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A Novel Computational Method to Calculate Nonlinear Normal Modes of Complex Structures
Date
2019-01-31
Author
Samandarı, Hamed
Ciğeroğlu, Ender
Metadata
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In this study, a simple and efficient computational approach to obtain nonlinear normal modes (NNMs) of nonlinear structures is presented. Describing function method (DFM) is used to capture the nonlinear internal forces under periodic motion. DFM has the advantage of expressing the nonlinear internal force as a nonlinear stiffness matrix multiplied by a displacement vector, where the off-diagonal terms of the nonlinear stiffness matrix can provide a comprehensive knowledge about the coupling between the modes. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations using DFM under harmonic motion assumption. A matrix manipulation based on dynamic stiffness concept was used to localize nonlinearities and reduce the number of nonlinear equations improving the efficiency of the approach, which becomes important in solving large complex structures. The nonlinear algebraic equations are solved numerically by using Newton’s method with Arc-Length continuation. The efficiency of proposed computational approach is demonstrated using a two-degree-of-freedom nonlinear system. The proposed approach has the potential to be applied to large-scale engineering structures with multiple nonlinear elements and strong nonlinearities.
Subject Keywords
Nonlinear normal modes
,
Describing function method
,
Nonlinear vibrations
,
Nonlinear numerical solver
URI
https://sem.org/imac
https://hdl.handle.net/11511/76092
https://link.springer.com/chapter/10.1007/978-3-030-12391-8_37
Conference Name
IMAC XXXVII: Conference Exposition on Structural Dynamics (2019)
Collections
Department of Mechanical Engineering, Conference / Seminar
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H. Samandarı and E. Ciğeroğlu, “A Novel Computational Method to Calculate Nonlinear Normal Modes of Complex Structures,” presented at the IMAC XXXVII: Conference Exposition on Structural Dynamics (2019), Orlando, United States Of America, 2019, Accessed: 00, 2021. [Online]. Available: https://sem.org/imac.