Skip to main content
SpringerLink
Log in

Dynamic response of open doubly curved sandwich shells with soft core subjected to a moving force

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

Abstract

This paper presents a forced vibration analysis of open doubly curved sandwich panels subjected to a moving constant force. In this paper, the effect of softness of the core is considered by implementing a semi-layerwise theory. To this aim, the first-order shear deformation theory is adopted for the face sheets and a higher-order theory which was obtained based on 3D elasticity theory is considered for the core. The presented formulation is general and as the deepness parameter is accounted in the strain–displacement relations, the formulation can be used for a wide range of deep as well as shallow doubly curved shells. To obtain the dynamic response of the system, the finite element method (FEM) along with the Newmark method is used. The proposed element is a higher-order one with nine nodes and each node has fifteen degrees of freedom. The effect of various parameters such as length-to-thickness ratio, in-plane aspect ratio, boundary conditions, lamination scheme, and fiber orientation angles on the dynamic response of the structure is examined. Additionally, the critical velocity of the force at which the structure experiences maximum dynamic deflection is obtained in each case. The results show that as the length-to-thickness ratio of the structure increases, the dynamic magnification factor curve increases with respect to non-dimensional velocity. This study provides insights into the dynamic behavior of doubly curved sandwich panels with soft cores and can aid in the design of such structures for specific applications. The results of this study can also serve as a benchmark for future studies on the forced vibration behavior of doubly curved sandwich panels.

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
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Joseph, S.V., Mohanty, S.: Free vibration and parametric instability of viscoelastic sandwich plates with functionally graded material constraining layer. Acta Mech. 230(8), 2783–2798 (2019)

    MathSciNet  Google Scholar 

  2. Malekzadeh, K., Khalili, M. R., Jafari, A., Mittal, R. K.: Dynamic response of in-plane pre-stressed sandwich panels with a viscoelastic flexible core and different boundary conditions. J. Compos. Mater. 40(16), 1449–1469 (2006)

    Google Scholar 

  3. Tian, A., Ye, R., Chen, Y.: A new higher order analysis model for sandwich plates with flexible core. J. Compos. Mater. 50(7), 949–961 (2016)

    Google Scholar 

  4. Ghavidel, N., Alibeigloo, A.: Free vibration analysis of cylindrical sandwich panel with electro-rheological core and FG-GPLRC facing sheets based on first order shear deformation theory referred by Qatu. J. Vib. Control 8, 10775463221148536 (2023)

    Google Scholar 

  5. Sahu, N. K., Biswal, D. K., Joseph, S. V., Mohanty, S. C.: Vibration and damping analysis of doubly curved viscoelastic-FGM sandwich shell structures using FOSDT. In: Structures. Elsevier (2020)

  6. Chalak, H. D., Chakrabarti, A., Iqbal, M. A., Sheikh, A. H.: An improved C0 FE model for the analysis of laminated sandwich plate with soft core. Finite Elem. Anal. Des. 56, 20–31 (2012)

    Google Scholar 

  7. Kant, T., Swaminathan, K.: Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Compos. Struct. 53(1), 73–85 (2001)

    Google Scholar 

  8. Kant, T., Swaminathan, K.: Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. J. Sound Vib. 241(2), 319–327 (2001)

    Google Scholar 

  9. Belarbi, M. O., Tati, A., Ounis, H., Khechai, A.: On the free vibration analysis of laminated composite and sandwich plates: a layerwise finite element formulation. Latin Am. J. Solids Struct. 14, 2265–2290 (2017)

    Google Scholar 

  10. Bacciocchi, M., Luciano, R., Majorana, C., Tarantino, A. M.: Free vibrations of sandwich plates with damaged soft-core and non-uniform mechanical properties: modeling and finite element analysis. Materials 12(15), 2444 (2019)

    Google Scholar 

  11. Biswal, D.K., Mohanty, S.C.: Free vibration study of multilayer sandwich spherical shell panels with viscoelastic core and isotropic/laminated face layers. Compos. B Eng. 159, 72–85 (2019)

    Google Scholar 

  12. Karakoti, A., Pandey, S., Kar, V.R.: Free vibration response of P-FGM and S-FGM sandwich shell panels: a comparison. Mater. Today Proc. 28, 1701–1705 (2020)

    Google Scholar 

  13. Hirane, H., Belarbi, M. O., Houari, M. S. A., Tounsi, A.: On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Eng. Comput. 8, 1–29 (2021)

    Google Scholar 

  14. Alambeigi, K., Mohammadimehr, M., Bamdad, M., Rabczuk, T.: Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation. Acta Mech. 231, 3199–3218 (2020)

    MathSciNet  Google Scholar 

  15. Chanda, A., Sahoo, R.: Static and dynamic responses of simply supported sandwich plates using non-polynomial zigzag theory. In: Structures. Elsevier (2021)

  16. Kapuria, S., Kulkarni, S.: Efficient finite element with physical and electric nodes for transient analysis of smart piezoelectric sandwich plates. Acta Mech. 214(1–2), 123–131 (2010)

    Google Scholar 

  17. Wang, M., Qin, Q., Wang, T.: On physically asymmetric sandwich plates with metal foam core subjected to blast loading: dynamic response and optimal design. Acta Mech. 228, 3265–3283 (2017)

    MathSciNet  Google Scholar 

  18. Malekzadeh, K., Khalili, M. R., Olsson, R., Jafari, A.: Higher-order dynamic response of composite sandwich panels with flexible core under simultaneous low-velocity impacts of multiple small masses. Int. J. Solids Struct. 43(22–23), 6667–6687 (2006)

    Google Scholar 

  19. Wang, A., Chen, H., Zhang, W.: Nonlinear transient response of doubly curved shallow shells reinforced with graphene nanoplatelets subjected to blast loads considering thermal effects. Compos. Struct. 225, 111063 (2019)

    Google Scholar 

  20. Yang, M., Qiao, P.: Higher-order impact modeling of sandwich structures with flexible core. Int. J. Solids Struct. 42(20), 5460–5490 (2005)

    Google Scholar 

  21. Fatt, M.S.H., Sirivolu, D.: Blast response of double curvature, composite sandwich shallow shells. Eng. Struct. 100, 696–706 (2015)

    Google Scholar 

  22. Khanjani, M., Shakeri, M., Sedighi, M.: A parametric study on the stress analysis and transient response of thick-laminated-faced cylindrical sandwich panels with transversely flexible core. Aerosp. Sci. Technol. 48, 1–20 (2016)

    Google Scholar 

  23. Katariya, P.V., Panda, S.K.: Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings. Eng. Comput. 35(3), 1009–1026 (2019)

    Google Scholar 

  24. Mirfatah, S. M., Tayebikhorami, S., Shahmohammadi, M. A., Salehipour, H., Civalek, Ö.: Geometrically nonlinear analysis of sandwich panels with auxetic honeycomb core and nanocomposite enriched face-sheets under periodic and impulsive loads. Aerosp. Sci. Technol. 135, 108195 (2023)

    Google Scholar 

  25. Sankar, A., El-Borgi, S., Ganapathi, M., Ramajeyathilagam, K. : Parametric instability of thick doubly curved CNT reinforced composite sandwich panels under in-plane periodic loads using higher-order shear deformation theory. J. Vib. Control 24(10), 1927–1950 (2018)

    MathSciNet  Google Scholar 

  26. 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(5), 1903–1918 (2020)

    MathSciNet  Google Scholar 

  27. Wattanasakulpong, N., Eiadtrong, S.: Transient responses of sandwich plates with a functionally graded porous core: Jacobi–Ritz method. Int. J. Struct. Stab. Dyn. 23(04), 2350039 (2023)

    MathSciNet  Google Scholar 

  28. Songsuwan, W., Wattanasakulpong, N., Vo, T.P.: Nonlinear vibration of third-order shear deformable FG-GPLRC beams under time-dependent forces: Gram–Schmidt–Ritz method. Thin-Walled Struct. 176, 109343 (2022)

    Google Scholar 

  29. Quan, T.Q., Duc, N.D.: Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading. Thin-Walled Struct. 170, 108606 (2022)

    Google Scholar 

  30. Cong, P. H., Khanh, N. D., Khoa, N. D., Duc, N. D.: New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT. Compos. Struct. 185, 455–465 (2018)

    Google Scholar 

  31. Nguyen, D.D., Tran, Q.Q., Nguyen, D.K.: New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature. Aerosp. Sci. Technol. 71, 360–372 (2017)

    Google Scholar 

  32. Song, Q., Liu, Z., Shi, J., Wan, Y.: Parametric study of dynamic response of sandwich plate under moving loads. Thin-Walled Struct. 123, 82–99 (2018)

    Google Scholar 

  33. Songsuwan, W., Wattanasakulpong, N., Kumar, S.: Nonlinear transient response of sandwich beams with functionally graded porous core under moving load. Eng. Anal. Bound. Elem. 155, 11–24 (2023)

    MathSciNet  Google Scholar 

  34. Kiani, Y.: Dynamics of FG-CNT reinforced composite cylindrical panel subjected to moving load. Thin-Walled Struct. 111, 48–57 (2017)

    Google Scholar 

  35. Kiani, Y.: Analysis of FG-CNT reinforced composite conical panel subjected to moving load using Ritz method. Thin-Walled Struct. 119, 47–57 (2017)

    Google Scholar 

  36. Bahranifard, F., Malekzadeh, P., Haghighi, M.G.: Moving load response of ring-stiffened sandwich truncated conical shells with GPLRC face sheets and porous core. Thin-Walled Struct. 180, 109984 (2022)

    Google Scholar 

  37. Sadripour, S., Jafari-Talookolaei, R.-A., Malekjafarian, A.: An efficient nine-node quadrilateral element for free vibration analysis of deep doubly curved soft-core sandwich shells. Acta Mech. 8, 24 (2023)

    Google Scholar 

  38. Frostig, Y., Thomsen, O.T.: High-order free vibration of sandwich panels with a flexible core. Int. J. Solids Struct. 41(5–6), 1697–1724 (2004)

    Google Scholar 

  39. Sadripour, S., Jafari-Talookolaei, R.-A., Malekjafarian, A.: Free vibration analysis of deep doubly curved soft-core sandwich panels with different boundary conditions. In: Structures. Elsevier (2022)

  40. Kardomateas, G.A., Rodcheuy, N., Frostig, Y.: First-order shear deformation theory variants for curved sandwich panels. AIAA J. 56(2), 808–817 (2018)

    Google Scholar 

  41. Ramian, A., Jafari-Talookolaei, R. A., Valvo, P. S., Abedi, M.: Free vibration analysis of sandwich plates with compressible core in contact with fluid. Thin-Walled Struct. 157, 107088 (2020)

    Google Scholar 

  42. Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics. Wiley (2017)

    Google Scholar 

  43. Zienkiewicz, O. C., Taylor, R. L.: The Finite Element Method: Solid Mechanics, vol. 2. Butterworth-Heinemann (2000)

    Google Scholar 

  44. Rao, M. K., Scherbatiuk, K., Desai, Y. M., Shah, A. H: Natural vibrations of laminated and sandwich plates. J. Eng. Mech. 130(11), 1268–1278 (2004)

    Google Scholar 

  45. Zhen, W., Wanji, C., Xiaohui, R.: An accurate higher-order theory and C0 finite element for free vibration analysis of laminated composite and sandwich plates. Compos. Struct. 92(6), 1299–1307 (2010)

    Google Scholar 

  46. Rahmani, O., Khalili, S., Thomsen, O.T.: A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads. Compos. Struct. 94(7), 2129–2142 (2012)

    Google Scholar 

Download references

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Saman Sadripour

  2. Department of Mechanical Engineering, New Uzbekistan University, Tashkent, Uzbekistan

    Ramazan-Ali Jafari-Talookolaei

  3. Structural Dynamics and Assessment Laboratory, School of Civil Engineering, University College Dublin, Dublin, Ireland

    Abdollah Malekjafarian

Authors
  1. Saman Sadripour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramazan-Ali Jafari-Talookolaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdollah Malekjafarian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramazan-Ali Jafari-Talookolaei.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sadripour, S., Jafari-Talookolaei, RA. & Malekjafarian, A. Dynamic response of open doubly curved sandwich shells with soft core subjected to a moving force. Acta Mech 235, 2231–2257 (2024). https://doi.org/10.1007/s00707-023-03821-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-023-03821-x

Search

Navigation