On the solution of large‐amplitude vibration of carbon nanotube‐based double‐curved shallow shells

Abstract

The article deals with the large‐amplitude vibration of carbon nanotube‐based double‐curved shallow shells (CNTBDCSSs). After mathematical modeling of CNTBDCSSs, the von Karman‐type nonlinear basic relations of CNTBDCSSs are created, and then the nonlinear equations of motion are derived. Using an extended mixing rule, the CNTBDCSSs are estimated approximately by introducing some performance parameters. Four different carbon nanotube distributions are considered. The nonlinear basic equations are solved applying superposition, Galerkin, and semi‐inverse methods; and the frequency–amplitude relation for the large‐amplitude vibration of CNTBDCSSs is obtained. The nonlinear frequency to linear frequency ratio of CNTBDCSSs is determined as a function of the amplitude. The results are compared with published results to check the reliability and accuracy of the proposed formulation. It follows a systematic investigation aimed at checking the sensitivity of the nonlinear response to some reinforcement parameters and geometry, as the distribution of CNTs within the matrix.

Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

“…In what follows, we provide an analytical solution to the problem of a simplysupported doubly-curved shell. Thus, the structural deflection can be approximated as [21,36] w…”

“…Among various problems is the linear and nonlinear vibration behavior of composite shell structures involving the presence of different distributions of CNTs. Composite shells, indeed, can include uniform or nonuniform patterns of CNTs, depending on the desired mechanical properties of the structures [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In this framework, a pioneering work on the nonlinear vibrations of composite shell structures was represented by [9], which considered a linear distribution of CNTs within the material.…”

“…In this framework, a pioneering work on the nonlinear vibrations of composite shell structures was represented by [9], which considered a linear distribution of CNTs within the material. Following this work, some linear and nonlinear free vibration problems were proposed in [10][11][12][13][14][15][16][17] and [18][19][20][21][22][23][24], respectively, for Nanomaterials 2021, 11, 2090 2 of 15 unconstrained shallow shells and panels reinforced by CNTs, while proposing different numerical methods to solve the related problems.…”

Modeling and Solution of Large Amplitude Vibration Problem of Construction Elements Made of Nanocomposites Using Shear Deformation Theory

“…In this study, by considering von Kármán kinematic nonlinearity, assumptions (11) and using Donnell-type nonlinear theory, the relationship between strains with displacements and angles of rotation for CNT patterned constructions with double curvature can be constructed as follows [ 1 , 36 , 41 ]: where …”

“…Huang et al [ 35 ] presented geometric nonlinear analysis of auxetic hybrid laminated beams containing CNT reinforced composite materials. Avey and Yusufoglu [ 36 ], within the framework of classical shell theory, studied large-amplitude vibrations of double-curved shallow shells based on carbon nanotubes. Yusufoglu and Avey [ 37 ] presented nonlinear dynamic behavior of hyperbolic paraboloidal shells reinforced by carbon nanotubes with various distributions.…”