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- W4302307972 abstract "AbstractNonlinear normal modes (NNMs) provide a useful framework for understanding nonlinear vibrations. This article discusses the NNMs of cyclically symmetric piecewise linear systems possessing N degrees of freedom. Such structures find practical applications, for example, in modeling turbomachine blade assemblies. We compute the system’s NNMs via a shooting-based method. In contrast to standard applications of this technique, our nonlinear system does not possess a clear underlying linear system, which is required to initiate the numerical method. To overcome this, we propose a linear system that incorporates cyclic symmetry and tends to the nonlinear system in the limiting case. This methodology is used to compute the NNMs of systems with 3 and 7 degrees of freedom. These examples show that the underlying linear system provides significant qualitative inferences about the NNMs, such as their mode shapes. Further, the NNMs split into groups with different frequencies based on their nodal diameters. These observations are generalized to the N degree of freedom case.KeywordsNonlinear vibrationsNonlinear normal modesContact nonlinearityCyclic symmetry" @default.
- W4302307972 created "2022-10-06" @default.
- W4302307972 creator A5003946047 @default.
- W4302307972 creator A5061507042 @default.
- W4302307972 date "2022-10-07" @default.
- W4302307972 modified "2023-09-26" @default.
- W4302307972 title "Nonlinear Normal Modes of an N Degrees of Freedom Cyclically Symmetric Piecewise Linear System" @default.
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- W4302307972 doi "https://doi.org/10.1007/978-3-031-15758-5_119" @default.
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