scholarly journals Coupled Bending-Bending-Torsion Vibration of a Pre-Twisted Beam with Aerofoil Cross-Section by the Finite Element Method

2003 ◽  
Vol 10 (4) ◽  
pp. 223-230
Author(s):  
Bulent Yardimoglu ◽  
Daniel J. Inman
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Higher Order ◽  
Coupling Coefficients ◽  
Cross Sectional ◽  
Torsion Vibration ◽  
Proper Order ◽  
Proposed Model

The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.

A Slice Finite Element Model for Bending Analysis of Curved Beams

2011 ◽  
Vol 338 ◽  
pp. 282-285 ◽  
Author(s):  
Wen Guang Jiang ◽  
Li Juan Yan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Finite Element Modelling ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Curved Beams ◽  
Pure Bending ◽  
Cross Sectional ◽  
Bending Analysis ◽  
Constraint Equations

The pure bending analysis of curved beams may be performed by finite element modelling of only a representative slice sector of the beam cross-section, by establishing exact deformation relationships between degrees of freedom of corresponding nodes on the corresponding artificial cross-sectional boundaries. These deformation relationships can be conveniently realized using constraint equations between nodal degrees of freedom. Numerical example has been given to demonstrate the accuracy and effectiveness of the proposed method.

Contribution of Lamb wave modes in the formation of higher order modes cluster (HOMC) guided waves

2021 ◽  
pp. 095440622110424
Author(s):  
Z Abbasi ◽  
F Honarvar
Keyword(s):  
Finite Element ◽  
Wave Packet ◽  
Lamb Wave ◽  
Guided Waves ◽  
Element Model ◽  
Higher Order ◽  
Guided Wave ◽  
Cross Sectional ◽  
Higher Order Modes ◽  
Wave Modes

In recent years, Higher Order Modes Cluster (HOMC) guided waves have been considered for ultrasonic testing of plates and pipes. HOMC guided waves consist of higher order Lamb wave modes that travel together as a single nondispersive wave packet. The objective of this paper is to investigate the effect of frequency-thickness value on the contribution of Lamb wave modes in an HOMC guided wave. This is an important issue that has not been thoroughly investigated before. The contribution of each Lamb wave mode in an HOMC guided wave is studied by using a two-dimensional finite element model. The level of contribution of various Lamb wave modes to the wave cluster is verified by using a 2D FFT analysis. The results show that by increasing the frequency-thickness value, the order of contributing modes in the HOMC wave packet increases. The number of modes that comprise a cluster also increases up to a specific frequency-thickness value and then it starts to decrease. Plotting of the cross-sectional displacement patterns along the HOMC guided wave paths confirms the shifting of dominant modes from lower to higher order modes with increase of frequency-thickness value. Experimental measurements conducted on a mild steel plate are used to verify the finite element simulations. The experimental results are found to be in good agreement with simulations and confirm the changes observed in the level of contribution of Lamb wave modes in a wave cluster by changing the frequency-thickness value.

A New Rectangular Plate Element for Vibration Analysis of Laminated Composites

1998 ◽  
Vol 120 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Guan-Liang Qian ◽  
Suong V. Hoa ◽  
Xinran Xiao
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Rectangular Plate ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Model ◽  
Higher Order ◽  
Transverse Displacement

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.

Transmission Loss of Variable Cross Section Apertures

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
J. Li ◽  
L. Zhou ◽  
X. Hua ◽  
D. W. Herrin
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Sound Propagation ◽  
Transmission Loss ◽  
Element Model ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Cross Sectional ◽  
Radiation Impedance ◽  
The Cross

Openings in enclosures or walls are frequently the dominant path for sound propagation. In the current work, a transfer matrix method is used to predict the transmission loss of apertures assuming that the cross-sectional dimensions are small compared with an acoustic wavelength. Results are compared with good agreement to an acoustic finite element approach in which the loading on the source side of the finite element model (FEM) is a diffuse acoustic field applied by determining the cross-spectral force matrix of the excitation. The radiation impedance for both the source and termination is determined using a wavelet algorithm. Both approaches can be applied to leaks of any shape and special consideration is given to apertures with varying cross section. Specifically, cones and abrupt area changes are considered, and it is shown that the transmission loss can be increased by greater than 10 dB at many frequencies.

scholarly journals Coupled Bending-Bending-Torsion Vibration of a Rotating Pre-Twisted Beam with Aerofoil Cross-Section and Flexible Root by Finite Element Method

2004 ◽  
Vol 11 (5-6) ◽  
pp. 637-646 ◽  
Author(s):  
Bulent Yardimoglu ◽  
Daniel J. Inman
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Centrifugal Force ◽  
Axial Stress ◽  
Element Model ◽  
Torsional Stiffness ◽  
Extended Model ◽  
Beam Model ◽  
Cross Sectional

The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.

A Finite Element Model for Cables With Nonsymmetrical Geometry and Loads

1994 ◽  
Vol 116 (1) ◽  
pp. 14-20 ◽  
Author(s):  
T. T. Le ◽  
R. H. Knapp
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Circular Cross Section ◽  
Element Model ◽  
Computer Code ◽  
Deformation Analysis ◽  
Contact Points

A new two-dimensional finite element model is proposed for the deformation analysis of cable cross sections. The deformations of the cable cross section are of considerable design interest because of their effect on the induced torque or rotation of the cable. This model accounts for material orthotropy and nonsymmetrical geometry and loads. Each component of the cable is assumed to possess a circular cross section and is modeled as a macro-element having nodal degrees-of-freedom at all contact points with adjoining components. Usual finite element procedures are applied to solve for the unknown displacements at contact nodal points. The model is implemented in a computer code and is verified by test results obtained for an as-built cable.

scholarly journals Analysis of stiffened laminated composite plates by finite element based on higher-order displacement theory

2008 ◽  
Vol 30 (2) ◽  
pp. 112-121 ◽  
Author(s):  
Tran Ich Thinh ◽  
Tran Huu Quoc
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Element Model ◽  
Higher Order ◽  
Plate Element ◽  
Laminated Composite Plates ◽  
Element Free

In this paper, authors use a finite element model based on higher-order displacement plate theory for analysis of stiffened laminated composite plates. Transverse shear deformation is included in the formulation making the model applicable for both moderately thick and thin composite plates. The plate element used is a nine-noded isoparametric one with nine degrees of freedom at each node. The stiffness of stiffener is reflected at all nine nodes of plate element in which it is placed. Accordingly, the stiffeners can be positioned anywhere within the place element. Free vibration and deflection of stiffened laminated composite plates are carried out, and results are compared with existing analytical and other solutions.

Mechanical Numerical Analysis for L-Shape Traffic Signs Bar with Variable Cross-Section

2013 ◽  
Vol 444-445 ◽  
pp. 1250-1254
Author(s):  
Ben Ning Qu ◽  
Ran Guo ◽  
Bang Cheng Yang
Keyword(s):  
Finite Element ◽  
Theoretical Calculation ◽  
Cross Section ◽  
Simulation Analysis ◽  
Element Model ◽  
Thin Wall ◽  
Variable Cross ◽  
Axial Line ◽  
Traffic Sign ◽  
Cross Sectional

L-shape traffic sign bar is composed of a stand column and a cantilever bar using bolted connection. The cross-section of stand column and a cantilever bar is closed thin wall with regular octagon and their cross sectional area is variable along axial line. The finite element simulation analysis for the bar is done under gravities and wind loads. Three-dimensional finite element model of bar is set up and stress field and displacement field is given under different load and their combination. Stress and displacement values of key parts are extracted and compared with theoretical calculation. Indicates that the theoretical calculation and finite element calculation is correct.

Hybrid Dynamic Modeling and Analysis of High-speed Thin-rimmed Gears

2021 ◽  
pp. 1-23
Author(s):  
Changzhao Liu ◽  
Yu Zhao ◽  
Yong Wang ◽  
Tie Zhang ◽  
Hanjie Jia
Keyword(s):  
Finite Element ◽  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Modeling And Analysis ◽  
Lumped Parameter ◽  
Proposed Model ◽  
Angular Displacements

Abstract In this study, a hybrid dynamic model of high-speed thin-rimmed gears is developed. In this model, the translational and angular displacements (including the rigid and vibration displacements) with a total of six degrees of freedom (DOFs) are selected as the generalized coordinates for each gear, and the meshing force distributions along the contact line and between the teeth are considered. Thus, the model can be implemented under stationary and non-stationary conditions. The condensed finite element models are developed with the centrifugal and inertia forces for gear bodies. This paper proposes a novel method to couple the lumped parameter model and condensed finite element model for the hybrid dynamic model system, which considers the variation of the meshing tooth during the gear operation, namely, the variations of the acting point of meshing force. Based on the model, the dynamic analysis of high-speed thin-rimmed gears is conducted under stationary speed and acceleration processes. The effects of the flexible gear body, high speed, and tooth errors on the system dynamics and tooth load distribution are investigated. The analysis results are also compared with the current reference and pure finite element method to validate the proposed model.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

Sign in / Sign up

Export Citation Format

Share Document