Mathematics, Vol. 11, Pages 2407: A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

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Mathematics, Vol. 11, Pages 2407: A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

Mathematics doi: 10.3390/math11102407

Authors:
Emad E. Ghandourah
Ahmed Amine Daikh
Samir Khatir
Abdulsalam M. Alhawsawi
Essam M. Banoqitah
Mohamed A. Eltaher

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions.

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