4.7 ILLUSTRATIVE EXAMPLE IDENTIFICATION OF “BODY” MODES The above defined metric for quantification of overall body mode coherence is applied to the illustrative example system modes resulting in the following result. Table 3: Identification of Overall Body Modes using “Body” Mode Coherence The “body” mode coherence modal filter automatically separates the overall body modes from shell breathing modes, even for modes that have minimal modal effective mass. Note that shell breathing modes have “zero” coherence. This metric provides greater effectiveness than the modal effective mass metric that is generally used to identify body modes that produce significant base reaction loads (and consequently fails to designate self-equilibrating body modes). 5. CONCLUSIONS Finite element models of modern structural systems, such as aircraft, spacecraft, and automobiles, are typically composed of thousands to millions of grid points due to the sophistication of commercial CAE software products and mechanical (static and dynamic) fidelity requirements. The level of complexity in modern dynamic system models has produced a challenge to engineering understanding of the character and classification of normal modes. While geometric displays of normal modes provide the engineer with an intuitive, subjective impression of their character, they fail to define objective, quantitative metrics to clearly characterize normal modes. This paper described and demonstrated a variety of modal metrics, often employed in aerospace applications to quantitatively characterize normal modes on the basis of kinetic and strain energy distributions and modal effective mass. The energy based metrics were segmented into rationally defined components (rather than the system model’s grid points) that clearly indicate modal activity distributions. Overall direction of modal activity was also clearly defined based on directionally summed kinetic energy components and modal effective mass. A new metric for characterizing and filtering system modes, based on shape function families, was introduced. This shape family metric appears to effectively segregate overall body modes and breathing modes of shell-type structures, without the use of tedious mode-by-mode graphical reviews. REFERENCES [1] Harris’ Shock and Vibration Handbook, 6th Ed, A. Piersol and T. Paez (Ch. 23, R. Coppolino), McGraw-Hill, 2010 [2] The Finite Element Method: Its Basis and Fundamentals, 6th Ed, O. Zienkiewicz, R. Taylor, and J. Zhou, Elsevier,2005 [3] “Coupling of Substructures for Dynamic Analysis”, R. Craig and M. Bampton, AIAA Journal, Vol. 6, July 1968 [4] “Vibration Analysis of Structures by Component Mode Substitution”, W. Benfield and R. Hruda, AIAA Journal, Vol. 9, July1971 [5] Peterson’s Stress Concentration Factors, 3rd Ed, W. Pilkey and D. Pilkey, Wiley, 2008 373
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