Modal Analysis Techniques for Nonlinear Large-Scale Structural Systems.
Final rept. 20 Jan 93-19 Jul 97,
MICHIGAN UNIV ANN ARBOR DIV OF RESEARCH DEVELOPMENT AND ADMINISTRATION
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The objective of this research was to develop, and to implement computationally, modal analysis methodologies for large-scale, complex, nonlinear structures. These methods are based on nonlinear modes of vibration defined and constructed in terms of invariant manifolds. The motivation for the research stems from the fact that the dynamics of nonlinear structures are typically decomposed in terms of the linearized systems modes, often yielding poor modal convergence and too large reduced-order models. During this grant, major theoretical advances were made on the fundamentals of modal analysis for nonlinear systems. Novel constructive methodologies were formulated and validated for single- and multi-mode motions of nonlinear systems. Exact optimal reduced-order models were developed for free response nonlinear modal analysis, and approximate ones were proposed for the forced response case. All these methods share a common foundation, namely the groundbreaking definition, by the principal investigators, of nonlinear modes of vibration in terms of invariant manifolds in the systems phase space. The methods developed were validated and their effectiveness was demonstrated for several nonlinear structural systems such as beams, and results showed nonlinear modal analysis to be significantly more accurate and economical than classical linear modal analysis.
- Theoretical Mathematics