Large-amplitude vibrations of thin-walled rotating laminated composite cylindrical shell with arbitrary boundary conditions

2020 ◽  
Vol 156 ◽  
pp. 106966 ◽  
Author(s):  
Chaofeng Li ◽  
Peiyong Li ◽  
Bingfu Zhong ◽  
Xueyang Miao
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Large Amplitude ◽  
Laminated Composite ◽  
Composite Cylindrical Shell ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Thin Walled ◽  
Large Amplitude Vibrations

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

Free vibration analysis of laminated composite conical, cylindrical shell and annular plate with variable thickness and general boundary conditions

2021 ◽  
Author(s):  
Kwang Hun Kim ◽  
Songhun Kwak ◽  
Kwangil An ◽  
Kyongjin Pang ◽  
Pyol Kim
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Conical Shell ◽  
Annular Plate ◽  
Laminated Composite ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Arbitrary Boundary

Abstract This paper presents a unified solution method to investigate the free vibration behaviors of laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first order shear deformation theory(FSDT) and displacement components are extended Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generating by the integrating process are disposed by boundary conditions, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are verified through convergence and validation studies. Effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.

scholarly journals An Extended Kantorovich Method Used for Static Solution of an Arbitrarily Edge Supported Sandwich Cylindrical Shell Panel

2019 ◽  
Vol 8 (6) ◽  
pp. 4184-4193
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Laminated Composite ◽  
Static Solution ◽  
Radial Component ◽  
Kantorovich Method ◽  
Power Series Method ◽  
Arbitrary Boundary ◽  
Shell Panel

Exact solution of complex problems like composite shells with arbitrarily supported boundary conditions through analytical three-dimensional (3-D) approach is mathematically challenging. In the present work an analytical 3-D elasticity solution for the static bending problem of a laminated composite cylindrical shell panel having any arbitrary boundary conditions is proposed. The governing Partial Differential Equations (PDE) problems are obtained by the application of the Ressiner-type mixed variational principle in cylindrical coordinate system. The extended Kantrovich method [10] is applied to solve these equations by reducing them to Ordinary Differential Equations (ODE). Further, the set of ODEs corresponding to the radial component & the circumferential components are solved utilizing modified power series method & Pagano’s approach respectively. Through numerical studies of sandwich shell panels it is shown that this method accurately predicts the deflections, stresses, boundary effects and interfacial disruptions being generated of laminate scheme, material property variations and configuration of the shell panel. Crucially, this is achieved with just two or three terms and few iterations, hence attributes faster computation as compared to other numerical techniques.

scholarly journals Free Vibration Analysis of Closed Moderately Thick Cross-Ply Composite Laminated Cylindrical Shell with Arbitrary Boundary Conditions

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 884 ◽  
Author(s):  
Dongyan Shi ◽  
Dongze He ◽  
Qingshan Wang ◽  
Chunlong Ma ◽  
Haisheng Shu
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Governing Equation ◽  
Present Method ◽  
Composite Shell ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Composite Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shell

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 on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.

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