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 A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

2019 ◽  
Vol 24 (2) ◽  
pp. 217-227
Author(s):  
Mostafa Talebitooti
Keyword(s):  
Boundary Conditions ◽  
Conical Shell ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Algebraic Equations ◽  
Discrete Elements ◽  
Arbitrary Boundary ◽  
Stiffened Shells

A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

scholarly journals Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 1010 ◽  
Author(s):  
Bin Qin ◽  
Xing Zhao ◽  
Huifang Liu ◽  
Yongge Yu ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Variational Approach ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Arbitrary Boundary ◽  
Correlated Parameters ◽  
Laminated Composite Beams

A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Free vibration and buckling analysis of laminated composites and sandwich microbeams using a transverse shear-normal deformable beam theory

2019 ◽  
Vol 26 (3-4) ◽  
pp. 214-228 ◽  
Author(s):  
Armagan Karamanli ◽  
Metin Aydogdu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transverse Shear ◽  
Couple Stress Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Aspect Ratios

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios.

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.

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