STABILITY AND VIBRATION ANALYSIS OF NON-PRISMATIC THIN-WALLED COMPOSITE SPATIAL MEMBERS OF GENERIC SECTION

2005 ◽  
Vol 05 (04) ◽  
pp. 489-520 ◽  
Author(s):  
S. RAJASEKARAN ◽  
K. NALINAA
Keyword(s):  
Cross Sections ◽  
Vibration Analysis ◽  
Gaussian Quadrature ◽  
Middle Surface ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Mass Matrices ◽  
Jacobi Iteration ◽  
Generic Section ◽  
Thin Walled

This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.

Structural Undamped Free Vibration Analysis Based on Coefficient Reduced-Basis Method

2014 ◽  
Vol 556-562 ◽  
pp. 4214-4217
Author(s):  
Yong Hong Li ◽  
Shu Zhan Li
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Reduced Basis Method ◽  
Mode Shapes ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Reduced Basis ◽  
Linear Elastic ◽  
Basis Method

Using reduced-basis method, design parameters are needed to be separated from the linear elastic operators, which is time-consuming. So, an improved reduced-basis method - coefficient reduced-basis method is introduced to calculate the low order natural frequencies and mode shapes of structure. In this method, the computing process of design parameters separated from the linear elastic operators is simplified. In this paper, a truck frame is taken as an example, frequencies and mode shapes from coefficient reduced-basis method are obtained. Comparing with results from the finite element method, coefficient reduced-basis method can obtain accurate results efficiently.

scholarly journals Vibration analysis of thin-walled composite beams with I-shaped cross-sections

2011 ◽  
Vol 93 (2) ◽  
pp. 812-820 ◽  
Author(s):  
Thuc Phuong Vo ◽  
Jaehong Lee ◽  
Kihak Lee ◽  
Namshik Ahn
Keyword(s):  
Cross Sections ◽  
Vibration Analysis ◽  
Composite Beams ◽  
Thin Walled

Modal Analysis Using Implicit Boundary Finite Element Methods

2014 ◽  
Author(s):  
Zhiyuan Zhang ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
B Spline ◽  
Boundary Method ◽  
Mass Matrices ◽  
Background Mesh ◽  
The Given

Modal analysis is widely used for linear dynamic analysis of structures. The finite element method is used to numerically compute stiffness and mass matrices and the corresponding eigenvalue problem is solved to determine the natural frequencies and mode shapes of vibration. Implicit boundary method was developed to use equations of the boundary to apply boundary conditions and loads so that a background mesh can be used for analysis. A background mesh is easier to generate because the elements do not have to conform to the given geometry and therefore uniform regular shaped elements can be used. In this paper, we show that this approach is suitable for modal analysis and modal superposition techniques as well. Furthermore, the implicit boundary method also allows higher order elements that use B-spline approximations. Several test examples are studied for verification.

scholarly journals Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

2020 ◽  
Vol 10 (21) ◽  
pp. 7802
Author(s):  
Jarosław Latalski ◽  
Daniele Zulli
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Beam Theory ◽  
Middle Surface ◽  
Fem Model ◽  
Out Of Plane ◽  
Thin Walled ◽  
Generalized Beam Theory ◽  
Load Conditions

The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

Free Vibration Analysis of Uniform and Asymmetric Composite Pretwisted Rotating Thin Walled Beam

2017 ◽  
Author(s):  
Touraj Farsadi ◽  
Özgün Şener ◽  
Altan Kayran
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Wind Turbine ◽  
Vibration Analysis ◽  
Structural Model ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Analysis Tool ◽  
Thin Walled

Composite pretwisted rotating thin walled beams (TWB) can be used as the structural model for composite helicopter and wind turbine blades for the study of aeroelastic response of the blades. In the present study, semi-analytical solution is performed for the free vibration analysis of uniform and asymmetric composite pretwisted rotating TWB. The approximation of the Green-Lagrange strain tensor is adopted to derive the strain field of the system. The Euler–Lagrange governing equations of the dynamic system and the related boundary conditions are derived via Hamilton’s principle. In order to solve the governing set of equations, the Extended Galerkin’s Method (EGM) is employed. For this purpose, the structural variables are separated in space and time and the assumed mode shapes are defined to satisfy the essential boundary conditions. For the purpose of validating the TWB model developed, the commercial finite element analysis tool, MSC Nastran is used to compare the results of modal analysis obtained by the present structural model with the finite element solution. With the results obtained in this paper, it is aimed to ascertain the effect of various coupling in circumferentially asymmetric stiffness (CAS) and circumferentially uniform stiffness CUS configurations, pretwist, angular velocity and fibre orientation, on the natural frequencies and the mode shapes of the rotating thin-walled composite beams. The results are expected to propose better predictions of the vibrational behavior of thin walled structures in general, and in the design of rotor blades of turbomachinery, rotorcraft and wind turbine systems, in particular.

Sign in / Sign up

Export Citation Format

Share Document