Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method

Kawamura, Shozo; Naito, Takayoshi; Zahid, Hossain Md.; Minamoto, Hirofumi

doi:10.1016/j.apacoust.2007.01.004

Cited by 11 publications

(6 citation statements)

References 4 publications

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“…Studies have shown that NLROMs accurately predict the response spectra for fatigue life analysis of a nonlinear system [23,24] and reduce the computational burden. This work discusses how the reduced order models for each substructure can be assembled to satisfy force equilibrium and compatibility, identical to the approach presented by Kawamura et al [25]. The result is a coupled set of nonlinear equations of motion that can be integrated to predict the general response of the assembly to various inputs.…”

Section: Introductionmentioning

confidence: 97%

“…The result is a coupled set of nonlinear equations of motion that can be integrated to predict the general response of the assembly to various inputs. The difference between this approach and [25] is that this approach can handle subcomponent models whose closed-form equations of motion are not directly known, such as a nonlinear finite element model.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

Kuether

Allen

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The analysis of large, complicated structures can be simplified and made more computationally efficient if smaller, simpler subcomponents can be treated and assembled. Modal substructuring methods allow one to reduce the order of the model at the subcomponent level. Modes are also an intrinsic property of the subcomponent, so they lead to certain physical insights. While modal substructuring is relatively well developed for linear systems, it's counterpart has not yet been developed for nonlinear subcomponent models. This work presents two modal substructuring techniques that can be used to predict the nonlinear dynamic behavior of an assembly. The first method uses the nonlinear normal modes of each subcomponent in a quasi-linear model to estimate the nonlinear modes of the assembly. In the second approach, a small number of linear modes are used to create a nonlinear reduced order model of each substructure, and the reduced models are assembled to build the nonlinear equations of motion of the assembly. Each approach is compatible with the finite element method, allowing for analysis of realistic engineering structures with global nonlinearities. The two methods are validated by using them to predict the nonlinear modes of a simple assembly of geometrically nonlinear beams, and both are found to perform well.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

Kuether

Allen

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…He Huan et al [9] proposed a hybrid coordinates CMS approach for a localized nonlinear system. Kawamura and Naito [10] presented a method for the analysis of nonlinear forced vibration of a multi-degree-of-freedom system. As a result, it was shown that the approach proposed in this paper is effective in the case with rigid modes in components.…”

Section: Introductionmentioning

confidence: 99%

An improved component mode synthesis method for interval uncertainty analysis

He¹,

Wang²,

Chen³

et al. 2017

J. vibroeng.

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In order to improve the computational efficiency of the large-scale structures with uncertainty parameters, this paper present a methodological approach for interval uncertainty treatment based on an improved free interface Component Mode Synthesis (CMS) method. Firstly, the structure is divided into substructures and the perturbation method is employed for the eigenvalue analysis of substructures with the interval non-deterministic characteristics. To reduce the mode truncation error, the residual flexibility matrix is considered by constructing a set of weighted orthogonal modal vectors with low-order system modal vectors and system matrices. Different from the previous studies, this method proposed in this paper avoids calculating directly inverse of the stiffness matrix, which makes it easier to get the residual flexibility matrix. Then the synthesis equations including parameters perturbation can be deduced in terms of the interface compatibility conditions. Finally, two examples including with a numerical example as well as an experiment example are given to demonstrate the effectiveness and the efficiency of the proposed method.

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“…The first type is the dynamic substructure methods, which are frequently combined with time-domain methods. The fixed-interface component mode synthesis (CMS) approach [5][6][7] is the most widely used dynamic substructure method. In this method, the structure is divided into two parts (linear and nonlinear parts).…”

Section: Introductionmentioning

confidence: 99%

Prediction method for steady-state response of local rubbing blade-rotor systems

Zhao

Yao

et al. 2015

J Mech Sci Technol

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Blade-rotor systems frequently encounter the problem of blade-to-case rubbing, which affects their safety and stability. Numerical simulation can be used to predict the steady-state response of these systems. However, such simulation is frequently computationally expensive because of the high dimensions of the dynamic model of a blade-rotor system. To overcome this problem, a new method that combines the receptance-based dimension-reduction approach with the incremental harmonic balance (IHB) method is presented in this study. First, a dynamic model of a blade-rotor system is developed using the finite element method, and the number of dimensions of the model is reduced by the receptance method. Subsequently, the steady-state response is obtained by the improved IHB method to conveniently manage the large number of super-harmonic components of the local rubbing system. Finally, the precision and efficiency of the proposed method is verified by comparing its results with those obtained by the Newmark-b method. The proposed method is found to be efficient in analyzing local rubbing blade-rotor systems with high dimensions, local nonlinearities, and rich super-harmonics.

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Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method

Cited by 11 publications

References 4 publications

Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

An improved component mode synthesis method for interval uncertainty analysis

Prediction method for steady-state response of local rubbing blade-rotor systems

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