A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

Abstract

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.

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…A large variety of types of structural elements is considered, including beams [187,194,195,206,213,228,232], plates [193,202,203,214,218,220,227], shells [204], composite beams [186,198,201,207,211,215,224,225], composite plates [155,185,191,199,200,210,212,222,223,226], composite shells [190,216,219,221], nanobeams [184,189,196], FG nanoplates [192,197,208,[229][230][231], and FG nanoshells/nanopanels [188,209,217].…”

In-Plane Wave Propagation Analysis of Human Breast Lesions Using a Higher-Order Nonlocal Model and Deep Learning

“…The combination of these effects within the framework of a newly introduced mathematical model solves the rigid-tumour-soft-cell paradox as it allows for both a reduction and increase in the stiffness due to the cancer's formation and growth. Based on the higher-order version of the nonlocal strain gradient model (HNSM), the stress is related to strain as [44][45][46]…”

“…where σ ij , C ijkl , ε kl , and Θ stg are the stress tensor, elastic property matrix, strain, and strain gradient parameter, respectively. Furthermore, the coefficients in Equation ( 2) are given by λ nls 1 = (κ 1 cell ) 2 and λ nls 0 = (κ 0 cell ) 2 , which are, respectively, the first and second nonlocal stress parameters [46][47][48][49]. Γ 10 ( f ), Γ 1 ( f ), and Γ 0 ( f ) are the combined, first-order, and zeroth-order nonlocal operators, respectively.…”

Analysis of torsional buckling of a cylindrical sandwich shell with a magnetorheological fluid core layer

“…Daikh et al [11] analyzed structures consisting of plates and shells coated with an FG graphene-reinforced composite. Ghandourah et al [12] suggested an innovative model for shell structures with functionally graded materials (FGMs) to study the free vibration response incorporating the porosities and microstructure-dependent effects. They employed the Galerkin method to solve the equations of motion by applying the principle of Hamilton.…”