Vibration characteristics of moderately thick doubly curved functionally graded composite panels reinforced by carbon nanotube are analyzed. Here, special cases of doubly curved shell panels such as spherical, cylindrical and hyperbolic paraboloid panels and five different distributions of carbon nanotubes through the thickness direction are considered. By utilizing the modified rule of mixture, mechanical properties are estimated. The equations of motion are derived via the first-order shear deformation theory, and non-dimensional frequencies are obtained by the use of Galerkin’s method. The suggested model is justified by a good agreement between the results given by present model and available data in the literature. The influences of volume fraction of carbon nanotubes, thickness ratio, aspect ratio, curvature ratio, and shallowness ratio on the frequencies of moderately thick doubly curved nanocomposite shell panels are also examined. Furthermore, the effect of various boundary conditions on the frequency analysis of doubly curved nanocomposite panels is studied, and the corresponding mode shapes are depicted.

Frequency analysis of doubly curved functionally graded carbon nanotube-reinforced composite panels

In this article, a semi-analytical solution is provided to investigate the free vibration characteristics of rotating truncated conical shells surrounded by a Winkler–Pasternak type foundation. It is assumed that the material of the shell is composed of epoxy as matrix and graphene nanoplatelets (GPLs) as reinforcement dispersed in both thickness and length directions of the shell. The shell is modeled based on first-order shear deformation theory and the equivalent mechanical properties are evaluated using the rule of the mixture and the Halpin–Tsai model. The governing equations are derived by implementing Hamilton’s principle incorporating centrifugal acceleration, Coriolis acceleration, and the initial hoop tension. Utilizing trigonometric functions, an analytical solution is presented to solve the governing equations in the circumferential direction and a numerical solution is provided in the longitudinal direction by utilizing differential quadrature method. The convergence and accuracy of the present results are examined with those available in the literature. A parametric study is provided to check the influences of boundary conditions, rotational speed, circumferential wave number, mass fraction and dispersion pattern of the GPLs, and Winkler and shear coefficients of the foundation on the natural frequencies of the shell. It is concluded that an increment in the mass fraction of the GPLs increases the natural frequencies and the GPLs scattering near the inner surface and the small radius of the shell have a higher reinforcing effect.

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

Nonlinear vibration suppression of laminated composite conical shells on elastic foundations with magnetostrictive layers

The excitation frequencies of parametric vibration of laminated non-homogeneous orthotropic conical shells (LNHOCSs) under axial load periodically varying with time, are determined using the classical shell theory (CST). The basic equations are found using the Donnell-Mushtari shell theory and reduce to the Mathieu-Hill type differential equation, in which the instability is examined by the Bolotin method. To validate of current results was made a comparison with the previous studies. The effects of stacking sequences, axial load factors, non-homogeneity, as well as the variation of geometric characteristics on the backward and forward excitation frequencies (BFEFs) of conical shells are studied in detail.

Determination of the excitation frequencies of laminated orthotropic non-homogeneous conical shells

Abstract This study offers a unique solution for the free vibration of rotating FGP sandwich cylindrical shells under different boundary conditions. A new type of sandwich structures with a metal-foam core and two coating FGM layers is investigated. Equations of motion governing the free vibration of rotating shells are derived by the first-order, shear-deformation shell theory. Single-term modal functions are introduced in Rayleigh-Ritz method to efficiently determine natural frequencies of the shell. After result validations, the influence of volume fraction index, distribution schemes, core-layer thickness, porosity coefficient, rotating velocity, geometrical parameters, and boundary conditions on the shell natural frequencies are studied.

Free vibration analysis of rotating FGP sandwich cylindrical shells with metal-foam core layer

In this paper, free vibration analysis of fiber reinforced composite (FRC) conical shells resting on Pasternak-type elastic foundation is investigated. Two kinds of fiber distribution in the thickness direction, namely, uniformly distributed and functionally graded are considered. The material properties of FRC conical shells are estimated through a volume fraction power law. The equations of motion are derived through variational formulation. The governing equations are developed based on the classical shells theory and Sanders assumptions. Galerkin and Ritz methods are employed to solve the governing equations and determine natural frequencies of the conical shell. The conical shell assumed to be clamped at the both ends. Results are presented on the effect of fiber volume fraction, semi-vertex angle, thickness to radius ratio and elastic foundation stiffness parameters on the frequency characteristics of the conical shells. A comparative study between Ritz and Galerkin methods is carried out. Validity of the present study is confirmed by comparing the results with the data available in the open literature for a special case. A good agreement is observed between them.

E. Zarouni

Papers

Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods