Skip to main content
SpringerLink
Log in

On the static and dynamic stability of spherical sandwich shell panels with viscoelastic material core and laminated composite face sheets under uniaxial and biaxial harmonic excitations

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The buckling and parametric resonance characteristics of laminated composite spherical sandwich shell panels with viscoelastic material (VEM) core are investigated in the present analysis considering full geometric nonlinearity in the Green–Lagrange sense. The study includes the longitudinal strain and normal strain in the transverse direction along with transverse shear deformation of the VEM core. The core displacements are considered to be varying linearly along the thickness and those of the face sheets follow first-order shear deformation theory. An eight-noded sandwich shell finite element of the serendipity family is adopted to discretize the sandwich shell panel domain. The finite element-based equation of motion is derived using Hamilton’s principle in the form of the Mathieu–Hill-type equation. The dynamic instability regions are obtained by applying Hsu’s criteria-based Saito–Otomi conditions to the transformed equation motion. An in-house finite element-based code is developed in the MATLAB platform to solve the stability problem and to establish the stability regions. A parametric study is carried out to investigate the influence of different system parameters on the critical buckling load and the parametric resonance of the sandwich shell panels. It is noted that an increase in core and constraining layer thicknesses increases the critical buckling load of the sandwich shell panels. The stability boundaries are observed to shift toward a higher-excitation-frequency region in the stability diagram with an increase in constraining layer thickness and a decrease in aspect ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Rao, K.M.: Buckling analysis of anisotropic sandwich plates faced with fiber-reinforced plastics. AIAA J 23, 1247–53 (1985). https://doi.org/10.2514/3.9073

    Article  MATH  Google Scholar 

  2. Zenkour, A.M.: A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration. Int. J. Solids Struct. 42, 5243–58 (2005). https://doi.org/10.1016/j.ijsolstr.2005.02.016

    Article  MATH  Google Scholar 

  3. Sharnappa, S., Ganesan, N., Sethuraman, R.: Buckling and free vibration analysis of magnetic constrained layer damping (MCLD) beam. Finite Elem. Anal. Des. 45, 156–62 (2009). https://doi.org/10.1016/j.finel.2008.09.005

    Article  MathSciNet  Google Scholar 

  4. Shariyat, M.: A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Compos. Struct. 92, 130–43 (2010). https://doi.org/10.1016/j.compstruct.2009.07.007

    Article  Google Scholar 

  5. Zenkour, A.M., Sobhy, M.: Thermal buckling of various types of FGM sandwich plates. Compos. Struct. 93, 93–102 (2010). https://doi.org/10.1016/j.compstruct.2010.06.012

    Article  Google Scholar 

  6. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I., El, E.A.: A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. Int. J. Mech. Sci. 53, 237–47 (2011). https://doi.org/10.1016/j.ijmecsci.2011.01.004

    Article  Google Scholar 

  7. Shariyat, M.: A nonlinear double-superposition global-local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: a hierarchical constitutive model. Compos. Struct. 93, 1890–9 (2011). https://doi.org/10.1016/j.compstruct.2011.02.005

    Article  Google Scholar 

  8. Giunta, G., Metla, N., Koutsawa, Y., Belouettar, S.: Free vibration and stability analysis of three-dimensional sandwich beams via hierarchical models. Compos. Part B Eng. 47, 326–38 (2013). https://doi.org/10.1016/j.compositesb.2012.11.017

    Article  Google Scholar 

  9. Ranjbaran, A., Khoshravan, M.R., Kharazi, M.: Buckling analysis of sandwich plate using layerwise theory. J. Mech. Sci. Technol. 28, 2769–77 (2014). https://doi.org/10.1007/s12206-014-0512-9

    Article  Google Scholar 

  10. Ranjbaran, A., Khoshravan, M.R., Kharazi, M.: Analysis of buckling of sandwich plates with viscoelastic core using layerwise theory. Appl. Mech. Mater. 798, 462–9 (2015). https://doi.org/10.4028/www.scientific.net/AMM.798.462

    Article  Google Scholar 

  11. Chan, H.C., Foo, O.: Buckling of multilayer sandwich plates by the spline finite strip method. Int. J. Mech. Sci. 19, 447–56 (1977)

    Article  Google Scholar 

  12. Mohammadimehr, M., Shahedi, S.: High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM. Compos Part B Eng 108, 91–107 (2017). https://doi.org/10.1016/j.compositesb.2016.09.040

    Article  Google Scholar 

  13. Joseph, S.V., Mohanty, S.: Temperature effects on buckling and vibration characteristics of sandwich plate with viscoelastic core and functionally graded material constraining layer. J Sandw Struct Mater 2017:109963621772230. https://doi.org/10.1177/1099636217722309

  14. Lin, C.Y., Chen, L.W.: Dynamic stability of rotating composite beams with a viscoelastic core. Compos. Struct. 58, 185–94 (2002). https://doi.org/10.1016/S0263-8223200127-7

    Article  Google Scholar 

  15. Lin, C.-Y., Chen, L.-W.: Dynamic stability of rotating pre-twisted blades with a constrained damping layer. Compos. Struct. 61, 235–45 (2003). https://doi.org/10.1016/S0263-82230300048-5

    Article  Google Scholar 

  16. Wang, H.-J., Chen, L.-W.: Axisymmetric dynamic stability of rotating sandwich circular plates. J. Vib. Acoust. 126, 407 (2004). https://doi.org/10.1115/1.1688765

    Article  Google Scholar 

  17. Yeh, J.Y., Chen, L.W., Wang, C.C.: Dynamic stability of a sandwich beam with a constrained layer and electrorheological fluid core. Compos. Struct. 64, 47–54 (2004). https://doi.org/10.1016/S0263-8223(03)00212-5

    Article  Google Scholar 

  18. Tabassian, R., Rezaeepazhand, J.: Dynamic stability of smart sandwich beams with electro-rheological core resting on elastic foundation. J. Sandw. Struct. Mater. 15, 25–44 (2012). https://doi.org/10.1177/1099636212461494

    Article  Google Scholar 

  19. Sofiyev, A.H.: Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells. Compos. Part B Eng. 77, 349–62 (2015). https://doi.org/10.1016/j.compositesb.2015.03.040

    Article  Google Scholar 

  20. Yeh, J.Y., Chen, L.W.: Dynamic stability of a sandwich plate with a constraining layer and electrorheological fluid core. J. Sound Vib. 285, 637–52 (2005). https://doi.org/10.1016/j.jsv.2004.08.033

    Article  Google Scholar 

  21. Yeh, J.Y., Chen, L.W.: Dynamic stability analysis of a rectangular orthotropic sandwich plate with an electrorheological fluid core. Compos. Struct. 72, 33–41 (2006). https://doi.org/10.1016/j.compstruct.2004.10.010

    Article  Google Scholar 

  22. Kolahchi, R., Safari, M., Esmailpour, M.: Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium. Compos. Struct. 150, 255–65 (2016). https://doi.org/10.1016/j.compstruct.2016.05.023

    Article  Google Scholar 

  23. Heydarpour, Y., Malekzadeh, P.: Dynamic stability of rotating FG-CNTRC cylindrical shells under combined static and periodic axial loads. Int. J. Struct. Stab. Dyn. 18, 1850151 (2018). https://doi.org/10.1142/S0219455418501511

    Article  MathSciNet  Google Scholar 

  24. Biswal, D.K., Mohanty, S.C.: Free vibration and damping characteristics study of doubly curved sandwich shell panels with viscoelastic core and isotropic/laminated constraining layer. Eur. J. Mech.-A/Solids 72, 424–39 (2018). https://doi.org/10.1016/j.euromechsol.2018.06.008

    Article  MathSciNet  MATH  Google Scholar 

  25. Hsu, C.S.: On the parametric excitation of a dynamic system having multiple degrees of freedom. J. Appl. Mech. Trans. ASME 30, 367–72 (1963). https://doi.org/10.1115/1.3636563

    Article  MathSciNet  MATH  Google Scholar 

  26. Saito, H., Otomi, K.: Parametric response of viscoelastically supported beams. J. Sound Vib. 63, 169–78 (1979). https://doi.org/10.1016/0022-460X(79)90874-5

    Article  MATH  Google Scholar 

  27. Araujo, A.L., Mota Soares, C.M., Mota Soares, C.A.: Finite element model for hybrid active-passive damping analysis of anisotropic laminated sandwich structures. J. Sandw. Struct. Mater. 12, 397–419 (2010). https://doi.org/10.1177/1099636209104534

    Article  Google Scholar 

  28. Duigou, L., Mostafa Daya, E., Potier-Ferry, M.: Iterative algorithms for non-linear eigenvalue problems. Application to vibrations of viscoelastic shells. Comput. Methods Appl. Mech. Eng. 192, 1323–35 (2003). https://doi.org/10.1016/S0045-7825(02)00641-2

    Article  MATH  Google Scholar 

  29. Matsunaga, H.: Vibration and stability of thick simply supported shallow shells subjected to in plane stress. J. Sound Vib. 225, 41–60 (1999)

    Article  Google Scholar 

  30. Sahu, S.K., Datta, P.K.: Parametric resonance characteristics of laminated composite doubly curved shells subjected to non-uniform loading. J. Reinf. Plast. Compos. 20, 1556–1576 (2001)

    Article  Google Scholar 

  31. Kaw, A.K.: Composite, Second edn. CRC Press, Boca Raton (2006)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamilnadu, 632 014, India

    Deepak Kumar Biswal

  2. Department of Mechanical Engineering, National Institute of Technology, Rourkela, Odisha, 769008, India

    Sukesh Chandra Mohanty

Authors
  1. Deepak Kumar Biswal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sukesh Chandra Mohanty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deepak Kumar Biswal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Biswal, D.K., Mohanty, S.C. On the static and dynamic stability of spherical sandwich shell panels with viscoelastic material core and laminated composite face sheets under uniaxial and biaxial harmonic excitations. Acta Mech 231, 1903–1918 (2020). https://doi.org/10.1007/s00707-020-02618-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02618-6

Search

Navigation