scholarly journals Behavior of Uniform Anisotropic Beams of Rectangular Section under Transverse Impact of a Mass

1997 ◽  
Vol 4 (2) ◽  
pp. 125-141 ◽  
Author(s):  
Lu Chun ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Solution Procedure ◽  
Beam Deflection ◽  
Transverse Impact ◽  
Lagrange Principle ◽  
Arbitrary Boundary ◽  
Force Contact ◽  
Laminated Composite Beam

A numerical method is presented to investigate the dynamic response of uniform orthotropic beams subjected to an impact of a mass. Higher order shear deformation and rotary inertia are included in the analysis of the beams. The impactor and laminated composite beam are treated as a system. The nonlinear differential governing equations of motion are then derived based on the Lagrange principle and modified nonlinear contact law, and solved numerically. The solution procedure is applicable to arbitrary boundary conditions. Numerical results are compared with those available in the literature to demonstrate the validity of the method, and very good agreement is achieved. The effects of boundary conditions on the contact force, contact duration, stress distributions, and beam deflection are discussed.

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.

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

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.

Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 861-871 ◽  
Author(s):  
K. Suzuki ◽  
G. Shikanai ◽  
A. W. Leissa
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Power Series Expansion ◽  
Laminated Composite ◽  
Energy Functional ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Layer Stacking ◽  
Kinetic Energy Functional ◽  
Energy Principles

An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.

Vibration and Buckling Response of Width Tapered Laminated Composite Beams Using Ritz Method for Rotorcraft Blade

2010 ◽  
Author(s):  
Vijay Kumar Badagi ◽  
Rajamohan Ganesan
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Composite Beam ◽  
Ritz Method ◽  
Compressive Force ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Buckling Analysis ◽  
Laminated Composite Beam

In this study, Symmetric cross-ply linear width tapered laminated composite beam is considered. Due to the variety of width tapered composite beams and the complexity of the analysis, no closed-form analytical solution is available at present regarding free vibration response. Therefore in the present work, the Ritz method is used for the free vibration analysis with considering uni-axial compressive and tensile force. The elastic stiffness of the width tapered composite beam is analyzed compared to uniform laminated composite beam. Free vibration which is significant to investigate the dynamic characteristics of the structure using Ritz method with and without effect of axial tensile and compressive force is analyzed. The analysis is based on 1D laminated beam theory. The governing equations are obtained by means of Hamilton’s principle. Tsai-Wu failure analysis is considered to find the tensile and compressive failure force for each ply in the laminate. Buckling analysis is conducted to find the critical buckling force for the laminated composite beam-column subjected to different sets of boundary conditions. Simply supported, Clamped-free, Clamped-Clamped edge boundary conditions are considered. A detailed parametric study is conducted on tapered composite beams made of NCT/301 graphite-epoxy to investigate the effects of the ratio of the width of the thick section to thin section, boundary conditions, effects of axial and compressive force on natural frequency and buckling analysis.

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.

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.

Nonlinear Natural Frequencies of Rotating Composite Thin-Walled Beam with Geometrical Nonlinear

2013 ◽  
Vol 683 ◽  
pp. 779-782 ◽  
Author(s):  
Yong Sheng Ren ◽  
Shuang Shuang Sun ◽  
Chun Jin Zhang
Keyword(s):  
Free Vibration ◽  
Nonlinear Eigenvalue Problem ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Laminated Composite ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Energy Principle ◽  
Rotating Speed ◽  
Thin Walled

The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations.

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