Dynamic Models of Structures

This chapter presen ts an o v erview on mo dels, whic h are commonly used for civil structures and control actuators, and that are relevant to the problems that will b e addressed in the follo wing c hapters. This model is frequently used to describe the dynamics of civil structures [90], From physical viewpoint, M represents the inertial properties of the system; K represents its elasticity and C _d its energy dissipation properties. This section reviews several types of actuators and stress properties which affects the control problem definition. The induced dipoles cause the particles to align GÇ£head to tailGÇ¥ in chains and form columnar structures, parallel to the applied field. These chain-like structures hinder the flow of the fluid and thereby increase its apparent viscosity. The pressure needed to yield these c hain-lik e structures increases with the applied magnetic field, resulting in a field-dependent yield stress [37]. This power will be referred to as the damper power: It follows that for the structure we have w(t)ߦÆ_d (t) Gëñ 0 for all t . Note that even though one can find analogies b et w een them, the dissi-pativeness discussed here is different from the general concept of dissipative systems, whic his known from general control theory and is discussed in the next section. At the 1960s, a class of dynamic models, characterized by some input-output property, began to attract the attention of many researchers.