.032.
  • Dastjerdi, S., B. Akgöz, and Ö. Civalek. 2020. On the effect of viscoelasticity on behavior of gyroscopes. International Journal of Engineering Science 149:103236. doi:10.1016/j.ijengsci.2020.103236.
  • Di Paola, M., A. Pirrotta, and A. Valenza. 2011. Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results. Mechanics of Materials 43 (12):799–806. doi:10.1016/j.mechmat.2011.08.016.
  • Diethelm, K. 2010. The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type, 247. Berlin: Springer Science & Business Media. doi:10.1007/978-3-642-14574-2.
  • Du, S., F. An, and B. Liu. 2019. On the sound transmission loss of finite plates with constrained viscoelastic layer. Applied Acoustics 149:32–8. doi:10.1016/j.apacoust.2019.01.010.
  • Eldred, L. B., W. P. Baker, and A. N. Palazotto. 1995. Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials. AIAA Journal 33 (3):547–50. doi:10.2514/3.12471.
  • Enelund, M., and P. Olsson. 1999. Damping described by fading memory—analysis and application to fractional derivative models. International Journal of Solids and Structures 36 (7):939–70. doi:10.1016/S0020-7683(97)00339-9.
  • Enelund, M., L. Mähler, K. Runesson, and B. L. Josefson. 1999. Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws. International Journal of Solids and Structures 36 (16):2417–42. doi:10.1016/S0020-7683(98)00111-5.
  • Freundlich, J. 2019. Transient vibrations of a fractional Kelvin-Voigt viscoelastic cantilever beam with a tip mass and subjected to a base excitation. Journal of Sound and Vibration 438:99–115. doi:10.1016/j.jsv.2018.09.006.
  • Hatada, T., T. Kobori, M. Ishida, and N. Niwa. 2000. Dynamic analysis of structures with Maxwell model. Earthquake Engineering & Structural Dynamics 29 (2):159–76. doi:10.1002/(SICI)1096-9845(200002)29:2<159::AID-EQE895>3.0.CO;2-1.
  • Hedrih, K. 2005. Partial fractional differential equations of creeping and vibrations of plate and their solutions (first part). Journal of the Mechanical Behavior of Materials 16:305–14.
  • Hosseinkhani, A., D. Younesian, R. Shakeri, and S. Farhangdoust. 2021. Vibro-acoustic response analysis of fractional railpads in frequency domain. Mechanics Based Design of Structures and Machines 49 (2):286–18. doi:10.1080/15397734.2019.1688169.
  • Huang, Z., X. Wang, N. Wu, F. Chu, and J. Luo. 2019. A finite element model for the vibration analysis of sandwich beam with frequency-dependent viscoelastic material core. Materials 12 (20):3390. doi:10.3390/ma12203390.
  • Jones, D. I. G. 2001. Handbook of viscoelastic vibration damping. New York: John Wiley & Sons.
  • Kerwin, E. M. 1959. Damping of flexural waves by a constrained viscoelastic layer. The Journal of the Acoustical Society of America 31 (7):952–62. doi:10.1121/1.1907821.
  • Khalfi, B., and A. Ross. 2013. Transient response of a plate with partial constrained viscoelastic layer damping. International Journal of Mechanical Sciences 68:304–12. doi:10.1016/j.ijmecsci.2013.01.032.
  • Khalfi, B., and A. Ross. 2016. Transient and harmonic response of a sandwich with partial constrained layer damping: A parametric study. Composites Part B: Engineering 91:44–55. doi:10.1016/j.compositesb.2015.12.037.
  • Kim, S.-Y., and D.-H. Lee. 2009. Identification of fractional-derivative-model parameters of viscoelastic materials from measured FRFs. Journal of Sound and Vibration 324 (3-5):570–86. doi:10.1016/j.jsv.2009.02.040.
  • Lewandowski, R., and B. Chorążyczewski. 2010. Identification of the parameters of the Kelvin–Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers. Computers & Structures 88 (1-2):1–17. doi:10.1016/j.compstruc.2009.09.001.
  • Li, L., Y. Hu, and X. Wang. 2014. Harmonic response calculation of viscoelastic structures using classical normal modes: An iterative method. Computers & Structures 133:39–50. doi:10.1016/j.compstruc.2013.11.009.
  • Lion, A. 2001. Thermomechanically consistent formulations of the standard linear solid using fractional derivatives. Archives of Mechanics 53:253–73.
  • Mainardi, F. 2010. Fractional calculus and waves in linear viscoelasticity: An introduction to mathematical models. Singapore: World Scientific.
  • Mainardi, F., and G. Spada. 2011. Creep, relaxation and viscosity properties for basic fractional models in rheology. The European Physical Journal Special Topics 193 (1):133–60. doi:10.1140/epjst/e2011-01387-1.
  • Mead, D. J., and S. Markus. 1969. The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions. Journal of Sound and Vibration 10 (2):163–75. doi:10.1016/0022-460X(69)90193-X.
  • Mukhopadhyay, M. 2021. Structural dynamics: Vibrations and systems. New Delhi: Springer Nature.
  • Palmeri, A., F. Ricciardelli, A. De Luca, and G. Muscolino. 2003. State space formulation for linear viscoelastic dynamic systems with memory. Journal of Engineering Mechanics 129 (7):715–24. doi:10.1061/(ASCE)0733-9399(2003)129:7(715).
  • Park, S. W. 2001. Analytical modeling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures 38 (44-45):8065–92. doi:10.1016/S0020-7683(01)00026-9.
  • Podlubny, I. 1999. Fractional differential equations, Vol. 198 of Mathematics in Science and Engineering. San Diego, CA: Academic Press.
  • Podlubny, I. 2000. Matrix approach to discrete fractional calculus. Fractional Calculus and Applied Analysis 3:359–86.
  • Praharaj, R. K, and N. Datta. 2020. Application of fractional calculus in modelling viscoelastic foundation of ship structures for passive vibration control. international conference on offshore mechanics and arctic engineering, vol. 84331. American Society of Mechanical Engineers, V02BT02A018.
  • Praharaj, R. K., and N. Datta. 2020. Dynamic response of Euler–Bernoulli beam resting on fractionally damped viscoelastic foundation subjected to a moving point load. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234 (24):4801–12. doi:10.1177/0954406220932597.
  • Praharaj, R. K., and N. Datta. 2020. On the transient response of plates on fractionally damped viscoelastic foundation. Computational and Applied Mathematics 39 (4):1–20. doi:10.1007/s40314-020-01285-6.
  • Praharaj, R. K., and N. Datta. 2022. Dynamic response of plates resting on a fractional viscoelastic foundation and subjected to a moving load. Mechanics Based Design of Structures and Machines 50 (7):2317–32. doi:10.1080/15397734.2020.1776621.
  • Praharaj, R. K., and N. Datta. 2022. Dynamic response spectra of fractionally damped viscoelastic beams subjected to moving load. Mechanics Based Design of Structures and Machines 50 (2):672–86. doi:10.1080/15397734.2020.1725563.
  • Praharaj, R. K., N. Datta, and M. R. Sunny. 2020. Dynamic response of fractionally damped viscoelastic plates subjected to a moving point load. Journal of Vibration and Acoustics 142 (4):041002. doi:10.1115/1.4046485.
  • Pritz, T. 1996. Analysis of four-parameter fractional derivative model of real solid materials. Journal of Sound and Vibration 195 (1):103–15. doi:10.1006/jsvi.1996.0406.
  • Rao, M. D. 2003. Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. Journal of Sound and Vibration 262 (3):457–74. doi:10.1016/S0022-460X(03)00106-8.
  • Reddy, C. V. R., N. Ganesan, B. V. A. Rao, and S. Narayanan. 1980. Response of plates with unconstrained layer damping treatment to random acoustic excitation, part I: Damping and frequency evaluations. Journal of Sound and Vibration 69 (1):35–43. doi:10.1016/0022-460X(80)90433-2.
  • Rogers, L. C. 1989. An accurate temperature shift function and a new approach to modeling complex modulus. Proceeding of 60th Shock and Vibration Symposium. Virginia Beach, VA, November 14–16
  • Rossikhin, Y. A., and M. V. Shitikova. 2010. Application of fractional calculus for dynamic problems of solid mechanics: Novel trends and recent results. Applied Mechanics Reviews 63 (1):10801. doi:10.1115/1.4000563.
  • Rossikhin, Y. A., M. V. Shitikova, and P. T. Trung. 2016. Application of the fractional derivative Kelvin-Voigt Model for the analysis of impact response of a Kirchhoff-Love Plate. WSEAS Transactions on Mathematics 15:498–501.
  • Sharma, L. K., G. Bhardwaj, and N. Grover. 2021. Finite element framework for static analysis of temperature dependent IHSDT based functionally graded CNT reinforced plates. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2021.1999265.
  • Shermergor, T. D. 1971. On the use of fractional differentiation operators for the description of elastic-after effect properties of materials. Journal of Applied Mechanics and Technical Physics 7 (6):85–7. doi:10.1007/BF00914347.
  • Shin, Y. S., and G. J. Maurer. 1991. Vibration response of constrained viscoelastically damped plates: Analysis and experiments. Finite Elements in Analysis and Design 7 (4):291–7. doi:10.1016/0168-874X(91)90044-Y.
  • Singh, M. P., and L. M. Moreschi. 2002. Optimal placement of dampers for passive response control. Earthquake Engineering & Structural Dynamics 31 (4):955–76. doi:10.1002/eqe.132.
  • Singh, M. P., N. P. Verma, and L. M. Moreschi. 2003. Seismic analysis and design with Maxwell dampers. Journal of Engineering Mechanics 129 (3):273–82. doi:10.1061/(ASCE)0733-9399(2003)129:3(273).
  • Sun, W., X. Yan, and F. Gao. 2018. Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping. Mechanics Based Design of Structures and Machines 46 (2):209–24. doi:10.1080/15397734.2017.1327359.
  • Yazdi, A. A. 2019. Nonlinear aeroelastic stability analysis of three-phase nano-composite plates. Mechanics Based Design of Structures and Machines 47 (6):753–68. doi:10.1080/15397734.2019.1610436.
  • Yi, S. M. F. Ahmad, and H. H. Hilton. 1996. Dynamic responses of plates with viscoelastic free layer damping treatment. Journal of Vibration and Acoustics 118 (3).
  • Zarraga, O., I. Sarría, J. García-Barruetabeña, and F. Cortés. 2019. Dynamic analysis of plates with thick unconstrained layer damping. Engineering Structures 201:109809. doi:10.1016/j.engstruct.2019.109809.
  • Zarraga, O., I. Sarría, J. García-Barruetabeña, M. J. Elejabarrieta, and F. Cortés. 2020. General homogenised formulation for thick viscoelastic layered structures for finite element applications. Mathematics 8 (5):714. doi:10.3390/math8050714.
  • Zhang, Y., G. Jin, M. Chen, T. Ye, C. Yang, and Y. Yin. 2020. Free vibration and damping analysis of porous functionally graded sandwich plates with a viscoelastic core. Composite Structures 244:112298. doi:10.1016/j.compstruct.2020.112298.

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