Fundamental Structural-Acoustic Idealizations for Structures with Fuzzy Internals

Abstract

Fundamental issues relative to structural vibration and to scattering of sound from structures with imprecisely known internals are explored, with the master structure taken as a rectangular plate in a rigid baffle, which faces an unbounded fluid medium on the external side. On the internal side is a fuzzy structure, consisting of a random array of point-attached spring-mass systems. The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function rhp(fl) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value fl. The theory also predicts that the exact value of the damping in the fuzzy structure is of little importance, because the structure, even in the limit of zero damping, actually absorbs energy with an apparent frequency-dependent damping constant proportional to dfhp(u))/doi incorporated into the dynamical description of the master structure. A small finite value of damping within the internals will cause little appreciable change to this limiting value.

TRAX: An approach for the time rational analysis of complex dynamic systems

“…The linear time invariant dynamic system and its time response are first introduced in section (2). The theory of the exact frequency average is then summarised in section (3) and its scalar and matrix rational approximations at individual frequencies are discussed in section (4).…”

“…Data: the system matrices and vectors, A, B, c, f , as defined in equation (2). A frequency of interest, ω, as described in equation (8), an averaging width, a, and a rational order, R. Result: the rational estimation, p g pgq R pωq, of the Gaussian average.…”

“…There have been many efforts to extract and identify such simplified, important, patterns of the system's behaviour, either from deterministic or from statistical points of view. The consideration of fuzzy, complex, or reverberant components as for example in [1,2,3,4,5,6] of a vibrating system falls within this realm where parts of the system made of a myriad of vibrating elements are replaced by a small number of components that provide equivalent properties.…”

Vibration damping in low-frequency range due to structural complexity. A model based on the theory of fuzzy structures and model parameters estimation

“…In 1991, this theory of fuzzy structures has been revisited by V.W. Sparrow [16] who has initialized new researches in this area in the United States of America [17][18][19][20][21][22][23][24]. Recently, the author has presented [25] a survey of its theory of fuzzy structures including new results concerning probabilistic fuzzy constitutive law with spatial memory (Type II law) [26,27] and developed within the context of sound radiation and acoustic scattering problems.…”

Coupling and attenuation of waves in plates by randomly distributed attached impedances

“…Others have considered a simple model of a plate with enormous numbers of attached mass-spring systems. [3][4][5] Descriptive information of the attached oscillators is assumed to be known only in some statistical sense. This ''fuzzy structure'' approach is appealing because the heterogeneities need not be described in detail.…”