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Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

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Abstract

The solutions to H ∞ and H 2 optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H ∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H 2 optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H ∞ and H 2 optimization procedures shows that for a beam under random force excitation, use of H2 optimum parameters resulting in smaller mean square motion than the other optimization.

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Authors and Affiliations

  1. Ferdowsi University of Mashhad, Mashhad, Iran

    B. Noori

  2. Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

    A. Farshidianfar

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  1. B. Noori
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  2. A. Farshidianfar
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Correspondence to B. Noori.

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Noori, B., Farshidianfar, A. Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization. Arch Appl Mech 83, 1773–1787 (2013). https://doi.org/10.1007/s00419-013-0777-y

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  • DOI: https://doi.org/10.1007/s00419-013-0777-y

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