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.

Vibration Analysis of Linear Beam With Moving Loads Based on Riccati Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Lu Sun ◽  
Xue Rui ◽  
Dieter Bestle ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Mode Shapes ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

The paper presents the dynamic response of an Euler-Bernoulli beam supported by an elastic foundation and subjected to a moving step load. The Riccati transfer matrix method for linear multibody systems (Riccati MSTMM) is employed to find eigenfrequencies and mode shapes of the supported beam. A comparison of results obtained with the finite element method (FEM) indicates that the Riccati MSTMM is more accurate when using the same number segments. Based on these results, the dynamic response of the beam with moving step load is investigated for different propagation velocities by mode superposition, and the effect of loads is discussed.

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 The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

Comparison of Methods for Modeling a Hydraulic Loader Crane With Flexible Translational Links

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Henrik C. Pedersen ◽  
Torben O. Andersen ◽  
Brian K. Nielsen
Keyword(s):  
Order Approximation ◽  
Mode Shapes ◽  
Beam Equation ◽  
Flexible Structure ◽  
Bernoulli Beam ◽  
Finite Segment ◽  
Single Beam ◽  
Beam Elements ◽  
Euler Bernoulli Beam ◽  
Mode Order

When modeling flexible robots and structures for control purposes, most often the assumed modes (AMs) method is used to describe the deformation in combination with a floating reference frame formulation. This typically has the benefit of obtaining a low-order, but accurate model of the flexible structure, if the number of modes and AMs are properly chosen. The basis for using this method is, however, that the vibrations (deflections) are time and position independent, i.e., the expression is separable in space and time. This holds for the classic Euler–Bernoulli beam equation, but essentially does not hold for translational links. Hence, special care has to be taken when including flexible translational links. In the current paper, different methods for modeling a hydraulic loader crane with a telescopic arm are investigated and compared using both the finite segment (FS) and AMs method. The translational links are approximated by a single beam, respectively, multiple beam elements, with both one and two modes and using different mode shapes. The models are all validated against experimental data and the comparison is made for different operating scenarios. Based on the results, it is found that in most cases a single beam, low mode order approximation is sufficient to accurately model the mechanical structure and this yields similar results as the FS method.

Approximate analytical solution for vibration of a 3-PRP planar parallel robot with flexible moving platform

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 71-97 ◽  
Author(s):  
Mahdi Sharifnia ◽  
Alireza Akbarzadeh
Keyword(s):  
Analytical Solution ◽  
Solution Method ◽  
Parallel Robot ◽  
Mode Shapes ◽  
Constrained Motion ◽  
Bernoulli Beam ◽  
Actual Length ◽  
Prismatic Joint ◽  
Moving Platform ◽  
Euler Bernoulli Beam

SUMMARYIn this research, using an approximate analytical method, vibration analysis of a 3-PRP (active prismatic—P, passive revolute—R, passive prismatic—P) planar parallel robot having a flexible moving platform is presented. A specific architecture of the 3-PRP parallel robot, also known as the ST (Star-Triangle) parallel robot, is considered. The moving platform of the robot, called the star, is assumed to be made of three flexible beams shaped like a star. For analytical modeling, each of the three beams of the star is assumed to be a discrete Euler–Bernoulli beam with a passive prismatic joint. Continuity equations at the center of the star are used to relate vibrations of the three beams. The vibration behavior of each beam is modeled using previously developed constrained motion equations for a planar Euler–Bernoulli beam having a prismatic joint. In this paper, previously presented “constrained assumed modes method” is further developed to solve the constrained motion equation for the ST parallel robot. The solution method is used to obtain the vibration of the robot for the inverse dynamics problem and simultaneously provides generalized constraint forces. Furthermore, the solution method can be used for the direct dynamics problem of the ST robot. Several input trajectories are considered to investigate the different behavior for the center of the star. For each of the trajectories, three different groups of mode shapes are considered and their vibrational responses are compared. In this research, for the first time, effects of the passive prismatic joint parameters such as mass, rotational moment of inertia, and its actual length are considered in an analytical model. Finally, the analytical solution and a FEM (Finite Element Method) software solution are compared.

Comparison of Adomian Decomposition Method and Differential Transformation Method for Vibration Problems of Euler-Bernoulli Beam

2012 ◽  
Vol 157-158 ◽  
pp. 476-483
Author(s):  
Zhi Feng Liu ◽  
Chun Hua Guo ◽  
Li Gang Cai ◽  
Wen Tong Yang ◽  
Zhi Min Zhang
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Differential Transformation ◽  
Adomian Decomposition ◽  
Vibration Problems ◽  
Euler Bernoulli Beam

In this paper, we compare the Differential transformation method and Adomian decomposition method to solve Euler-Bernoulli Beam vibration problems. The natural frequencies and mode shapes of the clamped-free uniform Euler-Bernoulli equation are calculated using the two methods. The Adomian decomposition method avoids the difficulties and massive computational work inherent in Differential transformation method by determining the very rapidly convergent analytic solutions directly. We found the solution between the two methods to be quite close. According to calculation of eigenvalues, natural frequencies and mode shapes, we compare the convergence of Differential transformation method and Adomian decomposition method. The two methods can be alternative ways to solve linear and nonlinear higher-order initial value problems.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

scholarly journals Transverse Vibration of Clamped-Pinned-Free Beam with Mass at Free End

2019 ◽  
Vol 9 (15) ◽  
pp. 2996 ◽  
Author(s):  
Jonathan Hong ◽  
Jacob Dodson ◽  
Simon Laflamme ◽  
Austin Downey
Keyword(s):  
Transverse Vibration ◽  
Theoretical Calculations ◽  
Beam Theory ◽  
High Rate ◽  
Harsh Environments ◽  
Mode Shapes ◽  
Engineering Systems ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Free Beam

Engineering systems undergoing extreme and harsh environments can often times experience rapid damaging effects. In order to minimize loss of economic investment and human lives, structural health monitoring (SHM) of these high-rate systems is being researched. An experimental testbed has been developed to validate SHM methods in a controllable and repeatable laboratory environment. This study applies the Euler-Bernoulli beam theory to this testbed to develop analytical solutions of the system. The transverse vibration of a clamped-pinned-free beam with a point mass at the free end is discussed in detail. Results are derived for varying pin locations and mass values. Eigenvalue plots of the first five modes are presented along with their respective mode shapes. The theoretical calculations are experimentally validated and discussed.

scholarly journals Natural Frequencies and Mode Shapes of Statically Deformed Inclined Risers

2016 ◽  
Author(s):  
Feras K. Alfosail ◽  
Ali H. Nayfeh ◽  
Mohammad I. Younis
Keyword(s):  
Natural Frequencies ◽  
Equilibrium Configuration ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Galerkin Approach ◽  
Inclination Angles ◽  
Linear Vibrations ◽  
Euler Bernoulli Beam ◽  
Beam Mode ◽  
Good Agreement

In this work, we investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler-Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, a Galerkin expansion of fifteen axially loaded beam mode shapes are used to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and exact mode shapes for various values of inclination angles and applied tension. The obtained results are validated against a boundary-layer analytical solution and are found in good agreement. This constructs a basis to study the nonlinear forced vibrations of inclined risers.

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