Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Periodically layered isolators exhibit transmissibility "stop bands" or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4 × 10-4. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.

Original languageEnglish (US)
Pages (from-to)85-101
Number of pages17
JournalJournal of Sound and Vibration
Volume268
Issue number1
DOIs
StatePublished - Nov 13 2003

Fingerprint

isolators
Analytical models
formulations
Elastomers
Damping
elastomers
cells
Modal analysis
damping
Experiments
Geometry
Metals
frequency ranges
attenuation
synthesis
geometry
approximation
metals

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

@article{d11f9a282de6414d8ea9203b78ba90e6,
title = "Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression",
abstract = "Periodically layered isolators exhibit transmissibility {"}stop bands{"} or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4 × 10-4. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.",
author = "Szefi, {J. T.} and Edward Smith and Lesieutre, {George A.}",
year = "2003",
month = "11",
day = "13",
doi = "10.1016/S0022-460X(02)01574-2",
language = "English (US)",
volume = "268",
pages = "85--101",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

AU - Szefi, J. T.

AU - Smith, Edward

AU - Lesieutre, George A.

PY - 2003/11/13

Y1 - 2003/11/13

N2 - Periodically layered isolators exhibit transmissibility "stop bands" or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4 × 10-4. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.

AB - Periodically layered isolators exhibit transmissibility "stop bands" or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4 × 10-4. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.

UR - http://www.scopus.com/inward/record.url?scp=0242499446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242499446&partnerID=8YFLogxK

U2 - 10.1016/S0022-460X(02)01574-2

DO - 10.1016/S0022-460X(02)01574-2

M3 - Article

AN - SCOPUS:0242499446

VL - 268

SP - 85

EP - 101

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 1

ER -