Vol.8, No.4 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION December, 2009 Earthq Eng & Eng Vib (2009) 8: 469-479 DOI: 10.1007/s11803-009-9126-0 Design of controlled elastic and inelastic structures A. M. Reinhorn 1† , O. Lavan 2‡ and G.P. Cimellaro 3§ 1. Dept. of Civil, Structural & Environmental Engineering, Univ. at Buffalo- The State University of NewYork, USA 2. Faculty of Civil and Environmental Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel 3. Dept. of Structural & Geotechnical Engineering DISTR, Politecnico di Torino, Turin 10129, Italy Abstract: One of the founders of structural control theory and its application in civil engineering, Professor Emeritus Tsu T. Soong, envisioned the development of the integral design of structures protected by active control devices. Most of his disciples and colleagues continuously attempted to develop procedures to achieve such integral control. In his recent papers published jointly with some of the authors of this paper, Professor Soong developed design procedures for the entire structure using a design – redesign procedure applied to elastic systems. Such a procedure was developed as an extension of other work by his disciples. This paper summarizes some recent techniques that use traditional active control algorithms to derive the most suitable (optimal, stable) control force, which could then be implemented with a combination of active, passive and semi-active devices through a simple match or more sophisticated optimal procedures. Alternative design can address the behavior of structures using Liapunov stability criteria. This paper shows a unified procedure which can be applied to both elastic and inelastic structures. Although the implementation does not always preserve the optimal criteria, it is shown that the solutions are effective and practical for design of supplemental damping, stiffness enhancement or softening, and strengthening or weakening. Keywords: active control; integral control; design – redesign procedure; inelastic structures; viscoelastic braces Correspondence to: A. M. Reinhorn, Dept. of Civil, Structural & Environmental Engineering, Univ. at Buffalo- The State Univ. of New York, 135 Ketter Hall, Buffalo, NY 14260, USA Tel: 716-645-2839 E-mail: reinhorn@buffalo.edu † Clifford C Furnas Eminent Professor; ‡ Senior Lecturer; § Assistant Professor Received October 11, 2009; Accepted October 31, 2009 1 Introduction In the last 30 years, the possibility of integrated design of structural/control systems in which both the structure and its vibration control system are optimized simultaneously has been extensively researched. Integrated design of optimal structural/control systems has been acknowledged as an advanced methodology for space structures, but not many applications can be found in civil engineering. Numerous researchers addressed the (i) topology; (ii) shape; and (iii) size optimization of structures using some form of control devices (see references provided by Cimellaro et al., 2009b which are not repeated here). The fundamental idea of redesign was proposed by Smith et al. (1992) and more recently, by Gluck et al. (1996) in a form close to the one presented in this paper. The idea of redesign is incorporated into the integrated design of structural/control systems as a second stage of a two stage procedure. (1) First stage: a desired structure is chosen based on best practice using engineering experience and is assumed to be fixed. An “active” often “adaptable” controller is designed to obtain a desired performance requirement, e.g., drift, absolute acceleration, base shear, etc. of the initial structure. The dynamic response of the initial structure in this stage is defined as the “ideal response.” (2) Second stage: the structure and the controller are redesigned by modifying the structural system to deliver part of the controller actions, and part is preserved to be delivered by active components to achieve a common goal prescribed by the performance obtained in the first step. The structure is therefore redesigned for better economy and controllability by modifying the structural system itself, i.e., changing stiffness, damping, and weights, and by reducing the amount of active control power needed to achieve the “ideal response.” In the following sections, this idea is developed progressively from simple elastic structures to inelastic structures. 2 Design of simple elastic structure with supplemental viscoelastic braces The first development of this idea for simple frame structures and structural systems was suggested by Gluck et al. (1996), for a frame structure braced by control devices (active or passive) that control its vibration, for which the equation of motion may be written as: