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RESEARCH PAPERS

A Hybrid Inverse Mode Problem for Fixed-Fixed Mass-Spring Models

[+] Author and Article Information
Izuru Takewaki, Tsuneyoshi Nakamura

Department of Architectural Engineering, Kyoto University, Sakyo, Kyoto 606, Japan

Yasumasa Arita

Shimizu Corporation, Minato-ku, Tokyo 104, Japan

J. Vib. Acoust 118(4), 641-648 (Oct 01, 1996) (8 pages) doi:10.1115/1.2888346 History: Received June 01, 1995; Online February 26, 2008

Abstract

A hybrid inverse mode problem is formulated for a fixed-fixed mass-spring model. A problem of eigenvalue analysis and its inverse problem are combined in this hybrid inverse mode formulation. It is shown if all the masses and the mid-span stiffnesses of the model are prescribed, then the stiffnesses of the left and right spans (side-spans) can be found for a specified lowest eigenvalue and a specified set of lowest-mode drifts in the side-spans. Sufficient conditions are introduced and proved for a specified eigenvalue and a specified set of drifts in the side-spans to provide positive stiffnesses of the side-spans and to be those in the lowest eigenvibration. A set of solution stiffnesses in the side-spans is derived uniquely in closed form.

Copyright © 1996 by The American Society of Mechanical Engineers
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