Journal of Computational Methods in Engineering

Journal of Computational Methods in Engineering

Nonlinear free vibration analysis of moderately thick sandwich plates with viscoelastic core using finite strip method

Document Type : Original Article

Authors
Arezoo Hajrahimi
Nasrin Jafari
Saeed Sarrami
Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran
10.47176/jcme.43.1.1028
Abstract
Sandwich plates as structural members, have received a lot of attention in industrial structures and large construction projects due to their low specific weight, resistance to fatigue and high bending strength. Since Industrial structures are commonly reposed to dynamic loads, plate vibration can result in injury to structures, especially when the excitation frequency is close to the natural frequency of the structure. Therefore, nonlinear vibration analysis of plates is one of the most attended topics in the dynamics of structures. In this article, the nonlinear free vibration of sandwich plates with a viscoelastic core is studied based on von Karman's assumptions and using the First-order shear deformation theory. The viscoelastic properties of the plate core follow Boltzmann's integral law. Also, the Laplace transform is used to convert equations from the time domain to the Laplace domain. For the discretization of the equations, the finite strip numerical method is used. Finally, by numerically solving an eigenvalue problem in the Laplace-Carson domain, the nonlinear frequencies of sandwich plates with a viscoelastic core with different vibration amplitudes are calculated. The results show that, with the increase of the vibration amplitude and the coefficients of the relaxation function of the viscoelastic core, the ratio of the nonlinear frequencies decreases in this type of plates.
Keywords
Sandwich plates
Viscoelastic core
Finite strip method
Nonlinear free vibration
Boltzmann's integral
Von Karman's assumptions
First-order shear deformation theory
Subjects
  1. Shooshtari, A., and Rafiee, M., “Nonlinear Forced Vbration Analysis of Clamped Functionally Graded Beams”, Acta Mechanica, 221, No. 1, pp. 23-38, 2011.
  2. Cheung, Y. K., Zhu, D. S., and Iu, V. P., “Nonlinear Vibration of Thin Plates With Initial Stress by Spline Finite Strip Method”, Thin-Walled Structures, 32, No. 4, pp. 275-287, 1998.
  3. Yongqiang, L., and Dawei, Z., “Geometrically Nonlinear Norced Vibrations of The Symmetric Honeycomb Sandwich Panels Affected by The Water”, Composite Structures, 93, No. 2, pp. 880-888, 2011.
  4. He, X. Q., Wang, J. B., Liu, B., and Liew, K. M., “Analysis of Nonlinear Forced Vibration of Multi-Layered Graphene Sheets”, Computational Materials Science , Vol. 61, pp.194-199, 2012.
  5. Dașdemir, A. “Forced Vibrations of Pre-Stressed Sandwich Plate-Strip with Elastic Layers and Piezoelectric Core”, International Applied Mechanics , Vol. 54, No. 4, pp.480-493, 2018.
  6. Zhang, J., Zhu, X., Yang, X., and Zhang, W., “Transient Nonlinear Responses Of an Auxetic Honeycomb Sandwich Plate Under Impact Loads”, International Journal of Impact Engineering , Vol. 134 , 103383,2019.
  7. Zhou, Z., Chen, M., Xiong, Y., Jia, W., Dong, W., and Xie, K., “Experimental And Mixed Analytical–Numerical Studies for Free and Forced Vibrations of Z-Reinforced Sandwich Plates Stiffened by Steel Ribs”, Composite Structures, Vol. 272, p. 114221,2021.
  8. Eshmatov, B. Kh. “Nonlinear Vibrations and Dynamic Stability of Viscoelastic Orthotropic Rectangular Plates”, Journal of Sound and Vibration, 300, No. 3-5, pp. 709-726, 2007.
  9. Mahmoudkhani, S., Haddadpour, H., and Navazi, H. M., “The Effects of Nonlinearities on The Vibration of Viscoelastic Sandwich Plates”, International Journal of Non-Linear Mechanics, Vol. 62, pp. 41-57, 2014.
  10. Amabili, M., “Nonlinear Vibrations of Viscoelastic Rectangular Plates”, Journal of Sound and Vibration, Vol. 362, pp.142-156, 2016.
  11. Silva, V. A. C., “Uncertainty Propagation and Numerical Evaluation of Viscoelastic Sandwich Plates Having Nonlinear Behavior”, Journal of Vibration and Control, 26, No. 7-8, pp. 447-458, 2020.
  12. Loghman, E., Kamali, A., Bakhtiari-Nejad, F., and Abbaszadeh, M., “Nonlinear Free and Forced Vibrations of Fractional Modeled Viscoelastic FGM Micro-Beam”, Applied Mathematical Modelling , Vol. 92, pp. 297-314, 2021.
  13. Jafari, N., and Azhari, M., “Free Vibration Analysis of Viscoelastic Plates With Simultaneous Calculation of Natural Frequency and Viscous Damping”, Mathematics and Computers in Simulation , Vol. 185, pp. 646-659, 2021.
  14. Neng-hui, Z., and Chang-jun, C., “Non-Linear Mathematical Model of Viscoelastic Thin Plates With It’s Applications”, Computer Methods in Applied Mechanics and Engineering, 165, No. 1-4, pp.307-319, 1998.
  15. Jafari, N., Azhari, M., and Boroomand, B., “Geometrically Nonlinear Analysis of Time-Dependent Composite Plates Using Time Function Optimization”, International Journal of Non-Linear Mechanics, Vol. 116, pp. 219-229, 2019.
  16. Amabili, M., “ Nonlinear Vibrations and Stability of Shells and Plates”, Cambridge University Press, 2008.
  17. Jafari, N., and Azhari, M., “Nonlinear Free Vibration Analysis of Moderately Thick Viscoelastic Plates With Various Geometrical Properties”, Steel and Composite Structures, Vol. 48, No. 3 , p. 293, 2019.
  18. Zamani, H. A., Aghdam, M. M., and Sadighi, M., “Free Vibration Analysis of Thick Viscoelastic Composite Plates on Visco-Pasternak Foundation Using Higher-Order Theory”, Composite Structures, 182, pp. 25-35, 2017.
  19. Touati, D., and Cederbaum, G., “Dynamic Stability of Nonlinear Viscoelastic Plates”, International Journal of Solids and Structures, Vol. 31, No. 17, pp. 2367-2376, 1994.
  20. Liew, K. M., Xiang, Y., and Kitipornchai, S., “Transverse Vibration of Thick Rectangular Plates-I. Comprehensive Sets of Boundary Conditions”, Computers & Structures, Vol. 49, No. 1, pp. 1-29, 1993.
  21. Khdeir, A. A., and Librescu, L., “Analysis of Symmetric Cross-Ply Laminated Elastic Plates Using a Higher-Order Theory: Part II-Buckling and Free Vibration”, Composite Structures, Vol. 9, No. 4, pp. 259-277, 1988.
  22. Singha, M. K., and Daripa, R., “Nonlinear Vibration and Dynamic Stability Analysis of Composite Plates”, Journal of Sound and Vibration, Vol. 328, No. 4-5, pp.541-554, 1999.

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