Secondary systems modeled as fuzzy sub-structures

Vibrating secondary systems attached to a primary vibrating structure (called the master structure) modify the dynamical properties of the master structure. In engineering practice the dynamical properties of the secondary systems are often very incompletely known. This uncertain knowledge may in the simplest case be modeled by attaching random single degree of freedom oscillators, called fuzzies, to the master structure at randomly distributed points of the structure. Each of these fuzzies are characterized by a random triplet of mass, eigenfrequency, and damping ratio. This characterization can be combined with a model of the random distribution of the fuzzies over the structure by letting the entire system of fuzzies be characterized as a triplet of random fields over the structure. Two specific examples, a Poisson point pulse field and a Poisson square wave field, of such a triplet field are considered for a rigid one-degree of freedom master structure. Approximate distribution properties of the impedance, the frequency response function and other related functions of the imposed frequency are obtained by use of Winterstein approximation technique. This information can be used to determine the probabilistic properties of the impulse response function, say, or of the nonergodic steady state response to stationary excitation, say. The study prepares for a finite element model of a flexible master structure with a fuzzy subsystem attached to it.