Experimental Validation of Two Damping Force Models for the ANCF

2007 ◽  
Author(s):  
Hyun-Woo Kim ◽  
Wan-Suk Yoo ◽  
Jeong-Hyun Sohn
Keyword(s):  
Computer Simulations ◽  
Experimental Validation ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Experimental Measurements ◽  
Damping Force ◽  
Absolute Nodal Coordinate ◽  
Elastic Bodies ◽  
Physical Experiments ◽  
Quadratic Damping

Many researchers have studied computer-aided simulations of elastic bodies undergoing large deflections and large deformations. But there have been few attempts to validate the numerical formulations used in these studies. The main aim of this paper is to validate the absolute nodal coordinate formulation (ANCF) by comparing the results to experimental measurements on beams. Physical experiments with a highspeed camera were carried out to capture the large displacement of the beam and to verify the results of computer simulations. To consider the damping forces, Rayleigh’s damping and quadratic damping are employed and compared to the experimental results. Numerical results obtained from computer simulations were compared with the results from the physical experiments according to the 1st mode and the 2nd mode of the beam, respectively.

Comparison of Physical Experiments and Computer Simulation With ANCF: Large Deformation of a Thin Cantilever Beam

2003 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Jeong-Han Lee ◽  
Jeong-Hyun Sohn ◽  
Su-Jin Park ◽  
Oleg Dmitrochenko ◽  
...  
Keyword(s):  
Cantilever Beam ◽  
High Speed ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Data Acquisition System ◽  
High Speed Camera ◽  
Large Deflections ◽  
Absolute Nodal Coordinate ◽  
Elastic Bodies ◽  
Physical Experiments

Many papers have studied computer-aided simulations of elastic bodies undergoing large deflections and large deformations. But there have not been many attempts to check the validity of the numerical formulations used in these studies. The main aim of this paper is to demonstrate the validity of one of such numerical formulations, the absolute nodal coordinate formulation (ANCF), by comparing the results it generates with the results of real experiments. Large oscillations of a thin cantilever beam are studied in this paper to numerically model the beam that also accounts for the effects of an attached endpoint weight and damping forces. The experiments were carried out using a high-speed camera and a data acquisition system.

Large Oscillations of a Thin Cantilever Beam: Physical Experiments and Simulation Using the Absolute Nodal Coordinate Formulation

2003 ◽  
Vol 34 (1/2) ◽  
pp. 3-29 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Jeong-Han Lee ◽  
Su-Jin Park ◽  
Jeong-Hyun Sohn ◽  
Oleg Dmitrochenko ◽  
...  
Keyword(s):  
Cantilever Beam ◽  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
Physical Experiments ◽  
The Absolute

Rational Finite Elements and Flexible Body Dynamics

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Peng Lan ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Elements ◽  
Computer Aided Design ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Finite Rotations ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Computer Aided ◽  
Curve Representation ◽  
Aided Design

The goal of this study is to develop the dynamic differential equations of the first finite element based on the rational absolute nodal coordinate formulation (RANCF) and to demonstrate its use in the nonlinear dynamic and vibration analysis of flexible bodies that undergo large displacements, including large deformations and finite rotations. New RANCF elements, which correctly describe rigid body displacements, will allow representing complex geometric shapes that cannot be described exactly using nonrational finite elements. Developing such rational finite elements will facilitate the integration of computer aided design and analysis and will allow for developing analysis models that are consistent with the actual geometry. In order to demonstrate the feasibility of developing RANCF finite elements, an Euler–Bernoulli beam element, called in this investigation as the cable element, is used. The relationship between the nonrational absolute nodal coordinate formulation (ANCF) finite elements and the nonrational Bezier curves is discussed briefly first in order to shed light on the transformation between the control points used in the Bezier curve representation and the ANCF gradient coordinates. Using similar procedure and coordinate transformation, the RANCF finite elements can be systematically derived from the computer aided design geometric description. The relationships between the rational Bezier and the RANCF interpolation functions are obtained and used to demonstrate that the new RANCF finite elements are capable of describing arbitrary large deformations and finite rotations. By assuming the weights of the Bezier curve representation to be constant, the RANCF finite elements lead to a constant mass matrix, and as a consequence, the Coriolis and centrifugal inertia force vectors are identically equal to zero. The assumption of constant weights can be used to ensure accurate representation of the geometry in the reference configuration and also allows for the use of the same rational interpolating polynomials to describe both the original geometry and the deformation. A large strain theory is used to formulate the nonlinear elastic forces of the new RANCF cable element. Numerical examples are presented in order to demonstrate the use of the RANCF cable element in the analysis of flexible bodies that experience large deformations and finite rotations. The results obtained are compared with the results obtained using the nonrational ANCF cable element.

Quantitative Validation of Dynamic Stiffening Represented by Absolute Nodal Coordinate Formulation

2009 ◽  
Author(s):  
Yoshiki Sugawara ◽  
Ken Shinohara ◽  
Nobuyuki Kobayashi
Keyword(s):  
Numerical Analysis ◽  
Large Deformation ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Time History ◽  
Flexible Beam ◽  
Space Applications ◽  
Absolute Nodal Coordinate ◽  
Dynamic Stiffening ◽  
Quantitative Validation

In recent years, various flexible structures which undergo large deformations are often applied to deployment mechanisms of space applications due to the requirements for a large structure. It is necessary to grasp their complex behaviors before the launch to escape failures as much as possible. The dynamics due to the large deformations and the overall motions are especially quite important. To overcome the difficulties of ground check about their dynamics, a powerful numerical analysis method is required strongly. In the past decade Absolute Nodal Coordinate Formulation (ANCF) method has been developed for the flexible multibody systems with large deformation and various applications have been applied to ANCF for practical use. However, there are not enough researches which validate the method by the comparison with experimental data. Especially, there are few study which conducts a quantitative validation of ANCF about overall motion with large deformation. In this paper, dynamic stiffening is focused on as one of the important overall motion. A mathematical model of two dimensional simple flexible beam is constructed based on ANCF. To simulate the dynamic stiffening by the derived model, the flexible beam is rotated horizontally in a certain angular velocity and the time history of the deformation is analyzed. Then, the results of the numerical analysis are compared with the data of corresponding experiments quantitatively.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H.R. Yi ◽  
Huliang Dai ◽  
H Yan ◽  
Z.L. Guo ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Strong Relationship ◽  
Excitation Amplitude ◽  
Pipe Conveying Fluid ◽  
Base Excitation ◽  
Absolute Nodal Coordinate ◽  
Nonlinear Behaviors ◽  
Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

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