Substructuring in Engineering Dynamics

Allen, Matthew S.; Rixen, Daniel; Seijs, Maarten van der; Tiso, Paolo; Abrahamsson, Thomas; Mayes, Randall L.

doi:10.1007/978-3-030-25532-9

Cited by 61 publications

(41 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As recently shown in (van Ophem et al, 2018;Mencik, 2021) the forced vibration response of 2D periodic finite LRMs comprised of a repetition of UCs can be efficiently performed by means of dynamic sub-structuring, with the UCs constituting the individual sub-structures. To reduce the computational cost of large sub-structured FE models, MOR is often applied to the sub-structures before assembly, for which the use of CMS methods such as the Craig-Bampton method is wellestablished (Gruber and Rixen, 2016;Allen et al, 2020). This method reduces the interior DOFs of the sub-structures using a truncated set of eigenmodes resulting from a modal analysis before assembly, as is performed in the BMS, and was e.g.…”

Section: Introductionmentioning

confidence: 99%

Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach

Belle¹,

Claeys²,

Desmet³

et al. 2022

Front. Mech. Eng.

View full text Add to dashboard Cite

Metamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically modeled using the finite element method. Since their sub-wavelength nature and often intricate design can lead to large unit cell models, model reduction methods such as the Generalized Bloch Mode Synthesis have been proposed to greatly accelerate dispersion curve calculations. In order to calculate forced vibro-acoustic responses of finite periodic elastic metamaterial plates composed of an assembly of unit cells, however, full order finite element models rapidly become computationally unaffordable. Therefore, in this work the Generalized Bloch Mode Synthesis is incorporated in a sub-structuring approach, which enables fast forced vibration response calculations of finite elastic metamaterial plates based on a single reduced order unit cell model. The main advantage as compared to a regular Craig-Bampton approach is the additional local reduction of unit cell boundary degrees of freedom, whereby a compatible basis for the identical neighboring unit cells is incorporated. In addition, by combining this Generalized Bloch Mode Synthesis based sub-structuring approach with the Elementary Radiator Approach, efficient sound transmission loss computations of finite periodic metamaterial plates are enabled. The performance of the proposed approach for fast vibro-acoustic response predictions is demonstrated for different cases.

show abstract

Section: Introductionmentioning

confidence: 99%

Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach

Belle¹,

Claeys²,

Desmet³

et al. 2022

Front. Mech. Eng.

View full text Add to dashboard Cite

show abstract

“…Dynamic substructuring addresses this issue and encompasses several methodologies that aim to decompose the system into individual entities, treat them separately and finally assemble them properly to obtain the global response. A detailed overview of the notion is provided in [4], whereas recent advances are discussed in [5,6], including comparative assessments, experimental techniques and industrial applications. Most of the methodologies that adhere to dynamic substructuring can approximate each component's underlying physics separately by employing some form of fundamental modes.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, substructural representations of nonlinear systems require additional treatment compared against traditional methodologies [6]. For example, Wu et al [8] augmented Rubin substructuring with information captured by modal derivatives to model a three-dimensional wind turbine blade with geometrical nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

“…The notion of exploiting dynamic substructuring to formulate a reduced-order representation is not new. Dynamic substructuring relies on modes that capture the overall dynamics in a set of reduced coordinates, thus implying a form of dimensionality reduction [6]. For instance, Gruber et al [13] derived a ROM for non classically damped linear systems utilizing dual CB-CMS, whereas linear parametric problems are addressed in [14], using CB-CMS modes interpolation on the proper subspace.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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.

show abstract

“…the eigenvectors of the linear system, also known as natural modes) included in the projection basis. Substructuring techniques are also widely exploited, where the model is divided in multiple subsystem which can be independently reduced to be later assembled back together [2,3,4,5].…”

Section: Introductionmentioning

confidence: 99%