Closed-form exact solution to H-infinity optimization of dynamic vibration absorbers: II. Application to different performance indexes for vibration isolation

Toshihiko Asami; Osamu Nishihara

doi:10.1117/12.384557

27 April 2000 Closed-form exact solution to H_(infinity) optimization of dynamic vibration absorbers: II. Application to different performance indexes for vibration isolation

Toshihiko Asami, Osamu Nishihara

Author Affiliations +

Proceedings Volume 3989, Smart Structures and Materials 2000: Damping and Isolation; (2000) https://doi.org/10.1117/12.384557
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

Abstract

Recently, Nishihara and Matsuhisa have proposed a new theory for attaining the H_(infinity) optimization of a dynamic vibration absorber (DVA) in the linear vibratory systems. The H_(infinity) optimization of DVA is a classical optimization problem, and already solved more than 50 years ago. All of us know the solution through the textbook written by Den Hartog. The new theory proposed them gives us the exact algebraic solution of the problem. In the first report, we have expounded the theory and showed the procedure of finding the algebraic solution to a typical performance index (compliance transfer function) of the viscous damped system. In this paper, we will apply this theory to another performance indexes: mobility and accelerance transfer functions for force excitation system, and the absolute and relative displacement responses to acceleration, velocity or displacement input to foundation for motion excitation system. We apply this theory not only the viscous damped system but also the hysteretic damped system. As a result, we found the closed-form exact solutions in every performance indexes when the primary system has no damping. The solutions obtained here are compared with the classical ones solved by the fixed-points theory. We further apply this theory to design of DVAs attached to damped primary systems, and found the closed-form exact solutions to some performance indexes of the hysteretic damped system.

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Toshihiko Asami and Osamu Nishihara "Closed-form exact solution to H_(infinity) optimization of dynamic vibration absorbers: II. Application to different performance indexes for vibration isolation", Proc. SPIE 3989, Smart Structures and Materials 2000: Damping and Isolation, (27 April 2000); https://doi.org/10.1117/12.384557

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KEYWORDS

Motion models

Nomenclature

Systems modeling

Vibration isolation

Information operations

Solids

Mechanical engineering

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