A simple approach for reducing the order of equations with higher order nonlinearity

Pan, Chaohong; Zhu, Xue‐Na; Liu, Zhengrong

doi:10.1016/j.amc.2012.02.031

“…The high-precision modal superposition method [16,26] reduces the actual residual error by expressing the unavailable modes as the sum of the available modes and the system matrix, and expanding them according to the explicit series of their contributions. However, these methods [15,30,31] do not consider further higher order terms, that is, these methods have the problem of truncation and expansion. Modal truncation is more common in continuous structure systems, which will produce nonlinear characteristic problems, and it is difficult to find these characteristic accurately even in a local range.…”

Section: Introductionmentioning

confidence: 99%

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Kang,

Yuan,

Su

et al. 2024

Nonlinear Dyn

0

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Modal analysis is a widely applied method to study the vibration phenomenon of continuum structures, but there is no clear method to solve the modal truncation problem at present. In order to determine the contribution of different modes to the whole system, a new mode truncation method based on perturbation theory is proposed in this paper. In the process of discretization, perturbation parameters are introduced into the modes, and the modal number in the continuum structure system is confirmed according to the norm error of stiffness matrix in different degrees of freedom (DOFs) systems. The results show that the DOF identified by the modal perturbation method is related to the perturbation parameters, and the smaller the perturbation parameters are, the fewer modes need to be considered. When the perturbation parameter is large enough, the response of the system can only be accurately explained by truncation to higher-order modes. Finally, the perturbation parameter is fixed to 1, and the modal perturbation is connected with the traditional Galerkin method, which means that the traditional discretization is a special case of the modal perturbation method, and the number of modes can still be determined by the induced norm. This method can significantly reduce the modal truncation error, which is of great significance to the dynamic analysis of engineering applications.

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Novel modal methods for transient analysis with a reduced order model based on enhanced Craig–Bampton formulation

Kim

¹

,

Seo

²

,

Lim

³

2019

Applied Mathematics and Computation

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Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Kang,

Yuan,

Su

et al. 2023

Preprint

0

View full text Add to dashboard Cite

Modal analysis is a widely applied method to study the vibration phenomenon of continuum structures, but there is no clear method to solve the modal truncation problem at present. In order to determine the contribution of different modes to the whole system, a new mode truncation method based on perturbation theory is proposed in this paper. In the process of discretization, perturbation parameters are introduced into the modes, and the modal number in the continuum structure system is confirmed according to the norm error of stiffness matrix in different degrees of freedom (DOFs) systems. The results show that the DOF identified by the modal perturbation method is related to the perturbation parameters, and the smaller the perturbation parameters are, the fewer modes need to be considered. When the perturbation parameter is large enough, the response of the system can only be accurately explained by truncation to higher-order modes. Finally, the perturbation parameter is fixed to 1, and the modal perturbation is connected with the traditional Galerkin method, which means that the traditional discretization is a special case of the modal perturbation method, and the number of modes can still be determined by the induced norm. This method can significantly reduce the modal truncation error, which is of great significance to the dynamic analysis of engineering applications.

show abstract

A simple approach for reducing the order of equations with higher order nonlinearity

Cited by 4 publications

References 38 publications

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Novel modal methods for transient analysis with a reduced order model based on enhanced Craig–Bampton formulation

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

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