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Treatment of transient vibration problems using new method for determination of function’s poles and residues

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Abstract

An approximate method is presented, using (with suitable corrections) only the compliance’s poles that are located nearly positive real axis in the complex frequency plane, for solving transient vibration problems containing different damping mechanisms. For determination of poles and its residues, a new method based on consideration of known values of a function in the vicinity of a pole is suggested which allows achieving a required accuracy due to an iteration process. Simple and sufficiently accurate approximate formulas are obtained for treatment mechanical systems with different damping mechanisms under the action of impulse loads. A particular attention is paid to the model, which can be considered as a correction of the ideal hysteretic model.

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, 32000, Haifa, Israel

    G. B. Muravskii

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  1. G. B. Muravskii
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Correspondence to G. B. Muravskii.

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Muravskii, G.B. Treatment of transient vibration problems using new method for determination of function’s poles and residues. Arch Appl Mech 87, 405–425 (2017). https://doi.org/10.1007/s00419-016-1200-2

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  • DOI: https://doi.org/10.1007/s00419-016-1200-2

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