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.

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.

A numerical method for static and free-vibration analysis of non-uniform Timoshenko beam–columns

2006 ◽  
Vol 33 (3) ◽  
pp. 278-293 ◽  
Author(s):  
Z Canan Girgin ◽  
Konuralp Girgin
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Beam Columns ◽  
Geometrical Properties ◽  
Stiffness Matrices

A generalized numerical method is proposed to derive the static and dynamic stiffness matrices and to handle the nodal load vector for static analysis of non-uniform Timoshenko beam–columns under several effects. This method presents a unified approach based on effective utilization of the Mohr method and focuses on the following arbitrarily variable characteristics: geometrical properties, bending and shear deformations, transverse and rotatory inertia of mass, distributed and (or) concentrated axial and (or) transverse loads, and Winkler foundation modulus and shear foundation modulus. A successive iterative algorithm is developed to comprise all these characteristics systematically. The algorithm enables a non-uniform Timoshenko beam–column to be regarded as a substructure. This provides an important advantage to incorporate all the variable characteristics based on the substructure. The buckling load and fundamental natural frequency of a substructure subjected to the cited effects are also assessed. Numerical examples confirm the efficiency of the numerical method.Key words: non-uniform, Timoshenko, substructure, elastic foundation, geometrical nonlinearity, stiffness, stability, free vibration.

Derivation of New Transcendental Member Stiffness Determinant for Vibrating Frames

2003 ◽  
Vol 03 (02) ◽  
pp. 299-305 ◽  
Author(s):  
F. W. Williams ◽  
D. Kennedy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Infinite Order ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Structural Stiffness ◽  
Trial And Error ◽  
Stiffness Matrices ◽  
Vibration Problems

Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall transcendental stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. The present paper gives the first ever derivation of the Bernoulli–Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

Vibration Analysis of Axially Loaded Beams Including Rotary Inertia: An Exact Dynamic Finite Element

2004 ◽  
Author(s):  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Dynamic Stiffness ◽  
Vibrational Analysis ◽  
Single Frequency ◽  
Rotary Inertia ◽  
Shape Functions ◽  
Bending Vibrations ◽  
Dynamic Finite Element ◽  
Axially Loaded

An ‘exact’ basis function Dynamic Finite Element (DFE) for the free vibrational analysis of axially loaded beams and assemblages composed of beams is presented. The shear deformation is neglected but the Rotary Inertia (RI) effects are taken into consideration. The dynamic trigonometric shape functions for bending vibrations of an axially loaded uniform beam element are first derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables based on these dynamic shape functions, leads to a single frequency dependent Dynamic Stiffness Matrix (DSM) that represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by an illustrative example of cantilever beam where the influence of Rotary Inertia (RI) effect and different axial loads on the natural frequencies of the system is demonstrated by numerical results.

Development of Stereolithography Simulation Process Based on the Dynamic Finite Element Method

2007 ◽  
Vol 340-341 ◽  
pp. 329-334
Author(s):  
You Min Huang ◽  
Cho Pei Jiang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Stiffness ◽  
Scanning Speed ◽  
Weight Coefficient ◽  
Experimental Result ◽  
Simulation Code ◽  
Dynamic Finite Element ◽  
Scanning Path ◽  
Element Method

In this study, a general simulation code is developed to analyze the shrinkage effect of polymerization and optimize the fabrication parameters including the scanning path, exposure time and scanning speed for the stereolithography system. The code is based on the dynamic finite element method. Liquid element is preconstructed without curing properties till the absorption energy exceeds the critical value of dynamic stiffness matrix assembling. A unit element block is utilized with a weight coefficient for expressing a laser Gaussian energy distribution during the discretizing of the scanning path into increments. A fan blade is proposed to validate the agreement between the simulation and experimental results. The prototype is a fabrication and the surface of blade was measured by the digitizing system ATOS (Advanced TOpometric Sensor) for comparing the deformation with analysis prediction. Consequently, the simulated result closely conforms to the experimental result.

Accurate Free Vibration Analysis for Rotating Shaft

1991 ◽  
Author(s):  
Bo Suk Yang ◽  
Walter D. Pilkey
Keyword(s):  
Shape Function ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Rotor Dynamics ◽  
Transfer Matrices ◽  
Rotating Shaft ◽  
Frequency Dependent ◽  
Dynamic Mass ◽  
Stiffness Matrices ◽  
Dynamics Analyses

Abstract This paper presents an approach for the derivation of dynamic mass, gyroscopic and stiffness matrices for rotor dynamics analyses. The axial, torsional and bending dynamic stiffness matrices are deduced from transfer matrices, and, in turn, the frequency-dependent element matrices are derived. The relationships between the dynamic stiffness matrix and the frequency-dependent element matrices are defined. Numerical examples show that this method gives more accurate results than those obtained using the conventional static shape function based element matrices.

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