Fundamental structural-acoustic idealizations for structures with fuzzy internals

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Abstract

Fundamental issues relative to structural vibration and to scattering ofsound 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 theorypredicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function mF(Ω) which gives a smoothed-out total mass, per unit plate area, of all those attachedoscillators which have their natural frequencies less than a given value Ω. 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 dmF(σ)/dσ incorporated into the dynamical description of the master structure. A small finite value of damping withinthe internals will cause little appreciable change to this limiting value.

Original languageEnglish (US)
Pages (from-to)339-348
Number of pages10
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume117
Issue number3
DOIs
StatePublished - Jan 1 1995

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Damping
damping
Acoustics
acoustics
structural vibration
rectangular plates
baffles
resonant frequencies
Natural frequencies
Scattering
Fluids
causes
fluids
scattering
energy

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Cite this

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abstract = "Fundamental issues relative to structural vibration and to scattering ofsound 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 theorypredicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function mF(Ω) which gives a smoothed-out total mass, per unit plate area, of all those attachedoscillators which have their natural frequencies less than a given value Ω. 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 dmF(σ)/dσ incorporated into the dynamical description of the master structure. A small finite value of damping withinthe internals will cause little appreciable change to this limiting value.",
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