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In this work, the free vibration of a spinning polymer/fiber/GNP laminated truncated conical shell with non-uniform thickness is analyzed. The conical shell is made of a polymeric matrix reinforced with aligned fibers and uniformly distributed graphene nanoplatelets (GNPs). The elastic constants and density of the nanocomposite are estimated utilizing micromechanical equations, the Halpin–Tsai model, and the rule of mixture. The conical shell is modeled via the first-order shear deformation theory (FSDT) incorporating relative, centrifugal, and Coriolis accelerations alongside the initial hoop tension. Hamilton’s principle is hired to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is hired to provide a numerical solution in the meridional direction alongside an analytical solution presented in the circumferential direction. The effects of several parameters on the natural frequencies and critical rotational speeds are inspected including thickness variation parameters, mass fractions of the fibers and the GNPs, stacking sequence, and boundary conditions. It is discovered that to achieve higher natural frequencies and critical rotational speeds, it is better to increase the mass fractions of the GNPs and fibers and align the fibers in parallel with the meridional direction.

This paper gives a relatively novel computational approach, the discrete singular convolution (DSC) algorithm, for the free vibration analysis of isotropic and orthotropic conical shells with different boundary conditions. The governing differential equations of vibration of the shell are formulated using Love's first approximation classical thin shell theory. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. Typical numerical results are presented illustrating the effect of various geometric and material parameters. The influence of boundary conditions on the frequency characteristics is also discussed. The obtained results are in excellent agreement with those in the literature.

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.