### 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 m_{F}(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 dm_{F}(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 language | English (US) |
---|---|

Pages (from-to) | 339-348 |

Number of pages | 10 |

Journal | Journal of Vibration and Acoustics, Transactions of the ASME |

Volume | 117 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering

### Cite this

}

*Journal of Vibration and Acoustics, Transactions of the ASME*, vol. 117, no. 3, pp. 339-348. https://doi.org/10.1115/1.2874456

**Fundamental structural-acoustic idealizations for structures with fuzzy internals.** / Pierce, A. D.; Sparrow, Victor Ward; Russell, Daniel Allen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fundamental structural-acoustic idealizations for structures with fuzzy internals

AU - Pierce, A. D.

AU - Sparrow, Victor Ward

AU - Russell, Daniel Allen

PY - 1995/1/1

Y1 - 1995/1/1

N2 - 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.

AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=0029344085&partnerID=8YFLogxK

U2 - 10.1115/1.2874456

DO - 10.1115/1.2874456

M3 - Article

VL - 117

SP - 339

EP - 348

JO - Journal of Vibration and Acoustics, Transactions of the ASME

JF - Journal of Vibration and Acoustics, Transactions of the ASME

SN - 1048-9002

IS - 3

ER -