A bilinear variational principle governing longitudinal vibration of rods with frequency-dependent material damping

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Abstract

The equations governing the longitudinal vibration of rods with frequency-dependent material damping are developed as the Euler equations of a bilinear variational principle. Frequency-dependent material damping and modulus are accommodated through the introduction of an augmenting thermodynamic field that interacts with the mechanical displacement field. These two primary dependent fields are supplemented with two corresponding adjoint fields for the purpose of addressing nonconservative system behavior. The variational function is nearly symmetric in the primary and adjoint variables, a formulation which may be particularly useful in computational simulation of system behavior using finite elements. The augmenting thermodynamic field is found to be effectively internal-no boundary conditions involve it alone.

Original languageEnglish (US)
Pages (from-to)210-211
Number of pages2
JournalJournal of Applied Mechanics, Transactions ASME
Volume60
Issue number1
DOIs
StatePublished - Jan 1 1993

Fingerprint

variational principles
Vibrations (mechanical)
rods
Damping
damping
Thermodynamics
vibration
thermodynamics
Euler equations
Boundary conditions
boundary conditions
formulations
simulation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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AB - The equations governing the longitudinal vibration of rods with frequency-dependent material damping are developed as the Euler equations of a bilinear variational principle. Frequency-dependent material damping and modulus are accommodated through the introduction of an augmenting thermodynamic field that interacts with the mechanical displacement field. These two primary dependent fields are supplemented with two corresponding adjoint fields for the purpose of addressing nonconservative system behavior. The variational function is nearly symmetric in the primary and adjoint variables, a formulation which may be particularly useful in computational simulation of system behavior using finite elements. The augmenting thermodynamic field is found to be effectively internal-no boundary conditions involve it alone.

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