Spectral Element Model for the Vibration of a Bending-Shear-Torsion Coupled Composite Timoshenko Beam

2010 ◽  
Author(s):  
Usik Lee ◽  
Injoon Jang
Keyword(s):  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Spectral Element ◽  
Beam Model ◽  
Shape Functions ◽  
Laminated Beams ◽  
Composite Timoshenko Beam ◽  
Dynamic Shape

In this paper, a spectral element model is developed for axially loaded bending-shear-torsion coupled composite laminated beams. The composite laminated beams are represented by the Timoshenko beam model based on the first-order shear deformation theory. The spectral element model is formulated by using the variational method from frequency-dependent dynamic shape functions. The dynamic shape functions are derived from exact wave solutions to the governing differential equations of motion which are transformed into the frequency-domain by using the DFT theory. The numerical results show that the present spectral model provides extremely accurate natural frequencies for an example problem when compared to the results obtained by using the conventional finite element model which is also presented in this paper.

Frequency-Domain Spectral Element Model of a Uniform Spinning Shaft

2012 ◽  
Vol 224 ◽  
pp. 264-267
Author(s):  
Usik Lee ◽  
In Joon Jang ◽  
Il Wook Park
Keyword(s):  
Differential Equations ◽  
Timoshenko Beam ◽  
Variational Approach ◽  
Element Model ◽  
Spectral Element ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Shape Functions ◽  
Wave Solutions ◽  
Spinning Shaft

This paper presents a spectral element model for the spinning uniform shaft represented by the Timoshenko beam model. The bearing-supports are represented by equivalent springs. The variational approach is used to formulate the spectral element model from the frequency-dependent shape functions derived from exact wave solutions to the governing differential equations.

Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity

2017 ◽  
Vol 17 (07) ◽  
pp. 1750077 ◽  
Author(s):  
Zhiyang Lei ◽  
Jinpeng Su ◽  
Hongxing Hua
Keyword(s):  
Timoshenko Beam ◽  
Control Method ◽  
Dynamic Properties ◽  
Element Model ◽  
Spectral Element ◽  
Coupling Mechanism ◽  
Beam Model ◽  
Coupling Coefficients ◽  
Coupling Vibration ◽  
Mass Eccentricity

Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton’s principle, the coupled governing equations are derived and mass and stiffness coupling coefficients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non--uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.

Spectral Element Modeling for Elastic Two-Layer Beams

2007 ◽  
Vol 26-28 ◽  
pp. 297-300
Author(s):  
Sung Jun You ◽  
In Joon Jang ◽  
Usik Lee
Keyword(s):  
Equations Of Motion ◽  
Element Model ◽  
Spectral Element ◽  
High Accuracy ◽  
Shape Functions ◽  
Governing Equations ◽  
Laminated Beam ◽  
Coupled Equations ◽  
Layered Beams ◽  
Layered Beam

This paper develops a spectral element model for elastic-elastic two-layered beams. First, the axial-bending coupled equations of motion for an elastic two-layer laminated beam are derived. The spectral element model is then formulated by using the wave solutions satisfying governing equations in frequency-domain as the frequency-dependent shape functions. The spectral element model is finally applied to a cantilevered elastic-elastic two-layered beam as an illustrative problem. The high accuracy of the present spectral element model is verified by comparing the SEM results with those obtained by conventional FEM.

Spectral Element Model for the PZT-Bonded Laminated Composite Beams

2012 ◽  
Vol 249-250 ◽  
pp. 838-841 ◽  
Author(s):  
Usik Lee ◽  
Il Wook Park ◽  
In Joon Jang
Keyword(s):  
Frequency Domain ◽  
Dynamic Stiffness ◽  
Laminated Composite ◽  
Element Model ◽  
Spectral Element ◽  
Composite Beams ◽  
Dft Theory ◽  
Shape Functions ◽  
Laminated Composite Beams ◽  
Dynamic Shape

This paper presents a spectral element model for the laminated composite beams with a surface-bonded PZT layer. The spectral element model represented by exact dynamic stiffness matrix is derived in the frequency-domain by using the frequency-dependent dynamic shape functions which are formulated from the free wave solutions satisfying the governing differential equations transformed into the frequency-domain by using the DFT theory. The performance of the present spectral element model is then evaluated by comparing its solutions with those obtained by using the conventional finite element model

scholarly journals Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

2020 ◽  
Vol 10 (15) ◽  
pp. 5102
Author(s):  
Carlos Valencia Murillo ◽  
Miguel Gutierrez Rivera ◽  
Junuthula N. Reddy
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Variable Thickness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Linear Elastic ◽  
Commercial Code ◽  
The Finite Element Model ◽  
Hp Finite Element

In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a Higher-order Shear Deformation Theory, and the equations of motion are obtained by means of Hamilton’s principle. Analysis is performed for isotropic linear elastic shells. A validation of the formulation is made by comparing the present results with those reported in the literature and with simulations in the commercial code ANSYS. Finally, results for shell like structures with variable thickness are presented, and their behavior for different ratios r/h and L/r is studied.

Free Vibration Analysis of Multilayered Functionally Graded Composite Cylinder

2010 ◽  
Author(s):  
M. H. Kargarnovin ◽  
M. Hashemi
Keyword(s):  
Free Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Element Model ◽  
Functionally Graded ◽  
Composite Cylinder ◽  
Shape Functions ◽  
Functionally Graded Composite

Free vibration of multilayered composite cylinder which volume fraction of fiber varies according to power law in longitudinal direction has been studied. Rule of mixture model and reverse of that are employed to represent elastic properties of this fibrous functionally graded composite. Strain-displacement relations employed are based on Reissner-Naghdi-Berry’s shell theory. The displacement finite element model of the governing equations of motion is derived by writing weak form of them. The Lagrangian shape functions for in-plane displacements and Hermitian shape functions for displacement in normal direction to the surface of mid-plane are utilized by defining a conformal quadrilateral element. The results show that by appropriate grading material properties of fiber in longitudinal direction the natural frequencies can be increased in comparison with traditional composite in which volume fraction of fiber does not vary.

scholarly journals Effects of Delamination on Guided Waves in a Symmetric Laminated Composite Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Seungwan Kim ◽  
Usik Lee
Keyword(s):  
Frequency Domain ◽  
Composite Beam ◽  
Guided Waves ◽  
Structural Integrity ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Element Model ◽  
Spectral Element ◽  
Composite Beams ◽  
Variation Method

For successful structural health monitoring and structural integrity evaluation of a laminated composite structure, it is important to study the effects of delamination on the propagations of the guided waves in a delaminated composite beam by using an accurate and computationally efficient method. Thus, we developed a “frequency-domain” spectral element model for the symmetric composite beams. First-order-shear-deformation-theory (FSDT) based Timoshenko beam theory and Mindlin-Herrmann rod theory are adopted for the flexural (bending) waves and axial (extensional) waves, respectively. A spectral element model is derived from the governing equations of motion by using the variation method in the frequency domain. After validating the accuracy of the proposed spectral element model, the model is used to investigate the effects of delamination on the propagation of guided waves in examples of composite beams.

scholarly journals Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Sangkyu Choi ◽  
Usik Lee
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Model ◽  
Spectral Element ◽  
Rotor System ◽  
Dynamic Responses ◽  
Disk System ◽  
Unbalanced Mass ◽  
Rotor Systems ◽  
Blade System

A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.

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