EFFECTS OF BASE POINTS AND NORMALIZATION SCHEMES ON THE NON-LINEAR NORMAL MODES OF CONSERVATIVE SYSTEMS

✍ Scribed by X.H. ZHANG

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 237 KB
• Volume: 256
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.4241

✦ Synopsis

In this paper, two factors that a!ect the behaviors of the non-linear normal modes (NNMs) of conservative vibratory systems are investigated. The "rst factor is the base points (which are equivalent to Taylor series expanding points) of the non-linear normal modes and the second one is the normalization schemes of the corresponding linear modes. For non-linear systems, in general only the approximated NNM manifolds are obtainable in practice, so di!erent base points may lead to di!erent forms of NNM oscillators and di!erent normalization schemes lead to di!erent forward and backward transformations which in turn a!ect the numerical computation errors. Three di!erent kinds of base points and two di!erent normalization schemes are adopted for comparison respectively. Two examples of non-linear systems with two and three degrees of freedom, respectively, are given as illustration. Simulations for various cases are made. The analysis and the simulation results indicated that, the best base points are the abstract base points determined via the linear normal mode, which would eliminate the third order terms containing velocity (for cubic systems) or quadratic terms (for quadratic systems) in equations of the NNM oscillators. A better invariance of the NNMs would also be maintained with such base points. The best scheme of normalization is the norm-one scheme that would minimize the numerical errors.