Finite elements for modeling frequency-dependent material damping using internal state variables

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Abstract

New developments in a method of modeling frequency-dependent material damping and modulus in structural dynamics analysis are reported. The fundamental feature of the general method is the introduction of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics. These ATF are directly motivated by the ``internal state variables'' of materials science. The coupled partial differential equations that govern the dynamic behavior of a uniaxial rod are numerically solved within the computational framework of the finite element method, resulting in ``ATF-damped'' finite elements. Previous work in the development of this modeling technique is characterized by the use of a single augmenting field, with application to lightly-damped rods, beams, and truss structures. New developments include: (1) demonstration of the ability to model the behavior of high-damping materials; and (2) the use of multiple augmenting fields to model materials whose behavior departs significantly from that of standard anelastic solids.

Original languageEnglish (US)
Pages (from-to)344-357
Number of pages14
JournalASTM Special Technical Publication
Issue number1169
StatePublished - 1992

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Damping
Thermodynamics
Continuum mechanics
Structural dynamics
Materials science
Dynamic analysis
Partial differential equations
Demonstrations
Finite element method

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

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title = "Finite elements for modeling frequency-dependent material damping using internal state variables",
abstract = "New developments in a method of modeling frequency-dependent material damping and modulus in structural dynamics analysis are reported. The fundamental feature of the general method is the introduction of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics. These ATF are directly motivated by the ``internal state variables'' of materials science. The coupled partial differential equations that govern the dynamic behavior of a uniaxial rod are numerically solved within the computational framework of the finite element method, resulting in ``ATF-damped'' finite elements. Previous work in the development of this modeling technique is characterized by the use of a single augmenting field, with application to lightly-damped rods, beams, and truss structures. New developments include: (1) demonstration of the ability to model the behavior of high-damping materials; and (2) the use of multiple augmenting fields to model materials whose behavior departs significantly from that of standard anelastic solids.",
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AB - New developments in a method of modeling frequency-dependent material damping and modulus in structural dynamics analysis are reported. The fundamental feature of the general method is the introduction of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics. These ATF are directly motivated by the ``internal state variables'' of materials science. The coupled partial differential equations that govern the dynamic behavior of a uniaxial rod are numerically solved within the computational framework of the finite element method, resulting in ``ATF-damped'' finite elements. Previous work in the development of this modeling technique is characterized by the use of a single augmenting field, with application to lightly-damped rods, beams, and truss structures. New developments include: (1) demonstration of the ability to model the behavior of high-damping materials; and (2) the use of multiple augmenting fields to model materials whose behavior departs significantly from that of standard anelastic solids.

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