A Generalization of Effective Mass for Selecting Free–Free Target Modes

[+] Author and Article Information
Daniel C. Kammer1

Department of Engineering Physics,  University of Wisconsin, 1500 Engineering Drive, Madison, WI 53706kammer@engr.wisc.edu

Joseph Cessna

Department of Engineering Physics,  University of Wisconsin, 1500 Engineering Drive, Madison, WI 53706

Andrew Kostuch

 Quartus Engineering Inc., 10251 Vista Sorrento Pkwy, San Diego, CA 92121


Corresponding author.

J. Vib. Acoust 129(1), 121-127 (Oct 05, 2006) (7 pages) doi:10.1115/1.2424980 History: Received December 21, 2005; Revised October 05, 2006

One of the most important tasks in pretest analysis and modal survey planning is the selection of target modes. The target modes are those mode shapes that are determined to be dynamically important using some definition. While there are many measures of dynamic importance, one of the measures that has been of greatest interest to structural dynamicists, is the contribution of each mode to the dynamic loads at an interface. Dynamically important modes contribute significantly to the interface loads and must be retained in any reduced analytical representation. These modes must be identified during a ground vibration test to validate the corresponding finite element model. Structural dynamicists have used interface load based effective mass measures to efficiently identify target modes for constrained structures. The advantage of these measures of dynamic importance is that they are absolute, in contrast to other measures that only indicate the importance of one mode shape relative to another. However, in many situations, especially in aerospace applications, structures must be tested in a free–free configuration. In the case of free–free elastic modes, the effective mass values are zero, making them useless measures of dynamic importance. This paper presents a new effective mass like measure of absolute dynamic importance that can be applied to free–free structures. The new method is derived based upon the free–free modal equations of motion. The approach is shown to be directly related to ranking mode shapes based on approximate balanced singular values. But, unlike the approximate balanced singular value approach, it is an absolute measure of importance. A numerical example of a general spacecraft system is presented to illustrate the application of the new technique. Dynamically important mode shapes were easily identified for modal acceleration, velocity, and displacement output. The new method provides an efficient technique for selecting target modes for a modal vibration test, or the reduction of a modal based analytical model to the dynamically important mode shapes.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 4

Cumulative sum for modal acceleration output measure

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Figure 5

Maximum singular value for frequency response matrix and EMf ranking for generic spacecraft

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Figure 1

Generic spacecraft finite element model

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Figure 2

Free–free elastic mode 3–0.83Hz

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Figure 3

Cumulative sum for modal velocity and modal displacement output measures



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