Open Access Open Access  Restricted Access Subscription Access

Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 1: Governing equations

Dang Thuy Dong, Dao Van Dung


Nonlinear vibration of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners subjected to mechanical and thermal loading are investigated based on the first-order shear deformation theory (FSDT) with von Karman type nonlinearity, taking into account initial geometrical imperfection and smeared stiffener technique. Four material models of the FGM sandwich shells are presented. Explicit expressions for natural frequencies, nonlinear frequency-amplitude relation, and time-deflection curves of the FGM sandwich shallow shells are derived using Galerkin method.


nonlinear vibration; FGM sandwich shallow shell; stiffener


X.-K. Xia and H.-S. Shen. Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment. Journal of Sound and Vibration, 314, (1), (2008), pp. 254–274. doi:10.1016/j.jsv.2008.01.019.

S. M. R. Khalili and Y. Mohammadi. Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach. European Journal of Mechanics-A/Solids, 35, (2012), pp. 61–74. doi:10.1016/j.euromechsol.2012.01.003.

S. Pandey and S. Pradyumna. Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory. European Journal of Mechanics-A/Solids, 51, (2015), pp. 55–66. doi:10.1016/j.euromechsol.2014.12.001.

B. S. Aragh and M. H. Yas. Effect of continuously grading fiber orientation face sheets on vibration of sandwich panels with FGM core. International Journal of Mechanical Sciences, 53, (8), (2011), pp. 628–638. doi:10.1016/j.ijmecsci.2011.05.009.

T. Dey and L. S. Ramachandra. Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings. Composites Part B: Engineering, 60, (2014), pp. 537–545. doi:10.1016/j.compositesb.2013.12.072.

A. H. Sofiyev and N. Kuruoglu. Dynamic instability of three-layered cylindrical shells containing an FGM interlayer. Thin-Walled Structures, 93, (2015), pp. 10–21. doi:10.1016/j.tws.2015.03.006.

D. V. Dung and D. T. Dong. Thermo-mechanical post-buckling analyses of functionally graded sandwich doubly curved shallow shells reinforced by FGM stiffeners with temperature-dependent material and stiffener properties resting on elastic foundations. In Proceedings of the Conference on Science and Structural Composite Materials Mechanics, Technology and Applications, Nha Trang, (2016). pp. 189–196.

D. V. Dung and D. T. Dong. Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory. Applied Mathematics and Mechanics, 38, (2), (2017), pp. 191–216. doi:10.1007/s10483-017-2166-9.

D. H. Bich, N. D. Duc, and T. Q. Quan. Nonlinear vibration of imperfect eccentrically stiffened functionally graded double curved shallow shells resting on elastic foundation using the first order shear deformation theory. International Journal of Mechanical Sciences, 80, (2014), pp. 16–28. doi:10.1016/j.ijmecsci.2013.12.009.

N. D. Duc and T. Q. Quan. Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment. European Journal of Mechanics-A/Solids, 47, (2014), pp. 101–123. doi:10.1016/j.euromechsol.2014.03.002.

Full Text: PDF


  • There are currently no refbacks.