Loop shaping of structural dynamics

Abstract

Dynamic response of a stature can be characterized by mass, stiffness, and damping. Design of a conventional structure is primarily based on stiffness characteristics because damping is assumed to be negligible. Although stiffness-based design is elective for satisfying requirements related to displacement, this approach leads to overestimated satisfaction of design specifications related to velocity and acceleration. To overcome limitations of a stiffness-based design, a method is presented for design of a structure that meets given dynamic specifications. An optimum level of damping is developed using loop shaping of transfer matrices. Structural characteristics of a laboratory four-story building are identified through an eigensystem realization algorithm for data filtered by wavelets. For given specifications of dynamic performance, optimal stiffness and damping matrices of the specifications of dynamic performance, optimal stiffness and damping matrices of the structure are achieved by solving an algebraic Riccatti equation. Based on the optimal solution, loop shaping of the transfer function matrix is performed to obtain the desired location and capacity of a series of individual dampers. In addition, a linearization scheme to control behavior of a magnetorheological damper is developed using a neural network. Finally, an example of an application of the linear viscous damping device is given by means of a widely used benchmark problem. It is shown that design of dynamic characteristics of a civil engineering structure can be achieved by means of loop shaping technique. In particular, the damping matrix of a structure controls the H[] norm of the transfer matrices. Therefore, application of loop shaping to the transfer matrices, which is a method of damping-based design, guarantees mitigation of the worst-case steady-state response.