Small strain vibration of a continuous, linearized viscoelastic rod of expanded polymer cushion material

Gregory S. Batt, James M. Gibert, Mohammed Daqaq

Research output: Contribution to journalArticle

Abstract

In this paper, the free and forced vibration response of a linearized, distributed-parameter model of a viscoelastic rod with an applied tip-mass is investigated. A nonlinear model is developed from constitutive relations and is linearized about a static equilibrium position for analysis. A classical Maxwell-Weichert model, represented via a Prony series, is used to model the viscoelastic system. The exact solution to both the free and forced vibration problem is derived and used to study the behavior of an idealized packaging system containing Nova Chemicals' Arcel® foam. It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss modulii necessitate the use of additional Prony series terms. It is also shown that the model is able to predict the modal frequencies and the primary resonance response at low acceleration excitation, both with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a nonlinear elastic model that extends beyond the scope of this work. Solution analysis and experimental data indicate little material vibration energy dissipation close to the first modal frequency of the mass/rod system.

Original languageEnglish (US)
Pages (from-to)330-347
Number of pages18
JournalJournal of Sound and Vibration
Volume349
DOIs
StatePublished - Jan 1 2015

Fingerprint

cushions
Prony series
rods
vibration
polymers
Polymers
forced vibration
free vibration
high acceleration
static tests
dynamic response
packaging
foams
softening
Dynamic response
Foams
Energy dissipation
Packaging
inhomogeneity
energy dissipation

ASJC Scopus subject areas

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

Cite this

Small strain vibration of a continuous, linearized viscoelastic rod of expanded polymer cushion material. / Batt, Gregory S.; Gibert, James M.; Daqaq, Mohammed.

In: Journal of Sound and Vibration, Vol. 349, 01.01.2015, p. 330-347.

Research output: Contribution to journalArticle

@article{a9ee9ff2dc824f45ae2b24407b588953,
title = "Small strain vibration of a continuous, linearized viscoelastic rod of expanded polymer cushion material",
abstract = "In this paper, the free and forced vibration response of a linearized, distributed-parameter model of a viscoelastic rod with an applied tip-mass is investigated. A nonlinear model is developed from constitutive relations and is linearized about a static equilibrium position for analysis. A classical Maxwell-Weichert model, represented via a Prony series, is used to model the viscoelastic system. The exact solution to both the free and forced vibration problem is derived and used to study the behavior of an idealized packaging system containing Nova Chemicals' Arcel{\circledR} foam. It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss modulii necessitate the use of additional Prony series terms. It is also shown that the model is able to predict the modal frequencies and the primary resonance response at low acceleration excitation, both with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a nonlinear elastic model that extends beyond the scope of this work. Solution analysis and experimental data indicate little material vibration energy dissipation close to the first modal frequency of the mass/rod system.",
author = "Batt, {Gregory S.} and Gibert, {James M.} and Mohammed Daqaq",
year = "2015",
month = "1",
day = "1",
doi = "10.1016/j.jsv.2015.03.039",
language = "English (US)",
volume = "349",
pages = "330--347",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Small strain vibration of a continuous, linearized viscoelastic rod of expanded polymer cushion material

AU - Batt, Gregory S.

AU - Gibert, James M.

AU - Daqaq, Mohammed

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper, the free and forced vibration response of a linearized, distributed-parameter model of a viscoelastic rod with an applied tip-mass is investigated. A nonlinear model is developed from constitutive relations and is linearized about a static equilibrium position for analysis. A classical Maxwell-Weichert model, represented via a Prony series, is used to model the viscoelastic system. The exact solution to both the free and forced vibration problem is derived and used to study the behavior of an idealized packaging system containing Nova Chemicals' Arcel® foam. It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss modulii necessitate the use of additional Prony series terms. It is also shown that the model is able to predict the modal frequencies and the primary resonance response at low acceleration excitation, both with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a nonlinear elastic model that extends beyond the scope of this work. Solution analysis and experimental data indicate little material vibration energy dissipation close to the first modal frequency of the mass/rod system.

AB - In this paper, the free and forced vibration response of a linearized, distributed-parameter model of a viscoelastic rod with an applied tip-mass is investigated. A nonlinear model is developed from constitutive relations and is linearized about a static equilibrium position for analysis. A classical Maxwell-Weichert model, represented via a Prony series, is used to model the viscoelastic system. The exact solution to both the free and forced vibration problem is derived and used to study the behavior of an idealized packaging system containing Nova Chemicals' Arcel® foam. It is observed that, although three Prony series terms are deemed sufficient to fit the static test data, convergence of the dynamic response and study of the storage and loss modulii necessitate the use of additional Prony series terms. It is also shown that the model is able to predict the modal frequencies and the primary resonance response at low acceleration excitation, both with reasonable accuracy given the non-homogeneity and density variation observed in the specimens. Higher acceleration inputs result in softening nonlinear responses highlighting the need for a nonlinear elastic model that extends beyond the scope of this work. Solution analysis and experimental data indicate little material vibration energy dissipation close to the first modal frequency of the mass/rod system.

UR - http://www.scopus.com/inward/record.url?scp=84929514585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929514585&partnerID=8YFLogxK

U2 - 10.1016/j.jsv.2015.03.039

DO - 10.1016/j.jsv.2015.03.039

M3 - Article

AN - SCOPUS:84929514585

VL - 349

SP - 330

EP - 347

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

ER -