Continuous element methods have frequently been used in the modal analysis of structures modeled as flexible beams, extensible strings and rods, but only rarely for purposes of control. In this paper, we define a strategy of active control using the exact transfer matrix of a two-cell planar truss. The closed-loop performance predictions of both collocated and non-collocated controllers are compared as a function of feedback controller parameters.
Abrahamsson, T.J.S. and Sälliström, J.H., 1989, “Eigensolutions of non-conservative continuous mechanical systems computed by use of a matrix interation method”, International Journal for Numerical Methods in Engineering28, 1827-1837.
2.
Banarjee, J.R., 1989, “Coupled bending-torsional dynamic stiffness matrix for beam elements”, International Journal for Numerical Methods in Engineering28, 1283-1298.
3.
Cetinkunt, S. and Yu, W.L., 1991, “Closed-loop behavior of a feedback controlled flexible arm: a comparative study”, International Journal of Robotics Research10, 263-275.
4.
Kevorkian, S. and Pascal, M., 2000, “The concept of impedance matrix: application to rectangular plates”, in Eighth Conference on Nonlinear Vibrations, Stability and Dynamics of Structure, July 23-27, 2000, Blacksburg, VA, USA.
5.
Kolousek, V., 1973, Dynamics in Engineering Structures, Butterworth, London.
Leung, A.Y.T., 1993, Dynamic Stiffness and Substructures, Springer-Verlag, London.
8.
Meirovitch, L., 1990, Dynamics and Control of Structures, John Wiley and Sons, New York.
9.
Pascal, M. and Sylla, M., 1993, “Modèle dynamique par approche continue d'une grande structure spatiale”, La Recherche Aérospatiale2, 67-77.
10.
Pascal, M., 1991, “Vibrations analysis of flexible multibody systems”, Dynamics of Systems and Structures6, 217-234.
11.
Poelaert, D., 1983, “DISTEL: a distributed element program for dynamic modelling and response analysis of flexible structures”, in Proceeding of the 4th Symposium of Dynamics and Control of Large Structures, Blacksburg, VA, USA.
12.
Preumont, A., Dufour, J.P., and Malekian, C., 1990, “Active damping by a local force feedback with piezoelectric actuators”, in Proceedings of the 31th AIAA/ASME/ASCE/AMS Structures, Structural Dynamics and Material Conference, Long Beach, CA, USA.
13.
Richards, T.H. and Leung, Y.T., 1977, “An accurate method in structural vibration analysis”, Journal of Sound and Vibration55(3), 363-376.
14.
Wittrick, W.H. and Williams, F.W., 1971, “A general algorithm for computing natural frequencies of elastic structures”, Quarterly Journal of Mechanical Applied Mathematics24, 263-284.