Understanding Large Order Finite Element Model Dynamic Characteristics Robert N. Coppolino, CTO Measurement Analysis Corporation 23850 Madison Street Torrance, California 90505 ABSTRACT State-of-the-art technologies in computation and software have led to ever increasing size of finite element models, simply because this is possible. While it is arguable that “degree-of-freedom” proliferation is unnecessary, there are some potential benefits to be realized, namely (1) commonality of stress and dynamic models and (2) employment of finite element models in the mid- and high-frequency ranges (normally the domain of statistical energy analysis). When large order finite element models are developed using appropriate wavelength-based rules, they are valid for high frequency, high modal density dynamic analysis. Such models do not suffer from the need for simplifying and/or “smearing” assumptions used in statistical energy analysis (SEA). This paper describes energy-based metrics that clearly identify the characteristics of normal modes, of large-order models. In addition, a modal filtering method, that employs shape function classes (e.g. overall body and bulge shapes) and modal coherence analysis, identifies “target” modes of interest which are a subset of a very large set of overall body, local and breathing modes. Illustrative models are used to demonstrate the procedures. 1. INTRODUCTION 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[1,2]. The level of complexity in modern dynamic system models has produced a challenge to engineering understanding of the character and classification of normal modes. Sophisticated geometric displays of normal modes provide the engineer with an intuitive, subjective impression of their character. However, they fail to define objective, quantitative metrics to clearly characterize normal modes. Since the 1960’s, the aerospace industry has developed and utilized mathematical tools that logically segment complex dynamic systems. The Craig-Bampton[3] and Benfield-Hruda[4] methods of component mode synthesis (CMS) are leading examples of procedures that have permitted effective analysis of complex dynamic systems (ahead of the great advances in computational hardware subsequent to the 1960s). Moreover, these methods yielded effective metrics for characterizing normal modes, utilizing quantities such as modal kinetic energy, modal strain energy, and modal participation and effective mass[1]. Component mode synthesis and its mode characterization metrics are quite straightforward when applied to branched, beam-like aerospace structures. They tend, however, to become awkward with structures that have highly distributed component interfaces (as in the case of automobile structures). Finally, it is noted that component mode synthesis may not be used at all on large-order finite element models, leaving the engineer with a more acute need for quantitative normal mode metrics. composed of distinct subsystems (e.g., fuselage, wings, vertical and horizontal stabilizers, engines, …). In addition, individual normal modes often have dominant directional activity (e.g., surge, sway, heave, roll, pitch, and yaw). Segmentation of modal kinetic and strain energies by directions and physical components are exploited in this paper to yield clear metrics for “naming” of normal modes. Another difficulty encountered in the analysis of shell-type aerospace structures is the result of the presence of many local shell breathing modes in the same frequency band as dominant body modes. Employment of modal effective mass as a metric provides one approach for discrimination of the two modal classes. A new, more effective means for mode discrimination, based on modal coherence with respect to “shape families”, is introduced and demonstrated in this paper. T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 367 Regardless of the engineer’s choice of dynamic analysis strategy (CMS or complete system), the structural system is always DOI 10.1007/978-1-4419-9305-2_26, © The Society for Experimental Mechanics, Inc. 2011
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