Transverse Vibration Analysis of the Deploying Beam by Simulation and Experiment

Title & Authors
Transverse Vibration Analysis of the Deploying Beam by Simulation and Experiment
Kim, Jaewon; Zhu, Kefei; Chung, Jintai;

Abstract
The transverse vibration of the deploying beam from rigid hub was analyzed by simulation and experiment. The linear governing equation of the deploying beam was obtained using the Euler-Bernoulli beam theory. To discretize the governing equation, the Galerkin method was used. After transforming the governing equation into the weak form, the weak form was discretized. The discretized equation was expressed by the matrix-vector form, and then the Newmark method was applied to simulate. To consider the damping effect of the beam, we conducted the modal test with various beam length. The mass proportional damping was selected by the relation of the first and second damping ratio. The proportional damping coefficient was calculated using the acquired natural frequency and damping ratio through the modal test. The experiment was set up to measure the transverse vibration of the deploying beam. The fixed beam at the carriage of the linear actuator was moved by moving the carriage. The transverse vibration of the deploying beam was observed by the Eulerian description near the hub. The deploying or retraction motion of the beam had the constant velocity and the velocity profile with acceleration and deceleration. We compared the transverse vibration results by the simulation and experiment. The observed response by the Eulerian description were analyzed.
Keywords
Deploying Beam;Transverse Vibration;Mass Proportional Damping;Eulerian Description;Lagrangian Description;
Language
Korean
Cited by
References
1.
Wang, P. K. C. and Wei, J. D., 1987, Vibrations in a Moving Flexible Robot Arm, Journal of Sound and Vibration, Vol. 116, No. 1, pp. 149-160.

2.
Stylianou, M. and Tabarrok, B., 1994, Finite Element Analysis of an Axially Moving Beam, Part 1: Time Integration, Journal of Sound and Vibration, Vol. 178, No. 4, pp. 433-453.

3.
Al-Bedoor, B. O. and Khulief, Y. A., 1996, An Approximate Analytical Solution of Beam Vibrations during Axial Motion, Journal of Sound and Vibration, Vol. 192, No. 1, pp. 159-171.

4.
Park, S. P., Yoo, H. H. and Chung, J., 2013, Vibrations of an Axially Moving Beam with Deployment or Retraction, AIAA Journal, Vol. 51, No. 3, pp. 686-696.

5.
Matsuzaki, Y., Tak, Y. and Toyama, M., 1995, Vibration of a Cantilevered Beam during Deployment and Retrieval: Analysis and Experiment, Smart Materials and Structures, Vol. 4, No. 4, pp. 334-339.

6.
Yuh, J. and Young, T., 1991, Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment, Journal of Dynamic Systems, Measurement, and Control, Vol. 113, No. 1, pp. 34-40.

7.
Wang, L., Chen, H. and He, X., 2011, Active $H{\infty}$ Control of the Vibration of an Axially Moving Cantilever Beam by Magnetic Force, Mechanical Systems and Signal Processing, Vol. 25, No. 8, pp. 2863-2878.

8.
Duan, Y. C., Wang, J. P., Wang, J. Q., Liu, Y. W. and Shao, P., 2014, Theoretical and Experimental Study on the Transverse Vibration Properties of an Axially Moving Nested Cantilever Beam, Journal of Sound and Vibration, Vol. 333, No. 13, pp. 2885-2897.