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research-article

The Udwadia-Kalaba Trajectory Control Applied to a Cantilever Beam - Experimental Results

[+] Author and Article Information
Raphael P. Spada

University of São Paulo, São Carlos School of Engineering, Dept. of Mechanical Engineering, Trabalhador São-Carlense 400, 13566-590 São Carlos, Brazil
spadaeu@yahoo.com.br

Rodrigo Nicoletti

University of São Paulo, São Carlos School of Engineering, Dept. of Mechanical Engineering, Trabalhador São-Carlense 400, 13566-590 São Carlos, Brazil
rnicolet@sc.usp.br

1Corresponding author.

ASME doi:10.1115/1.4036236 History: Received December 02, 2015; Revised March 03, 2017

Abstract

The Udwadia-Kalaba methodology is a possible way of explicitly obtaining the equations of motion of constrained systems. From these equations of motion, one can estimate the necessary forces in the constraint to keep the system in a given motion. Hence, the Udwadia-Kalaba methodology can also apply to active tracking control of sub-systems or the control of points of a structure. In this work, one investigates experimentally the benefits and drawbacks of such control strategy by applying it to the control of out-of-plane vibrations of a cantilever beam. The beam is excited by a shaker mounted near the clamped-end of the beam. A second shaker applies the control forces in the free-end of the beam, where an accelerometer is used for feedback. The vibration behavior of the beam under excitation/control is measured by a laser vibrometer. Results show that, the methodology changes the dynamic behavior of the structure by changing its boundary conditions at the point of control, thus shifting natural frequencies and mode shapes. Results also show that the successful implementation of the method experimentally is sensitive to the quality of modeling of the structure.

Copyright (c) 2017 by ASME
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