NEW ADMISSIBLE FUNCTIONS FOR THE DYNAMIC ANALYSIS OF A SLEWING FLEXIBLE BEAM

1998 ◽  
Vol 210 (5) ◽  
pp. 581-592 ◽  
Author(s):  
M.K. Kwak
Keyword(s):  
Dynamic Analysis ◽  
Flexible Beam ◽  
Admissible Functions

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Flexible Beam ◽  
Element Formulation ◽  
Shear Locking ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Bending Mode

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger–Reissner or the three-field Hu–Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.

Dynamic analysis of the flexible hub-beam system based on rigid-flexible coupling mechanism

2020 ◽  
Vol 234 (3) ◽  
pp. 536-545
Author(s):  
Xiaowei Guo ◽  
Xin Yang ◽  
Fuqiang Liu ◽  
Zhangfang Liu ◽  
Xiaolin Tang
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Flexible Beam ◽  
Coupling Mechanism ◽  
Mass System ◽  
Typical Structure ◽  
Concentrated Load ◽  
Flexible Coupling ◽  
Beam System ◽  
Tip Mass

The flexible hub-beam system is a typical structure of the rigid-flexible coupling dynamic system. In this paper, the dynamic property of the flexible hub-beam system is investigated. First, based on the dynamic analysis of the flexible beam in the flexible hub-beam system, the dynamic model of a flexible hub-beam-tip mass system is established and researched. Second, the dynamic response of the flexible beam under different external loads, including end concentrated load, end sinusoidal load, and uniform load, is analyzed and calculated. Finally, the influence of magnitude, direction, and type of load on the dynamic response of the flexible beam is also discussed. This research can provide a novel strategy for controlling the maximum stress of the structural components to be lower than the yield stress of the material, and flexible components remain in the linear elastic range even under the condition of high-speed rotation.

scholarly journals Efficient modal dynamic analysis of flexible beam–fluid systems

2015 ◽  
Vol 39 (1) ◽  
pp. 99-116 ◽  
Author(s):  
Najib Bouaanani ◽  
Benjamin Miquel
Keyword(s):  
Dynamic Analysis ◽  
Flexible Beam ◽  
Fluid Systems

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Finite Element Method and Absolute Nodal Coordinate Formulation

2005 ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Flexible Beam ◽  
Shear Locking ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Bending Mode ◽  
Asymmetric Bending ◽  
Element Method

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a finite element method (FEM) formulation, an absolute nodal coordinate (ANC) formulation with a continuum mechanics approach and an ANC formulation with an elastic line concept where the shear locking of the asymmetric bending mode is suppressed by the application of the Hellinger–Reissner principle. The comparison is made by means of an eigenfrequency analysis on two stylized problems. It is shown that the ANC continuum approach yields too large torsional and flexural rigidity and that shear locking suppresses the asymmetric bending mode. The presented ANC formulation with the elastic line concept resolves most of these problems.

Dynamic Analysis of Flexible Rotors Subjected to Torque and Force

1993 ◽  
Author(s):  
Jong-Seop Yun ◽  
Chong-Won Lee
Keyword(s):  
Numerical Analysis ◽  
Variational Principle ◽  
Dynamic Analysis ◽  
Natural Frequency ◽  
Stability Criterion ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Flexible Rotors ◽  
The Stability ◽  
Admissible Functions

Abstract The effect of the applied direction and magnitude of loads on the stability and natural frequency of flexible rotors is analyzed, when the rotors are subject to nonconservative torque and force. The stability criterion derived from the energy and variational principle is discussed and a general Galerkin’s method which utilizes admissible functions is employed for numerical analysis. Illustrative examples are treated to demonstrate the analytical developments.

scholarly journals Dynamic Analysis of a Multibody System Including a Very Flexible Beam Element

2005 ◽  
Vol 48 (2) ◽  
pp. 224-233 ◽  
Author(s):  
Jong-Hwi SEO ◽  
Il-Ho JUNG ◽  
Tae-Won PARK ◽  
Jang-Bom CHAI
Keyword(s):  
Dynamic Analysis ◽  
Multibody System ◽  
Beam Element ◽  
Flexible Beam

Dynamic Analysis and Active Vibration Control of Flexible Beams Using Piezoelectric Materials: an Optimal Approach

2010 ◽  
Vol 26-28 ◽  
pp. 1237-1241 ◽  
Author(s):  
Shahab Amelian ◽  
Hamid R. Koofigar
Keyword(s):  
Dynamic Analysis ◽  
Vibration Control ◽  
Piezoelectric Materials ◽  
Active Vibration Control ◽  
Beam Deflection ◽  
Flexible Beam ◽  
Flexible Beams ◽  
Active Vibration ◽  
Optimal Approach ◽  
Assumed Mode

Piezoelectric materials are used in various applications as active vibration control, fault detection in structures and piezoelectric accelerators, therefore, analysis of such materials seems to be necessary in modern mechanical constructions. In this paper, the dynamic analysis of the beam equipped with piezoelectric patches, used as both sensor and actuator, is presented and the beam deflection due to external inputs (force or voltage) is analyzed via modal analysis method. Then, constructing a model for the flexible beam, by the assumed mode approach, an active vibration control is developed by optimal positioning of piezoelectric patches. Simulation results are also presented to illustrate the effectiveness of the methods proposed for dynamic analysis and active vibration control.

A Pseudo-Static Model for Dynamic Analysis on Frequency Domain of Distributed Compliant Mechanisms

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Mingxiang Ling ◽  
Larry L. Howell ◽  
Junyi Cao ◽  
Zhou Jiang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Stiffness Matrix ◽  
Compliant Mechanisms ◽  
Dynamic Stiffness ◽  
Elastic Beam ◽  
Static Model ◽  
Flexible Beam ◽  
Element Analysis ◽  
Static Modeling

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

Concept of Coupled Displacement Field for Large Amplitude Free Vibrations of Shear Flexible Beams

2005 ◽  
Vol 128 (2) ◽  
pp. 251-255 ◽  
Author(s):  
G. Venkateswara Rao ◽  
K. Meera Saheb ◽  
G. Ranga Janardhan
Keyword(s):  
Displacement Field ◽  
Large Amplitude ◽  
Lateral Displacement ◽  
Nonlinear Ordinary Differential Equation ◽  
Free Vibrations ◽  
Flexible Beam ◽  
Flexible Beams ◽  
Uniform Shear ◽  
Single Term ◽  
Admissible Functions

Continuum solutions for solving the large amplitude free vibration problem of shear flexible beams using the energy method involves assuming suitable admissible functions for the lateral displacement and the total rotation. Use of even, single-term admissible functions leads to two coupled nonlinear temporal differential equations in terms of the lateral displacement and the total rotation, the solution of which is rather involved. This situation can be effectively tackled if one uses the concept of a coupled displacement field wherein the fields for lateral displacement and the total rotation are coupled through the static equilibrium equation of the shear flexible beam. This approach leads to only one undetermined coefficient, in the case of single-term admissible functions, which can easily be used in the principle of conservation of total energy, neglecting damping, to solve the problem. Finally, one gets a nonlinear ordinary differential equation of the Duffing type which can be solved using any available standard method. The effectiveness of the concept discussed above is brought out through the solution of the large amplitude free vibrations, in terms of the fundamental frequency, of uniform shear flexible beams, with axially immovable ends, using single-term admissible functions.

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