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Control law for variable damping device defined by a non‐linear differential equation
Author(s) -
Yamada Kazuhiko
Publication year - 1999
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/(sici)1096-9845(199905)28:5<529::aid-eqe828>3.0.co;2-d
Subject(s) - dissipation , impulse (physics) , law , control theory (sociology) , discretization , differential equation , mathematics , mathematical analysis , physics , classical mechanics , computer science , control (management) , artificial intelligence , political science , thermodynamics
This paper proposes a non‐linear control law for a variable damping device (VDD) aimed at reducing structural seismic responses. The VDD is attached to the structure by an auxiliary spring element composing a non‐linear Maxwell element. The VDD's damping coefficient is adjusted to control the reactive internal force in the non‐linear Maxwell element. A large controlled force is thus produced with little external power required to adjust the VDD's damping coefficient. The proposed control law defines the rate or increment of the VDD's damping coefficient at a certain moment by a differential equation or its discretized form. The controlled force vs. deformation relation plots parallelogram‐like hysteretic curves, which indicates quick action and energy dissipation. Fundamental characteristics of an SDOF model with the VDD controlled by the proposed law are examined for impulse, sin and seismic excitations. The law for the SDOF model is extended to one for an MDOF model. The control effect for a 3DOF model is examined by numerical experiments. Copyright © 1999 John Wiley & Sons, Ltd.