Damping performance of strain actuated beams. (English) Zbl 0931.74030

Balakrishnan, A. V.

Comput. Appl. Math. 18, No. 1, 31-86 (1999).

We present an analysis of active damping for Euler-Bernoulli beams of arbitrary shape made of self-straining material. The analysis includes the feed-through effect. We determine open-loop and closed-loop transfer functions as well as the time-domain response (state-space model based on the semigroup theory). The principal contribution is the construction of the root loci as a function of the feedback gain. Our main conclusion is that the unavoilable equivalent inductance in the differentiator circuit limits damping performance, and modes higher than the undamped circuit resonant frequency are actually destabilized.

MSC:

74H10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74K10	Rods (beams, columns, shafts, arches, rings, etc.)
74M05	Control, switches and devices (“smart materials”) in solid mechanics

Keywords:

Euler-Bernoulli beam; transfer functions; state-space model; semigroup theory; feedback gain