scholarly journals Vibration Analysis of Euler-Bernoulli Beams Partially Immersed in a Viscous Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wafik Abassi ◽  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Viscous Fluid ◽  
Cross Sections ◽  
Good Accuracy ◽  
Theoretical Study ◽  
Stokes Equations ◽  
Frequency Equation ◽  
The Finite Element Method ◽  
Coupled Vibration ◽  
New Approach ◽  
Vibrational Characteristics

The vibrational characteristics of a microbeam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical study of the modal analysis of microbeams partially immersed in a viscous fluid. A fixed-free microbeam vibrating in a viscous fluid is modeled using the Euler-Bernoulli equation for the beams. The unsteady Stokes equations are solved using a Helmholtz decomposition technique in a two-dimensional plane containing the microbeams cross sections. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results is compared with present method for validation and an acceptable match between them was obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

scholarly journals Transverse vibration analysis of Euler-Bernoulli beam carrying point masse submerged in fluid media

2015 ◽  
Vol 4 (2) ◽  
pp. 369 ◽  
Author(s):  
Adil El baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Frequency Equation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Coupled Vibration ◽  
Bernoulli Beam ◽  
New Approach ◽  
Acoustic Equation ◽  
Fluid Media ◽  
Arbitrary Position ◽  
Euler Bernoulli Beam

In the present paper, an analytical method is developed to investigate the effects of added mass on natural frequencies and mode shapes of Euler-Bernoulli beams carrying concentrated masse at arbitrary position submerged in a fluid media. A fixed-fixed beams carrying concentrated masse vibrating in a fluid is modeled using the Bernoulli-Euler equation for the beams and the acoustic equation for the fluid. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of a beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results are compared with present method for validation and an acceptable match between them were obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy.

The study of the elastic deformation of a flexible wheel by a cam wave generator

2020 ◽  
Vol 65 (1) ◽  
pp. 51-58
Author(s):  
Sava Ianici
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Theoretical Study ◽  
Elastic Field ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Wave Generator ◽  
Two Stages

The paper presents the results of research on the study of the elastic deformation of a flexible wheel from a double harmonic transmission, under the action of a cam wave generator. Knowing exactly how the flexible wheel is deformed is important in correctly establishing the geometric parameters of the wheels teeth, allowing a better understanding and appreciation of the specific conditions of harmonic gearings in the two stages of the transmission. The veracity of the results of this theoretical study on the calculation of elastic deformations and displacements of points located on the average fiber of the flexible wheel was subsequently verified and confirmed by numerical simulation of the flexible wheel, in the elastic field, using the finite element method from SolidWorks Simulation.

scholarly journals A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

2017 ◽  
Vol 232 (11) ◽  
pp. 2088-2102 ◽  
Author(s):  
Eduardo de la Guerra Ochoa ◽  
Javier Echávarri Otero ◽  
Enrique Chacón Tanarro ◽  
Benito del Río López
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thermal Effects ◽  
Good Accuracy ◽  
Computational Cost ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
New Approach ◽  
Ball On Disc

This article presents a thermal resistances-based approach for solving the thermal-elastohydrodynamic lubrication problem in point contact, taking the lubricant rheology into account. The friction coefficient in the contact is estimated, along with the distribution of both film thickness and temperature. A commercial tribometer is used in order to measure the friction coefficient at a ball-on-disc point contact lubricated with a polyalphaolefin base. These data and other experimental results available in the bibliography are compared to those obtained by using the proposed methodology, and thermal effects are analysed. The new approach shows good accuracy for predicting the friction coefficient and requires less computational cost than full thermal-elastohydrodynamic simulations.

The Accepting of Pipe Bends With Ovality and Thinning Using Finite Element Method

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
AR. Veerappan ◽  
S. Shanmugam ◽  
S. Soundrapandian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Cross Sections ◽  
Pressure Ratio ◽  
Empirical Relationship ◽  
The Finite Element Method ◽  
Element Method

Thinning and ovality are commonly observed irregularities in pipe bends, which induce higher stress than perfectly circular cross sections. In this work, the stresses introduced in pipe bends with different ovalities and thinning for a particular internal pressure are calculated using the finite element method. The constant allowable pressure ratio for different ovalities and thinning is presented at different bend radii. The allowable pressure ratio increases, attains a maximum, and then decreases as the values of ovality and thinning are increased. An empirical relationship to determine the allowable pressure in terms of bend ratio, pipe ratio, percent thinning, and percent ovality is presented. The pipe ratio has a strong effect on the allowable pressure.

Theoretical study of dynamic effects on fusion cross sections for reactions S32,34,36+Pb204,206,208

2021 ◽  
Vol 104 (3) ◽  
Author(s):  
Jian-Mei Yang ◽  
Zheng-Wei Song ◽  
Wei-Juan Zhao ◽  
Bing Wang
Keyword(s):  
Cross Sections ◽  
Theoretical Study ◽  
Dynamic Effects

Effect of fluid forcing on vestibular hair bundles

2005 ◽  
Vol 15 (5-6) ◽  
pp. 263-278
Author(s):  
J.-H. Nam ◽  
J.R. Cotton ◽  
J.W. Grant
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Hair Bundle ◽  
Structural Components ◽  
The Finite Element Method ◽  
Fluid Drag ◽  
Tip Link ◽  
Single Force

A dynamic 3-D hair bundle model including inertia and viscous fluid drag effects based on the finite element method is presented. Six structural components are used to construct the hair bundle – kinocilium, stereocilia, upper lateral links, shaft links, tip links, and kinocilial links. Fluid drag is distributed on the surface of cilia columns. Bundle mechanics are analyzed under two distinct loading conditions: (1) drag caused by the shear flow of the surrounding endolymph fluid (fluid-forced), (2) a single force applied to the tip of the kinocilium (point-forced). A striolar and a medial extrastriolar vestibular hair cell from the utricle of a turtle are simulated. The striolar cell bundle shows a clear difference in tip link tension profile between fluid-forced and point-forced cases. When the striolar cell is fluid forced, it shows more evenly distributed tip link tensions and is far more sensitive, responding like an on/off switch. The extrastriolar cell does not show noticeable differences between the forcing types. For both forcing conditions, the extrastriolar cell responds serially – the nearest tip links to the kinocilium get tensed first, then the tension propagates to the farther tip links.

Comparison of Static and Dynamic Stiffness for Beams Undergoing Flexural and Torsional Loading With an Intermediate Mass

2000 ◽  
Author(s):  
Arnoldo Garcia ◽  
Arnold Lumsdaine ◽  
Ying X. Yao
Keyword(s):  
Closed Form ◽  
Natural Frequency ◽  
Cross Sections ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Torsional Loading ◽  
Intermediate Mass ◽  
Form Equation

Abstract Many studies have been performed to analyze the natural frequency of beams undergoing both flexural and torsional loading. For example, Adam (1999) analyzed a beam with open cross-sections under forced vibration. Although the exact natural frequency equation is available in literature (Lumsdaine et al), to the authors’ knowledge, a beam with an intermediate mass and support has not been considered. The models are then compared with an approximate closed form solution for the natural frequency. The closed form equation is developed using energy methods. Results show that the closed form equation is within 2% percent when compared to the transcendental natural frequency equation.

scholarly journals Investigations on Torsion of the Two-Chords Single Laced Members

2017 ◽  
Vol 25 (2) ◽  
pp. 147-160
Author(s):  
Paweł Lorkowski ◽  
Bronisław Gosowski
Keyword(s):  
Cross Sections ◽  
Experimental Studies ◽  
The Finite Element Method ◽  
Second Moment ◽  
Steel Columns ◽  
Numerical Studies ◽  
Traction Network ◽  
Railway Traction ◽  
Parametric Analyses ◽  
The Relationship

Abstract The paper presents experimental and numerical studies to determine the equivalent second moment of area of the uniform torsion of the two-chord steel single laced members. The members are used as poles of railway traction network gates, and steel columns of framed buildings as well. The stiffness of uniform torsion of this kind of columns allows to the determine the critical loads of the spatial stability. The experimental studies have been realized on a single - span members with rotation arrested at their ends, loaded by a torque applied at the mid-span. The relationship between angle of rotation of the considered cross-section and the torque has been determined. Appropriate numerical model was created in the ABAQUS program, based on the finite element method. A very good compatibility has been observed between experimental and numerical studies. The equivalent second moment of area of the uniform torsion for analysed members has been determined by comparing the experimental and analytical results to those obtained from differential equation of non-uniform torsion, based on Vlasov’s theory. Additionally, the parametric analyses of similar members subjected to the uniform torsion, for the richer range of cross-sections have been carried out by the means of SOFiSTiK program. The purpose of the latter was determining parametrical formulas for calculation of the second moment of area of uniform torsion.

3D modelling of the flow distribution in the delta of Lake Øyeren, Norway

2010 ◽  
Vol 41 (2) ◽  
pp. 92-103 ◽  
Author(s):  
Peggy Zinke ◽  
Nils Reidar Bøe Olsen ◽  
Jim Bogen ◽  
Nils Rüther
Keyword(s):  
Water Level ◽  
Cross Sections ◽  
Stokes Equations ◽  
Morphological Changes ◽  
Flow Distribution ◽  
Field Measurements ◽  
Navier Stokes ◽  
Error Sources ◽  
Navier Stokes Equations ◽  
Water Level Measurements

A 3D numerical model was used to compute the discharge distribution in the channel branches of Lake Øyeren's delta in Norway. The model solved the Navier–Stokes equations with the k–ɛ turbulence model on a 3D unstructured grid. The bathymetry dataset for the modelling had to be combined from different data sources. The results for three different flow situations in 1996 and 1997 showed a relative accuracy of the computed discharges within the range of 0 to±20% compared with field measurements taken by an ADCP at 13 cross sections of the distributary channels. The factors introducing the most error in the computed results are believed to be uncertainties concerning the bathymetry. A comparison between the computational results of the older morphology data from 1985–1990 and the model morphology from 1995–2004 indicated that morphological changes in this period had already had consequences for the flow distribution in some channels. Other important error sources were the inevitable use of averaged water level gradients because of unavailable water level measurements within the delta.

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