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A one‐dimensional lumped parameter model representing impedance functions in general structural systems with proportional damping
Author(s) -
Saitoh Masato
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3323
Subject(s) - electrical impedance , cantilever , control theory (sociology) , mathematical analysis , stiffness , added mass , truss , spring (device) , mathematics , function (biology) , frequency response , degrees of freedom (physics and chemistry) , structural engineering , physics , engineering , computer science , vibration , acoustics , control (management) , quantum mechanics , artificial intelligence , evolutionary biology , biology , electrical engineering
SUMMARY This paper presents a one‐dimensional lumped parameter model (LPM) that accurately represents the impedance function between two nodes arbitrarily selected in general linear structural systems having proportional damping. Through a procedure based on the modal analysis, the impedance function can be transformed into an equivalent LPM consisting of units arranged in series, with each unit consisting of a spring, a dashpot, and a so‐called gyro mass element arranged in parallel. The gyro mass element generates a reaction force proportional to the relative acceleration of the nodes between where it is placed. Three application examples show that the LPMs accurately simulate the impedance functions in a mass–spring structure, a truss frame structure, and a cantilever plate. For a more efficient representation, a large number of units associated with high‐order modes in the high‐frequency region can be removed from the proposed gyro mass LPM (GLPM) as an approximation of the impedance functions in a target frequency region. The accuracy of the approximated GLPMs is improved by incorporating an additional unit associated with residual stiffness. This approximation greatly reduces the number of degrees of freedom of the GLPMs so that a marked decrease in the computational domain size and time can be expected for solving dynamic problems. Copyright © 2011 John Wiley & Sons, Ltd.