Reduction process based on proper orthogonal decomposition for dual formulation of dynamic substructures

Im, Sun-Young; Kim, Euiyoung; Cho, Maenghyo

doi:10.1007/s00466-019-01702-6

Cited by 12 publications

(7 citation statements)

References 25 publications

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“…The wide range of conventional methods includes analytic strategies for linear systems [1] and step-by-step time integration schemes [2,3]. Especially with emphasis on computational efficiency, several approximation schemes and model order reduction strategies have been proposed in the literature [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A Newmark space-time formulation in structural dynamics

et al. 2021

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In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set of equations of motion and the Newmark approximations are transformed into their corresponding space-time equivalents. The dynamic system is then represented by one algebraic space-time equation only. This equation is projected into a coupled pair of space-time equations, which is solved via the fixed point algorithm. The solution is iteratively assembled by enrichments, each of which is decomposed by a dyadic product of spatial and temporal enrichment vectors. The evolution of the spatial enrichment vectors is investigated during convergence and interpreted by comparing them to the set of linear modes of vibration. The new method is demonstrated by means of four numerical examples, presenting not only the excellent convergence behavior and the numerical efficiency but also the limits of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

A Newmark space-time formulation in structural dynamics

et al. 2021

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“…Yu et al 25 reduced a 22-DOF nonlinear system of a high-pressure rotor to a 2-DOF system, preserving the oil film oscillation property by employing a modified POD method. Im et al 26 proposed a new reduction process in which the dynamic substructures were reduced via POD. Lu et al 27 proposed a modified nonlinear POD method to reduce the order of the multiple DOFs of a rotor system.…”

Section: Introductionmentioning

confidence: 99%

An efficient method for vibration equations with time varying coefficients and nonlinearities

Yang

Xie

Chen

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.

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“…In a nonlinear context, Weeger et al [15] suggested a ROM based on modal derivatives, able to substitute all nonlinear terms via polynomials of the reduced state variables, whereas Joannin et al [16] coupled NNMs with modal synthesis to address nonlinear friction phenomena. As an alternative methodology to NNMs, modes derived through Proper Orthogonal Decomposition (POD) have been coupled with CMS in a substructural formulation in [17,18]. Through POD, a ROM can harvest information from a system's response and approximate the solution manifold spanning the dynamic behavior of a component.…”

Section: Introductionmentioning

confidence: 99%

On the Coupling of Reduced Order Modeling with Substructuring of Structural Systems with Component Nonlinearities

Vlachas

Tatsis

Agathos

et al. 2021

Conference Proceedings of the Society for Experimental Mechanics Series

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The emergence of digital virtualization has brought Reduced Order Models (ROM) into the spotlight. A successful reducedorder representation should allow for modeling of complex effects, such as nonlinearities, and ensure validity over a domain of inputs. Parametric Reduced Order Models (pROMs) for nonlinear systems attempt to accommodate both previous requirements [1]. Our work addresses a physics-based reduced representation of structural systems with localized nonlinear features. Via implementation of the approach described in [2], we achieve a substructuring formulation similar to Component Mode Synthesis. However, instead of individual component modes, reduction modes of a global nature are obtained from the corresponding linear monolithic system. In turn, this technique allows for a divide and conquer strategy that naturally couples the response between linear and nonlinear subdomains. A pROM able to exploit this modular formulation is developed as a next step. The framework treats each component independently, and individual projection bases are assembled by applying a Proper Orthogonal Decomposition (POD) on snapshots of each subdomain's response. Parametric dependencies on the boundary conditions and the structural and excitation traits are injected into the pROM utilizing clustering, following the methodology in [3]. To this end, a modified strategy is employed, relying on the Modal Assurance Criterion as a measure to indicate optimal training samples while defining regions with similar underlying dynamics on the domain of parametric inputs. A numerical case study of a 3D wind turbine tower featuring material nonlinearities exemplifies our approach. The derived pROM offers an accelerated approximation of the underlying high fidelity response and can be utilized for numerous tasks, including vibration control, residual life estimation, and condition assessment of hotspot locations.

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Reduction process based on proper orthogonal decomposition for dual formulation of dynamic substructures

Cited by 12 publications

References 25 publications

A Newmark space-time formulation in structural dynamics

A Newmark space-time formulation in structural dynamics

An efficient method for vibration equations with time varying coefficients and nonlinearities

On the Coupling of Reduced Order Modeling with Substructuring of Structural Systems with Component Nonlinearities

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