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Toward a multifrequency quasi-static ritz vector method for frequency-dependent acoustic system application

INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2012年第11期89卷 1451-1470页

作者： Yoon, Gil Ho Hanyang Univ Sch Mech Engn Seoul 133791 South Korea

Computational issues concerning the calculation of acoustic responses of a complex finite element (FE) model for various noise and vibration inputs have become prevalent. Such a model requires a significant amount of computation time because of repeated inversions of dynamic stiffness matrices. Thus, even state-of-the-art computer hardware and software often face limitations where a model order reduction (MOR) scheme can help. The established MOR schemes such as ritz vector or quasi-static ritz vector methods are efficient for general engineering systems, but these MOR methods become inaccurate for frequency response analyses in some acoustic systems with frequency-dependent mass and stiffness matrices and force vectors (hereinafter frequency-dependent acoustic systems). To cope with the inaccurate prediction by these methods for frequency-dependent acoustic systems, this research presents and applies the multifrequency quasi-static ritz vector method. Unlike the ritz vector or quasi-static ritz vector methods, the present multifrequency quasi-static ritz vector method employs direct Krylov subspace bases without an orthonormal procedure at multiple center frequencies. In comparison with the existing MOR scheme, a significant gain in computational efficiency is achieved, as well as enhanced accuracy. A comparison of these methods based on criteria such as efficiency, accuracy, and reliability was also conducted. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： model reduction method multifrequency quasi-static ritz vector method acoustic ritz vector method quasi-static ritz vector method

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Transient quasi-static ritz vector (TQSRV) method by Krylov subspaces and eigenvectors for efficient contact dynamic finite element simulation

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APPLIED MATHEMATICAL MODELLING 2015年第9期39卷 2740-2762页

作者： Yoon, Gil Ho Kim, Jun Hwan Jung, Kwang Ok Jung, Jae Won Hanyang Univ Sch Mech Engn Seoul South Korea Hanyang Univ Grad Sch Mech Engn Seoul South Korea

This paper presents a novel model,order reduction (MOR) method called the transient quasi-static ritz vector (TQSRV) method for efficient transient finite element (FE) analysis. Comparing with frequency response analysis, linear transient FE analysis with a fixed time step takes less computation time as an effective dynamic stiffness matrix assembled before time marching procedure is factorized once. Nevertheless as the number of degrees of freedom of a FE model has been dramatically increased for accurate engineering simulation, even the state-of-the-art computer and software often face their limitations. For fast but accurate transient FE analysis, we present a new MOR scheme called the TQSRV method with Krylov bases spanned at multiple angular velocities and several lowest eigenvectors. By calculating transient responses of reduced FE models and comparing it with the responses of full FE models, the effectiveness and accuracy of the TQSRV method are demonstrated. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Model order reduction method Transient quasi-static ritz vector method ritz vector method Quasi-static ritz vector method

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ritz vector-based substructuring method using interface eigenmode-shape pseudo-forces

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2023年第1期227卷

作者： Koh, Hyeong Seok Yoon, Gil Ho Hanyang Univ Mech Engn Seoul South Korea Hanyang Univ Sch Mech Engn Seoul South Korea

We propose a new ritz vector-based dynamic substructuring method which substitutes the unit pseudo-forces applied at the adjacent degrees of freedom (DOFs) using distributed forces. One of the main problems of the ritz vector and unit pseudo-force-based dynamic substructuring method is the strong dependence of the number of reduction bases on the interface DOF, which is not reduced by substructuring. This type of dependency causes the number of reduction bases obtained by the unit pseudo-forces to be always exceed or at least equal to the number of interface DOFs. The number of ritz vector bases required at adjacent interface DOFs is efficiently reduced by approximating the unit pseudo-force as a type of distributed force using an energy transfer approach. The distributed forces, called eigenmode-shape pseudo-forces, comprise low modes computed through the eigenvalue problem of substructures corresponding to adjacent DOFs, and a set of distributed forces is a subspace of the vector space spanned by the unit force vectors. The efficiency of the substructuring method may be increased by reducing the number of reduction bases. This approach was demonstrated through several numerical examples.

关键词： Interfacial pseudo-force Substructuring method Krylov subspace ritz vector method Quasi-static ritz vector method

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Efficient topology optimization of multicomponent structure using substructuring-based model order reduction method

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COMPUTERS & STRUCTURES 2020年 228卷 1页

作者： Koh, Hyeong Seok Kim, Jun Hwan Yoon, Gil Ho Hanyang Univ Mech Engn Seoul South Korea

This study develops a novel model reduction (MR) scheme called the multi-substructure multi-frequency quasi-static ritz vector (MMQSRV) method to compute dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization (TO) of dynamic systems with multiple substructures. The calculation of structural responses of dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time. The ever-increasingly complex phenomena of FE models with many degrees of freedom make it difficult to calculate FE responses in the time or frequency domain. To overcome this difficulty, model reduction schemes can be utilized to reduce the size of the dynamic stiffness matrix. This paper presents a new model order reduction method called MMQSRV, based on the quasi-static ritz vector method, with Krylov subspaces spanned at multiple angular velocities for efficient TO. Through several analysis and design examples, we validate the efficiency and reliability of the model reduction schemes for TO. (C) 2019 Published by Elsevier Ltd.

关键词： Topology optimization Model reduction schemes Substructure design Krylov subspace ritz vector method

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Structural topology optimization for frequency response problem using model reduction schemes

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2010年第25-28期199卷 1744-1763页

作者： Yoon, Gil Ho Kyungpook Natl Univ Sch Mech Engn Taegu South Korea

This study uses model reduction (MR) schemes such as the mode superposition (MS), ritz vector (RV), and quasi-static ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization in the frequency domain. The calculation of structural responses to dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time: that is mainly attributable to repeated inversions of dynamic stiffness matrices depending on time or frequency intervals, which hastens the dissemination of the MR schemes in the analysis. However, using well-established MR schemes in topology optimization has not been prevalent. Therefore, this study conducted a comprehensive investigation to highlight the drawbacks and advantages of these MR schemes for topology optimization. In the results, the MS method, which generates reduction bases by considering some of the lowest eigenmodes, can lose the accuracy in both approximated structural responses and sensitivity values due to locally vibrating eigenmodes and higher mode truncation in the solid isotropic material with penalization (SIMP) approach. In addition, the RV and QSRV methods, which generate reduction bases by considering the external force, mass, and stiffness matrices of a structure, can be used as alterative model reduction schemes for stable optimization. Through several analysis and design examples, the efficiency and reliability of the model reduction schemes for topology optimization are compared and validated. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Topology optimization Model reduction method ritz vector method Mode superposition method Quasi-static ritz vector method

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