Free vibration analysis of combined composite laminated cylindrical and spherical shells with arbitrary boundary conditions (original) (raw)
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Materials, 2020
A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters...
International Journal of Pressure Vessels and Piping, 2008
A mixed layerwise theory and differential quadrature (DQ) method (LW-DQ) for three-dimensional free vibration analysis of arbitrary laminated circular cylindrical shells is introduced. Using the layerwise theory in conjunction with the three-dimensional form of Hamilton's principle, the transversely discretized equations of motion and the related boundary conditions are obtained. Then, the DQ method is employed to discretize the resulting equations in the axial directions. The fast convergence behavior of the method is demonstrated and its accuracy is verified by comparing the results with those of other shell theories obtained using conventional methods and also with those of ANSYS software. In the case of arbitrary laminated shells with simply supported ends, the exact solution is developed for comparison purposes. It is shown that using few DQ grid points, converged accurate solutions are obtained. Less computational efforts of the proposed approach with respect to ANSYS software is shown.
Composite Structures, 2019
This paper presents a new class of refined beam theories for static and dynamic analysis of composite structures. These beam models are obtained by implementing higher-order expansions of Chebyshev polynomials for the three components of the displacement field over the beam cross-section. The Carrera Unified Formulation (CUF) is adopted to obtain higher-order beam models. The governing equations are written in terms of fundamental nuclei, which are independent of the choice of the expansion order and the interpolating polynomials. Static and free vibration analysis of laminated beams and thin walled boxes has been carried out. Results obtained with the novel Chebyshev Expansion (CE) model have been compared with those available in the literature. For comparison, Taylor-like Expansion (TE) and Lagrange Expansion (LE) CUF models, commercial codes, analytical and experimental data are exploited. The performances of refined beam models in terms of computational cost and accuracy in comparison to the reference solutions have been assessed. The analysis performed has pointed out the high level of accuracy reached by the refined beam models with lower computational costs than 2D and 3D Finite Elements.
Composites Part B: Engineering, 2001
The bending, buckling and free vibration problems of non-homogeneous composite laminated cylindrical shells are considered. Hamilton–Reissner's mixed variational principle is used to deduce a consistent first-order theory of composite laminated cylindrical shells with non-homogeneous elastic properties. The governing equations with their required boundary conditions are derived without introducing any shear correction factors. Numerical results for the transverse deflections, stresses, natural frequencies and critical buckling loads are presented to show the advantages of this theory. The influences of the non-homogeneity and thickness ratio on the shell structural response are investigated. The study concludes that the inclusion of the non-homogeneity effect is required, even if it is weak, for predicting the actual structural response of the shells.
Vietnam Journal of Mechanics, 2022
This study investigates the static and free vibration responses of orthotropic laminated composite spherical shells using various refined shear deformation theories. Displacement-based refined shear deformation theories are presented herein for the analysis of laminated composite spherical shells via unified mathematical formulations. Equations of motion associated with the present theory are derived within the framework of Hamilton's principle. Analytical solutions for the static and free vibration problems of laminated spherical shells are obtained using Navier's technique for the simply supported boundary conditions. Few higher order and classical theories are recovered from the present unified formulation; however, many other theories can be recovered from the present unified formulation. The numerical results are obtained for symmetric as well as anti-symmetric laminated shells. The present results are compared with previously published results and 3-D elasticity solution. From the numerical results, it is concluded that the present theories are in good agreement with other higher order theories and 3-D solutions.
Journal of Solid Mechanics, 2021
The present study analyzes the free vibration of multi-layered composite cylindrical shells and perforated composite cylindrical shells via a modified version of Reddy's third-order shear deformation theory (TSDT) under simple support conditions. An advantage of the proposed theory over other high-order theories is the inclusion of the shell section trapezoidal form coefficient term in the displacement field and strain equations to improve the accuracy of results. The non-uniform stiffness and mass distributions across reinforcement ribs and the empty or filled bays between the ribs in perforated shells were addressed via a proper distribution function. For integrated perforated cylindrical shells, the results were validated by comparison to other studies and the numerical results obtained via ABAQUS. The proposed theory was in good consistency with numerical results and the results of previous studies. It should be noted that the proposed theory was more accurate than TSDT.
Applied Sciences, 2016
The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.
Archive of Applied Mechanics, 2012
This paper focuses on the free vibration analysis of thick, rotating laminated composite conical shells with different boundary conditions based on the three-dimensional theory, using the layerwise differential quadrature method (LW-DQM). The equations of motion are derived applying the Hamilton's principle. In order to accurately account for the thickness effects, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equation applying the DQM in the meridional direction. This study demonstrates the applicability, accuracy, stability and the fast rate of convergence of the present method, for free vibration analyses of rotating thick laminated conical shells. The presented results are compared with those of other shell theories obtained using conventional methods and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell and excellent agreements are achieved.
Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM)
Composite Structures, 2007
Free vibration analysis of composite cylindrical shells with different boundary conditions is presented in this paper using differential quadrature method (DQM). Equations of motion are derived based on first order shear deformation theory taking the effects of shear deformation and rotary inertia terms into account. By applying the differential quadrature formulation and the required modified relationships for implementing the different boundary conditions, equations of motion of a circular cylindrical shell are transformed into a set of algebraic equations. By solving this algebraic system natural frequencies of circular cylindrical shells made of fibrous composite materials with different fibre angles are evaluated. The results thus obtained are then compared with some available results and a good agreement is observed. In all the cases studied here efficiency, ease and usefulness of the DQM are well illustrated.