Vibration source description in substructuring: A theoretical depiction

Rixen, Daniel J.; Boogaard, Anthonie; Seijs, M. V. van der; Schothorst, Gert van; Poel, Tjeerd van der

doi:10.1016/j.ymssp.2015.01.024

Cited by 26 publications

(8 citation statements)

References 19 publications

(36 reference statements)

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“…Besides, although the proposed method already has the excellent computational efficiency, it could be sped-up even further by incorporating the substructuring techniques, e.g., [46]. Furthermore, the framework of the SDS method generalised in this paper has paved the way for the SDS formulation for other types of Helmholtz equations or Maxwell equations.…”

Section: Discussionmentioning

confidence: 99%

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

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Citation: Liu, X. and Banerjee, J. R. (2017). A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems. Mechanical Systems and Signal Processing, 87, doi: 10.1016/j.ymssp.2016.10.017 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractA highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the exact general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J 0 ) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

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Section: Discussionmentioning

confidence: 99%

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

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“…From frequency based substructuring [27], transfer functions of the assembled system ( ) can be obtained as a function of the subsystems transfer functions ( ) and ( ) , as described by Eq. (4):in which the indexes ( ) , ( ) and ( ) represent target DoFs (passive system), the source active DoFs and the interface DoFs between active and passive systems, respectively.…”

Section: Component-based Tpamentioning

confidence: 99%

Combining classical and component-based TPA for equivalent load identification

Melo

Oliveira

2020

J Braz. Soc. Mech. Sci. Eng.

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The transfer path analysis (TPA) has become a rather standard tool for solving noise and vibration problems, as it helps understanding the mechanisms responsible for the generation and transmission of those quantities. By better understanding the intricate role of multiple sources and propagation paths, it is possible to diagnose and propose effective modifications that would addresses such issues at specific target locations. Although originally an experimental approach, hybrid methods that include modeled subsystems have been proposed, which allow the assessment of key system features even at stages prior to the construction of full physical prototypes. However, in classical TPA, the operational forces are characteristics of the complete system, which implies that, with each modification in one subsystem, it is necessary to redo all the tests for the correct determination of target functions. For this reason, in recent years, interest has been renewed in the development of faster and simpler techniques for analyzing energy transfer paths, which offer a compromise between workload and accuracy. More specifically, a set of methods called component-based TPA is highlighted, which consists of characterizing the excitation of a source through a set of equivalent forces (or even interface velocities) inherent only to the active subsystem. In this way, the responses at target locations on the passive subsystem could be calculated using these equivalent loads and the dynamics of the complete system, obtained numerically, experimentally or under a hybrid framework. This work presents a critical analysis of the component-based TPA methods and proposes the combined use of these methods with a classical TPA approach in the process of determining equivalent forces of the active subsystem. This set of equivalent forces, combined with the passive subsystem dynamics, allows the prediction of the vibrational behavior of the full assembly at targeted locations, without the need for a full experimental analysis of the assembled system. As the case study presented here consists of a modular academic setup, it allows the qualitative assessment of the method in distinct assembly boundary conditions, in which the subsystems are connected via rigid or flexible joints.

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“…This equation is known as the dual assembly formulation or LM-FBS, which will be validated later in the experimental part [11].…”

Section: Y Y Yb Byb Bymentioning

confidence: 99%

Structure-Borne Prediction on a Tire-Suspension Assembly Using Experimental Invariant Spindle Forces

Almirón¹,

Bianciardi²,

Corbeels³

2019

SAE Technical Paper Series

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R oad induced noise is getting more and more significant in context of the electrification of the powertrain. The automotive industry is seeking for technologies to predict the contribution of vehicle components upfront, early in the development process. Classical Transfer Path Analysis (TPA) is a well-established technique that successfully identifies the transmission paths of noise and vibration from different excitation sources to the target responses. But it has a drawback: it requires the physical availability of the full vehicle. To achieve shorter development cycles, to avoid costly time-consuming design iterations and due to the limited availability of prototypes, engineers derived a method that addresses these requirements. Component-based TPA is a relatively new structure borne substructuring approach that allows to characterize the source excitation by a set of equivalent loads (blocked forces) independently from the receiver structure and to predict its behavior when coupled to different receivers. Frequency Based Substructuring, FBS, is applied in order to obtain the coupled assembly. However, there are a number of challenges affecting its applicability, such as the proper modelling of the coupling degrees of freedom and the difficulty to access the interface connection points. Geometrical reduction aims to solve those inconveniences. This paper aims to investigate these challenges of componentbased TPA by measurements on a tire-wheel suspension in static condition. The source component (the tire-wheel) is characterized by a set of blocked forces and transfer functions identified on a dedicated tire-wheel test-rig. These calculated loads are combined with the FRFs of the fully assembled system. The FRFs are calculated by using experimental substructuring methods. The sensitivity of applying FBS together with geometrical reduction in the frame of component-based TPA will be analyzed.

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Vibration source description in substructuring: A theoretical depiction

Cited by 26 publications

References 19 publications

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Combining classical and component-based TPA for equivalent load identification

Structure-Borne Prediction on a Tire-Suspension Assembly Using Experimental Invariant Spindle Forces

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