Chapter 5 Response DOF Selection for Mapping Experimental Normal Modes-2016 Update Robert N. Coppolino Abstract A modified Guyan reduction strategy for response degree-of-freedom (DOF) selection to map experimental normal modes is described and demonstrated. The method employs static load patches, rather than point loads, in regions defined by 3-D elastic elements and other problematic zones on a highly detailed finite element model (FEM). Three key benefits are realized by the methodology, namely (1) definition of a well-posed test-analysis mass (TAM) matrix, (2) application of a previously published residual kinetic energy matrix for definition of appropriate measurement DOFs, and (3) elimination of irrelevant modes from the measured mode set. Improved qualities of the modified Guyan reduction strategy are demonstrated with a problematic spacecraft-type FEM, which cannot be readily treated using classical Guyan reduction methodology. 5.1 Introduction The United States Air Force Space Command [1] and NASA [2] maintain standards for the proper execution of spacecraft and launch vehicle modal tests, which require measured mode shapes satisfying strict orthogonality criteria. Modal vector orthogonality, based on the fundamental energy principles owing to Ritz [3], require a test-analysis mass (TAM) matrix that is most often developed by employment of the Guyan reduction method [4]. The TAM matrix, generally developed as part of the modal test planning process, is defined on the basis of proposed instrumented (accelerometer) degrees of freedom (DOF), which are a subset of a corresponding (often highly detailed) finite element model (FEM). Advances in computers and software resources and ever increasingly detailed FEMs rendered selection of an adequate instrumentation array and TAM matrix quite challenging. Development of a residual kinetic energy (RKE) method [5] provided a path for automated completion of an initially deficient instrumentation array and TAM matrix (employing Guyan reduction as the underlying principle). However, additional difficulties owing to (a) displacement pattern (Boussinesq) singularities for models based on 3-D finite elements [6] and (b) breathing modes of shells [7] rendered the popular Guyan reduction method to be deficient in such situations. In response to these challenges, a “modified” Guyan reduction strategy employing load patches [8], rather than concentrated point loads (implicitly) used in “classical” Guyan reduction, appears to remedy this situation. The present paper revisits the “modified” Guyan reduction method and introduces a generalized RKE procedure for reliable definition of an instrumentation array and TAM matrix. In addition, the generalized RKE procedure appears to be useful for other model order reduction strategies such as SEREP [9], modal sensitivity vector augmentation [10], and others. The generalized Guyan-RKE methodology is demonstrated on an aerospace-type branched shell configuration, which was previously studied [8]. Results of the demonstration indicate that (1) “classical” Guyan reduction produces a TAM matrix that fails to satisfy strict orthogonality criteria, (2) “modified” Guyan reduction produces TAM matrices satisfying strict orthogonality criteria (without the need for additional instrumentation degrees of freedom), and (3) RKE is a useful metric for discrimination of “body” and shell “breathing” modes as well as a means for improvement of the instrumentation array. R.N. Coppolino ( ) Measurement Analysis Corporation, 23850 Madison Street, Torrance, CA 90505, USA e-mail: bobcoppolino@gmail.com © The Society for Experimental Mechanics, Inc. 2016 M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29763-7_5 33
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