scholarly journals Free vibration analysis of extension-torsion coupled elements using a dynamic finite element (DFE) formulation

2021 ◽  
Author(s):  
Andrew Roach
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Structural Members ◽  
Cross Sectional ◽  
Dynamic Finite Element ◽  
Laminated Composite Beams

In this report, the extension-torsion coupled vibration behavior of several structural members is investigated. In order to solve the governing differential equations of motion for the problem, three different approaches, namely the dynamic stiffness matrix (DSM), finite element (FEM), and dynamic finite element (DFE) methods are used. Three different engineering applications of interest are identified, namely, a helical spring, a wire rope and laminated composite beams. For each of these applications, a method for determining the cross-sectional stiffness constants of interest is first introduced. Illustrative examples of each system are then studied where resulting natural frequencies and modes are compared to those available in literature. In order to determine the performance of each solution method in the determination of the dynamic behavior of these systems, all three (DSM, FEM, and DFE) methods are used in the examples, and a comparative study among the results is then carried out to gauge the accuracy of each approach.

scholarly journals Free vibration analysis of extension-torsion coupled elements using a dynamic finite element (DFE) formulation

2021 ◽  
Author(s):  
Andrew Roach
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Structural Members ◽  
Cross Sectional ◽  
Dynamic Finite Element ◽  
Laminated Composite Beams

In this report, the extension-torsion coupled vibration behavior of several structural members is investigated. In order to solve the governing differential equations of motion for the problem, three different approaches, namely the dynamic stiffness matrix (DSM), finite element (FEM), and dynamic finite element (DFE) methods are used. Three different engineering applications of interest are identified, namely, a helical spring, a wire rope and laminated composite beams. For each of these applications, a method for determining the cross-sectional stiffness constants of interest is first introduced. Illustrative examples of each system are then studied where resulting natural frequencies and modes are compared to those available in literature. In order to determine the performance of each solution method in the determination of the dynamic behavior of these systems, all three (DSM, FEM, and DFE) methods are used in the examples, and a comparative study among the results is then carried out to gauge the accuracy of each approach.

FREE VIBRATION ANALYSIS OF CROSS-PLY LAMINATED COMPOSITE BEAMS BY MIXED FINITE ELEMENT FORMULATION

2013 ◽  
Vol 13 (02) ◽  
pp. 1250056 ◽  
Author(s):  
ATİLLA ÖZÜTOK ◽  
EMRAH MADENCİ
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Mixed Finite Element ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Moment ◽  
Vertical Displacement ◽  
Laminated Composite Beams

In this study, a mixed-finite element method for free vibration analysis of cross-ply laminated composite beams is presented based on the "Euler–Bernoulli Beam Theory" and "Timoshenko Beam Theory". The Gâteaux differential approach is employed to construct the functionals of laminated beams using the variational method. By using these functionals in the mixed-type finite element method, two beam elements CLBT4 and FSDT8 are derived for the Euler–Bernoulli and Timoshenko beam theories, respectively. The CLBT4 element has four degrees of freedom (DOFs), containing the vertical displacement and bending moment as unknowns at the nodes, whereas the FSDT8 element has eight DOFs, containing the vertical displacement, bending moment, shear force and rotation as unknowns. A computer program is developed to execute the analyses for the present study. The numerical results of free vibration analyses obtained for different boundary conditions are presented and compared with results available in the literature, which indicates the reliability of the present approach.

COUPLED FREE VIBRATION ANALYSIS OF SHEAR-FLEXIBLE LAMINATED COMPOSITE I-BEAMS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250024
Author(s):  
NAM-IL KIM
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix ◽  
Analytical Technique

The coupled free vibration analysis of the thin-walled laminated composite I-beams with bisymmetric and monosymmetric cross sections considering shear effects is developed. The laminated composite beam takes into account the transverse shear and the restrained warping induced shear deformation based on the first-order shear deformation beam theory. The analytical technique is used to derive the constitutive equations and the equations of motion of the beam in a systematic manner considering all deformations and their mutual couplings. The explicit expressions for displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the dynamic stiffness matrix is determined using the force–displacement relationships. In addition, for comparison, a finite beam element with two-nodes and fourteen-degrees-of-freedom is presented to solve the equations of motion. The performance of the dynamic stiffness matrix developed by study is tested through the solutions of numerical examples and the obtained results are compared with results available in literature and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The vibrational behavior and the effect of shear deformation are investigated with respect to the modulus ratios and the fiber angle change.

scholarly journals Dynamic Finite Element Modelling And Free Vibration Analysis Of Delaminated Composite Beams

2021 ◽  
Author(s):  
Nicholas Erdelyi
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Accurate Analysis ◽  
Dynamic Finite Element ◽  
Current Trends ◽  
Stiffness Matrices ◽  
The Future ◽  
Future Work ◽  
Dynamic Element

The requirement for accurate analysis tools to predict the behaviour of delaminated composites has grown and will continue to grow into the future, due to the high demand of these materials on major structural components. In the following, a detailed analysis of single- and double-delaminated beams is made, using traditional finite element techniques, as well as two dynamic element-based techniques. The Dynamic Stiffness Matrix (DSM) and Dynamic Finite Element (DFE) techniques introduce the concept of frequency-dependent stiffness matrices and shape functions, respectively, and have been documented to exhibit excellent convergence qualities when compared to traditional finite elements. Current trends in the literature are critically examined, and insight into different types of modeling techniques and constraint types are introduced. In particular, the continuity (both kinematic and force) conditions at delamination tips plays a large role in each model’s formulation. In addition, the data previously available from a commercial finite element suite are also utilized to validate the natural frequencies of the systems analyzed here. Beam element-based techniques are used and the results are compared to those obtained using the dynamic element techniques and data from the literature. In each case excellent agreement between different techniques was observed. Finally, general concluding remarks are made on the usefulness of the presented theories, and some comments are made on the future work of this research path.

scholarly journals Dynamic Finite Element Modelling And Free Vibration Analysis Of Delaminated Composite Beams

2021 ◽  
Author(s):  
Nicholas Erdelyi
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Accurate Analysis ◽  
Dynamic Finite Element ◽  
Current Trends ◽  
Stiffness Matrices ◽  
The Future ◽  
Future Work ◽  
Dynamic Element

The requirement for accurate analysis tools to predict the behaviour of delaminated composites has grown and will continue to grow into the future, due to the high demand of these materials on major structural components. In the following, a detailed analysis of single- and double-delaminated beams is made, using traditional finite element techniques, as well as two dynamic element-based techniques. The Dynamic Stiffness Matrix (DSM) and Dynamic Finite Element (DFE) techniques introduce the concept of frequency-dependent stiffness matrices and shape functions, respectively, and have been documented to exhibit excellent convergence qualities when compared to traditional finite elements. Current trends in the literature are critically examined, and insight into different types of modeling techniques and constraint types are introduced. In particular, the continuity (both kinematic and force) conditions at delamination tips plays a large role in each model’s formulation. In addition, the data previously available from a commercial finite element suite are also utilized to validate the natural frequencies of the systems analyzed here. Beam element-based techniques are used and the results are compared to those obtained using the dynamic element techniques and data from the literature. In each case excellent agreement between different techniques was observed. Finally, general concluding remarks are made on the usefulness of the presented theories, and some comments are made on the future work of this research path.

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