scholarly journals Effects of Cable on the Dynamics of a Cantilever Beam with Tip Mass

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Yi-Xin Huang ◽  
Hao Tian ◽  
Yang Zhao
Keyword(s):  
Cantilever Beam ◽  
Spectral Element Method ◽  
Natural Frequencies ◽  
Spectral Element ◽  
Mode Shapes ◽  
Beam System ◽  
Double Beam ◽  
Tip Mass ◽  
Beam Mode ◽  
Element Method

The dynamic effects of cable attachment on a cantilever beam with tip mass are investigated by an improved Chebyshev spectral element method. The cabled beam is modeled as a double-beam system connected by springs at several discrete locations. By utilizing high order Chebyshev polynomials as basis functions and meshing the system at the locations of connections, precise numerical results of the natural frequencies and mode shapes can be obtained using only a few elements. The accuracy of this method is validated through comparing the results of finite element method and those of spectral element method in literature. The validated method is implemented to investigate the effects of parameters, including spring stiffness, number of connections, density, and Young’s modulus of cable. The results show that the mode shapes of the cabled beam system can be classified into two types: beam mode shapes and cable mode shapes, according to their main deformation. Their corresponding natural frequencies change in very different ways with the variation of system parameters. This work can be applied to optimize the dynamic characteristics of precise spacecraft structures with cable attachments.

scholarly journals Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Wang Hongjin ◽  
Meng Qingfeng ◽  
Feng Wuwei
Keyword(s):  
Cantilever Beam ◽  
Analytical Methods ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Inertial Force ◽  
Mode Shapes ◽  
Base Excitation ◽  
Inertial Moment ◽  
Tip Mass ◽  
Improved Methods

Two improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in detail by replacing the tip-mass with an equivalent inertial force and inertial moment acting at the free end of the cantilever based on D’Alembert’s principle. The concentrated equivalent inertial force and inertial moment are further represented as distributed loads using Dirac Delta Function. In this case, some typical natural frequencies and mode shapes of the cantilever model are calculated by the improved and unimproved analytical methods. The comparing results show that, after improvement, these two methods are in extremely good agreement with each other even the offset distance between the gravity center of the tip-mass and the attachment point is large. As further verification, the transient and steady displacement responses of the cantilever system under a sine base excitation are presented in which two improved methods are separately utilized. Finally, an experimental cantilever system is fabricated and the theoretical displacement responses are validated by the experimental measurements successfully.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

scholarly journals Structural Damping with Friction Beams

2008 ◽  
Vol 15 (3-4) ◽  
pp. 291-298 ◽  
Author(s):  
L. Gaul ◽  
J. Roseira ◽  
J. Becker
Keyword(s):  
Linear Models ◽  
Natural Frequencies ◽  
Normal Force ◽  
Normal Pressure ◽  
Friction Model ◽  
Mode Shapes ◽  
Work Piece ◽  
Numerical Predictions ◽  
Double Beam ◽  
Excitation Force

In the last several years, there has been increasing interest in the use of friction joints for enhancing damping in structures. The joints themselves are responsible for the major part of the energy dissipation in assembled structures. The dissipated work in a joint depends on both the applied normal force and the excitation force. For the case of a constant amplitude excitation force, there is an optimal normal force which maximizes the damping. A ‘passive’ approach would be employed in this instance. In most cases however, the excitation force, as well as the interface parameters such as the friction coefficient, normal pressure distribution, etc., are not constant. In these cases, a ‘semi-active’ approach, which implements an active varying normal force, is necessary. For the ‘passive’ and ‘semi-active’ approaches, the normal force has to be measured. Interestingly, since the normal force in a friction joint influences the local stiffness, the natural frequencies of the assembled structure can be tuned by adjusting the normal force. Experiments and simulations are performed for a simple laboratory structure consisting of two superposed beams with friction in the interface. Numerical simulation of the friction interface requires non-linear models. The response of the double beam system is simulated using a numerical algorithm programmed inMATLABwhich models point-to-point friction with the Masing friction model. Numerical predictions and measurements of the double beam free vibration response are compared. A practical application is then described, in which a friction beam is used to damp the vibrations of the work piece table on a milling machine. The increased damping of the table reduces vibration amplitudes, which in turn results in enhanced surface quality of the machined parts, reduction in machine tool wear, and potentially higher feed rates. Optimal positioning of the friction beams is based on knowledge of the mode shapes, which are obtained from experimental modal analysis. The modal damping and the natural frequencies for the two dominant modes are measured for several combinations of excitation force and normal force.

Large eddy simulation of the differentially heated cubic cavity flow by the spectral element method

2013 ◽  
Vol 86 ◽  
pp. 210-227 ◽  
Author(s):  
Christoph Bosshard ◽  
Abdelouahab Dehbi ◽  
Michel Deville ◽  
Emmanuel Leriche ◽  
Riccardo Puragliesi ◽  
...  
Keyword(s):  
Large Eddy Simulation ◽  
Spectral Element Method ◽  
Cavity Flow ◽  
Spectral Element ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Element Method
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