Dynamic control of structures subjected to constraints

This study presents a dynamic equation of constrained motion and illustrates its validity through a dynamic analysis on the structural control by a constraint. Minimizing a function of the variation in kinetic energy at constrained and unconstrained states with respect to the velocity variation, the dynamic equation is derived and it is shown that the result compares with the generalized inverse method proposed by Udwadia and Kalaba. It is investigated that the responses of a 10‐story building are controlled by a constraint due to the installation of a two‐bar structure. The structural responses are affected by various factors like the length of each bar, damping, stiffness of the bar structure, and the boundary positions between two structures. Under an assumption that the bars have the same mass density, this study determines the optimal boundary positions to minimize the total responses of the structure, and compares the responses and control forces by optimal feedback control with the results. Copyright © 2007 John Wiley & Sons, Ltd.