Closed-form exact solution to H-infinity optimization of dynamic vibration absorber: II. Development of an algebraic approach and its application to a standard problem

Osamu Nishihara; Toshihiko Asami

doi:10.1117/12.384589

27 April 2000 Closed-form exact solution to H-infinity optimization of dynamic vibration absorber: II. Development of an algebraic approach and its application to a standard problem

Osamu Nishihara, Toshihiko Asami

Author Affiliations +

Proceedings Volume 3989, Smart Structures and Materials 2000: Damping and Isolation; (2000) https://doi.org/10.1117/12.384589
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

Abstract

The fixed-points method for the dynamic vibration absorber (DVA) is widely accepted and the results are prevalent for practical applications. However, they usually have to fall back to a heuristic approach from the point of view of its optimization criterion. A typical design problem to minimize the maximum amplitude magnification factor of the primary system, for which the fixed-points method was originally developed, is an example of such common cases. In the present paper, a new algebraic formulation is developed to this classic problem and closed-form exact solutions to both the optimum tuning ratio and the optimum damping parameters are derived, on the assumption of undamped primary system. This algebraic approach is based on an observation of trade-off between two resonance amplitude magnification factors. Thus, the problem reduces to a solution of an algebraic equation, which is derived as a discriminant of quartic algebraic equation. In undamped case, it was proven that the optimum parameters, the minimum amplitude magnification factor, the resonance and antiresonance frequencies, and sensitivities of the amplitude magnification factors are totally algebraic. A numerical extension enables efficient solutions for the damped primary system and has more direct applicability.

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Osamu Nishihara and Toshihiko Asami "Closed-form exact solution to H-infinity optimization of dynamic vibration absorber: II. Development of an algebraic approach and its application to a standard problem", Proc. SPIE 3989, Smart Structures and Materials 2000: Damping and Isolation, (27 April 2000); https://doi.org/10.1117/12.384589

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