A unified quasi-three-dimensional solution for vibration analysis of rotating pre-twisted laminated composite shell panels

2021 ◽  
pp. 115072
Author(s):  
Yukun Chen ◽  
Tiangui Ye ◽  
Guoyong Jin ◽  
Heow Pueh Lee ◽  
Xianglong Ma
Keyword(s):  
Vibration Analysis ◽  
Composite Shell ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Dimensional Solution

Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders With Clamped Edge Boundaries

1997 ◽  
Vol 119 (3) ◽  
pp. 317-323 ◽  
Author(s):  
J. Q. Ye ◽  
K. P. Soldatos
Keyword(s):  
Vibration Analysis ◽  
Three Dimensional ◽  
Normal Modes ◽  
Free Vibration Analysis ◽  
Dimensional Solution ◽  
Simply Supported ◽  
Recursive Solution ◽  
Modes Of Vibration ◽  
Hollow Cylinders ◽  
Clamped Edge

Using fully three-dimensional elasticity considerations, this paper presents a free vibration analysis of cross-ply laminated hollow cylinders having clamped edge boundaries. The analysis is based on a recursive solution that has been published elsewhere and is suitable for three-dimensional vibration analysis of corresponding simply supported cylinders. Clamped boundary conditions are initially imposed by means of a number of fixed circles located at the edge(s) of the cylinder considered. Using certain dynamic considerations together with the Lagrange multipliers method, this is achieved by suitably coupling a certain number of different normal modes of vibration of the corresponding simply supported cylinder. Hence, an approximate solution, which however is practically very close to the exact three-dimensional solution, is finally obtained by appropriately increasing either the number of the coupled vibration modes or the number of fixed circles on a clamped edge.

scholarly journals Three-Dimensional Vibration Analysis of Laminated Composite Rectangular Plate with Cutouts

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3113
Author(s):  
Kai Xue ◽  
Wenhao Huang ◽  
Qiuhong Li
Keyword(s):  
Fourier Series ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Future Research ◽  
Analysis Model ◽  
Dimensional Solution ◽  
Element Analysis ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

The main purpose of this paper is to establish an analysis model of laminated composite rectangular plate with/without cutouts on the basis of three-dimensional elasticity theory and provide the exact three-dimensional solution. In the present work, the effect of the cutout is considered by subtracting the energies of cutouts from the total energy of the entire plate. The standard three-dimensional trigonometric cosine Fourier series and auxiliary Fourier series are chosen as admissible functions, and the Hamilton’s principle and Rayleigh-Ritz procedure are used to obtain the exact solution. In order to verify the effectiveness and reliability of the proposed method, some numerical results are obtained, and the results are compared with the ones available in the literature or finite element analysis. Finally, the effects of some key parameters which will affect the vibration characteristics are analyzed, and the non-dimensional frequency parameters are obtained, which can serve as benchmark data for the future research.

scholarly journals Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Salvatore Brischetto ◽  
Roberto Torre
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Curvilinear Coordinates ◽  
The Finite Element Method ◽  
Dimensional Solution ◽  
Isotropic Composite ◽  
Orthogonal Curvilinear Coordinates

AbstractThe paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

Three-Dimensional Vibration Analysis of Rotating Laminated Composite Blades

1993 ◽  
Author(s):  
O. G. McGee ◽  
H. R. Chu
Keyword(s):  
Vibration Analysis ◽  
Thickness Distribution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Fiber ◽  
Coriolis Acceleration ◽  
Composite Blade ◽  
Composite Blades

This work offers the first known three-dimensional (3-D) continuum vibration analysis for rotating, laminated composite blades. A cornerstone of this work is that the dynamical energies of the rotating blade are derived from a 3-D elasticity-based, truncated quadrangular pyramid model incorporating laminated orthotropicity, full geometric nonlinearity using an updated Lagrangian formulation and Coriolis acceleration terms. These analysis sophistications are included to accommodate the nonclassical directions of modern blade designs comprising thin, wide chord lifting surfaces of laminated composite construction. The Ritz method is used to minimize the dynamical energies with displacements approximated by mathematically complete polynomials satisfying the vanishing displacement conditions at the blade root section exactly. Several tables and graphs are presented which describe numerical convergence studies showing the validity of the assumed displacement polynomials used herein. Nondimensional frequency data is presented for various rotating, truncated quadrangular pyramids, serving as first approximations of practical blades employed in aircraft engines and fans. A wide scope of results explain the influence of a number of parameters coined to rotating, laminated composite blade dynamics, namely aspect ratio (a/b), chord ratio (c/b), thickness ratio (b/h), variable thickness distribution (hl/ht), blade pretwist angle (ϕo), composite fiber orientation angle (θ), and angular velocity (Ω). Additional examples are given which elucidate the significance of the linear and nonlinear kinematics used in the present 3-D formulation along with the importance of the Coriolis acceleration terms included in the analysis.

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