Large structures such as ships and airplanes can undergo a variety of complicated vibrations. Such structures typically consist of an outer body made of metal plating (for example, the hull of a ship) or perhaps a massive metallic frame (for example, the chassis of a truck), and a large variety of internal objects that are connected to either the plating or the frame. In designing such structures, it is highly desirable to have some method for predicting how they will vibrate under various conditions. The radiation of sound caused by these vibrations, either into the environment or into the empty portions of the structure, is also of interest because this sound is often either unwanted noise or a means of inferring information about the details of the structure or the excitation. Fuzzy-structure acoustics refers to a class of conceptual viewpoints in which precise, computationally intensive models of the overall structure are replaced by nonprecise analytical models, for which the initial information is said to be fuzzy.
Fuzzy-structure theories divide the overall structure into a master structure and one or more attached structures, the latter being referred to as the fuzzy substructures, the internal structures, or the internals. (An example of a master structure is the hull and major framework of a ship.) The master structure is presumed to be sufficiently well known at the outset that its vibrations or dynamical response could be predicted if the forces that were exerted on it were known. Some of the forces are exerted on it by the substructures at the points at which they are attached. Such forces can be very complicated; nevertheless, there is some hope that a satisfactory approximate prediction of the vibrations of the master structure itself can be achieved with a highly simplified model.
The fuzzy substructures can be regarded as structures that are not known precisely. Recently developed theories of fuzzy structures lead, after various plausible idealizations, to a formulation that requires only a single function, this being the modal mass per unit frequency bandwidth. The influence of fuzzy substructures attached to the master structure tends to resemble that of an added frequency-dependent mass attached to the master structure in parallel with a frequency-dependent dashpot connecting the master structure to a hypothetical rigid wall. The added mass is a frequency-weighted integral over the modal mass per unit natural frequency, the weighting being such that the natural modes whose natural frequencies are less than the driving frequency have a positive contribution, while those for which the natural frequencies are greater than the driving frequency have a negative contribution. The master structure can seem to be less massive than it actually is when the bulk of the substructure mass is associated with resonant frequencies less than the excitation frequency.
One implication of the newly emerging fuzzy-structure theories is that, insofar as there is concern with the vibrations of only the master structure, it is possible to drastically curtail the estimation or measurement of any parameters within the substructures that are associated with internal damping. See Vibration