Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint
In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1130105Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 649
 P. C. K. Wang, J. D. Wei, Vibration in a moving flexible robot arm, J. Sound Vib. 116 (1) (1987) 149–160.
 T. R. Kane, R. R. Ryan, A. K. Banarjee, Dynamics of a cantilever beam attached to a moving base, J. Guidance Control Dyn. 10 (2) (1987) 139–151.
 P. E. Gaultier, W. L. Cleghorn, A spatially translating and rotating beam finite element for modeling flexible manipulators, Mech. Mach. Theory 27 (4) (1992) 415–433.
 Y. C. Pan, R. A. Scott, A. G. Ulsoy, Dynamic modeling and simulation of flexible robots with prismatic joints, J. Mech. Des. 112 (1990) 307–314.
 Y. C. Pan, A. G. Ulsoy, R. A. Scott, Experimental model validation for a flexible robot with a prismatic joint, J. Mech. Des. 112 (1990) 315–323.
 J. Yuh, T. Young, Dynamic modeling of an axially moving beam in rotation: Simulation and experiment, J. Dyn. Syst. Measure Control 113 (1991) 34–40.
 S. K. Tadikonda, H. Baruh, Dynamics and control of a translating flexible beam with a prismatic joint, J. Dyn. Syst. Measure. Control 114 (1992) 422–427.
 B. O. Al-Bedoor, Y. A. Khulief, General planar dynamics of a sliding flexible link, J. Sound Vib. 206 (5) (1997) 641–661.
 M. Kalyoncu, F. M. Botsalı, Effect of axial shortening on the vibration of elastic robot arm, in: Proc. of Int. Symp., Second Turkish–German Joint Computer Application Days, Konya, Turkey, (1998). pp. 313–324.
 S_. Yu¨ ksel, M. Gu¨rgo¨ ze, On the flexural vibrations of elastic manipulators with prismatic joints, Comput. Struct. 62 (5) (1997) 897–908.
 Z. Yang, J. P. Sadler, Prediction of the dynamic response of flexible manipulators from a modal database, Mech. Mach. Theory 32 (6) (1997) 679–689.
 B. O. Al-Bedoor, Y. A. Khulief, Finite element dynamic modeling of a translating and rotating flexible link Comput. Methods Appl. Mech. Eng., 131 (1996), pp. 173–189
 M. Kalyoncu, F. M. Botsalı, Lateral and torsional vibration analysis of elastic robot manipulators with prismatic joint, in: Proc. Of ETCE2002, ASME Eng. Technol. Conf. on Energy, Houston, TX, USA, (2002), Paper STRUC-29024.
 N. G. Chalhoub, L. Chen, A structural flexibility transformation matrix for modelling open-kinematic chains with revolute and prismatic joints, J. Sound Vib. 218 (1) (1998) 45–63.
 M. Gürgöze, Ş. Yüksel, Transverse vibrations of a flexible beam sliding through a prismatic joint, J. Sound Vib. 223 (3) (1999) 467–482.
 O. A. Bauchau, On the modeling of prismatic joints in flexible multi-body systems, Comput. Methods Appl. Mech. Eng. 181 (2000) 87–105.
 M. Kalyoncu, F. M. Botsalı, Vibration analysis of an elastic robot manipulator with prismatic joint and a time varying end mass, Arabian J. Sci. Eng. 29 (1C) (2004) 27–38.
 A. Ankaralı, M. Kalyoncu, F. M. Botsalı, T. S_is_man, Mathematical modeling and simulation of a flexible shaft-flexible link system with end mass, Math. Comput. Model. Dyn. Syst. 10 (3-4) (2004) 187–200.
 A. M. H. Basher, Dynamic behavior of a translating flexible beam with a prismatic joint, Conf. Proc. – IEEE Southeast. (2000) 31–38.
 M. Farid, I. Salimi, Inverse dynamics of a planar flexible-link manipulator with revolute-prismatic joints, American Society of Mechanical Engineers, Des. Eng. Division (Publication) DE 111 (2001) 345–350.
 S. E. Khadem, A. A. Pirmohammadi, Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints, IEEE Trans. Syst. Man Cybernet.– B: Cybernetics 33 (2) (2003) 237–249.
 E. D. Stoenescu, D. B. Marghitu, Effect of prismatic joint inertia on dynamics of kinematic chains, Mech. Mach. Theory 39 (2004) 431–443.
 L. Akbaba, S_. Yu¨ ksel, Dynamic modeling of elastic robot arm in bending and torsion (in Turkish), J. Faculty Eng. Architecture Gazi Univ. 21 (2) (2006) 349–357.
 F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee, Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 12 (4) (2016) 349–357.
 Nayfeh A. H. Problems in perturbation. New York: Wiley: 1993.
 Nayfeh A. H, Mook DT. Nonlinear oscillation. New York: Wiley: 1979.
 Nayfeh A. H. Introduction to perturbation techniques. New York: Wiley: 1981.