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M.V. van der Seijs

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Experimental dynamic substructuring

Analysis and design strategies for vehicle development

Doctoral thesis - M.V. van der Seijs

Sound and vibration have a defining influence on our perception of product quality. They are especially well-known aspects in the automotive industry; a branch which sees, besides safety and driving comfort, ever-increasing expectations of the acoustic experience. After all, a smooth and silent driving experience appeals to a feeling of premiumness, a connotation no longer reserved to the top segment in the industry. While traditional combustion engines are gradually getting replaced by hybrid or full-electric drive-lines, other electromechanical (so-called mechatronic) systems make their entrance. As a consequence, the sound experience shifts from low-frequent engine roar to high-frequent humming and whining – a yet unfamiliar experience that calls for redefinition of the soundscape. To support such change, it is necessary that sound and vibration aspects can be considered in an early phase of development by means of simulations. This poses a true challenge: although state-of-art numerical modelling techniques can simulate the low-frequent dynamics fairly well, they often fail to provide reliable answers for the higher acoustic frequency range. This thesis presents techniques that aim to implement measurements of structural dynamics and active vibration sources into development processes. By characterising the passive and active dynamics of yet available components by means of measurements and combining those with numerical models, a hybrid simulation emerges that may provide answers to high-frequent problems in an early phase of development. This hybrid simulation is facilitated by use of Experimental Dynamic Substructuring: a methodology that determines structural dynamic aspects of complete products based on individually measured components.Part one of this thesis presents a variety of methods for simulation and substructuring that form the basic toolbox for generation, analysis, coupling and decoupling of dynamic models. Pivotal is the experimental approach, which means that dynamic models are obtained from measurements rather than numerical modelling efforts. To transform such measurements into a model that is compatible for coupling with other (numerical) models, the virtual point transformation is proposed. This method considers measured responses and applied forces around (user-chosen) points as locally rigid displacements and forces. Doing so, every connection point of a component can be described by three translations and three rotations with respect to a global reference frame, perfectly suited for substructuring. At the same time, the quality of the measurement and transformed frequency response functions can be quantified objectively using the proposed consistency functions. Altogether, the virtual point method bridges the gap between experimental and numerical modelling activities and enables us to exploit substructuring effectively for complex high-frequency systems. Part two presents a comprehensive study of Transfer Path Analysis (TPA); a collection of methods that contemplate a vibration problem as a source, transmission and receiver. A general framework for TPA is presented by re-interpreting eleven methods from the perspective of substructuring. It is shown that these methods can be categorised into three families, that in turn differ in the nature of characterisation of the source. The component-based TPA is regarded the most promising family, which allows to characterise a source independent of the environment in which it has been measured. The vibrations of the active source can be replaced by equivalent force spectra that, multiplied with the (simulated) FRFs of the assembled vehicle, predict what this source would sound like in the vehicle. Several practical methods are discussed to determine such equivalent forces: from forces measured against a blocked boundary, using free velocities, based on measurements on a compliant test bench or using the so-called in-situ and pseudo-forces methods. For further generalisation, a notation is presented that governs the abovementioned principles and facilitates the application and comparison of component-based TPA methods. In particular, it is shown that controllability and observability – concepts adopted from control theory – are strongly related to TPA; proper understanding of these principles yields interesting opportunities for analysis and simulation. The developed methods have been applied to analyse the vibrations of the electric power-assisted steering (EPS) system, which is reported on in part three. It is demonstrated that the virtual point transformation is able to determine accurate FRFs in a frequency range up to 6000 Hertz. Substructuring is applied to simulate the FRFs of a vehicle by applying the principle of substitute coupling, which employs a substitute beam during measurement in the vehicle to represent the dynamic effects of the steering system to couple. For the purpose of characterisation of the steering system’s excitations, several testing environments are discussed: a stiff test bench, more compliant test benches and the vehicle itself. Each configuration is accompanied by a specific method for source characterisation, for which it is demonstrated that the equivalent forces are indeed an environment-independent description of the active excitations of the steering system. It is shown that these forces can be used for the prediction of sound and vibrations in the vehicle. The presented applications offer, with understanding of substructuring and TPA theory, insights in the practical aspects of the methodology. This opens interesting opportunities for early-phase development of sound and vibration.@en

System equivalent model mixing

Journal article - Steven W.B. Klaassen, Steven W.B. Klaassen, M.V. van der Seijs, M.V. van der Seijs, D. de Klerk, D. de Klerk

This paper introduces SEMM: a method based on Frequency Based Substructuring (FBS) techniques that enables the construction of hybrid dynamic models. With System Equivalent Model Mixing (SEMM) frequency based models, either of numerical or experimental nature, can be mixed to for ...

An indicator sensor criterion for in-situ characterisation of source vibrations

Conference paper - M.V. van der Seijs, D. de Klerk, M.W.F. Wernsen

Component-based Transfer Path Analysis allows us to analyse and predict vibration propagation between an active source and passive receiver structures. The forces that characterise the active source are determined using sensors placed on the connected passive substructure. These ...

General framework for transfer path analysis: History, theory and classification of techniques

Journal article - M.V. van der Seijs, D. de Klerk, D. de Klerk, DJ Rixen

Transfer Path Analysis (TPA) designates the family of test-based methodologies to study the transmission of mechanical vibrations. Since the first adaptation of electric network analogies in the field of mechanical engineering a century ago, a multitude of TPA methods have emerge ...

A benchmark structure for validation of experimental substructuring, transfer path analysis and source characterisation techniques

Conference paper - M.V. van der Seijs, M.V. van der Seijs, E. A. Pasma, D. D. van den Bosch, Mathieu Wernsen

This paper presents a practical study on popular Experimental Dynamic Substructuring topics. A series of substructures is designed of such complexity to fit in right between “real life” structures as often found in industrial applications and “academic” structures which are typic ...

A benchmark structure for validation of experimental substructuring, transfer path analysis and source characterisation techniques

Conference paper - M.V. van der Seijs, M.V. van der Seijs, E. A. Pasma, D. D. van den Bosch, Mathieu Wernsen

Frequency Based Substructuring with the Virtual Point Transformation, flexible interface modes and a transmission simulator

Conference paper - Eric Pasma, Eric Pasma, M.V. van der Seijs, M.V. van der Seijs, Steven Klaassen, Steven Klaassen, Maarten van der Kooij

In this contribution, Frequency Based Substructuring is applied to a well-known benchmark structure with special attention to correct modelling of the interface problem. Various approaches with the Virtual Point Transformation are used to incorporate the effect of interface f ...

Frequency Based Substructuring with the Virtual Point Transformation, flexible interface modes and a transmission simulator

Conference paper - Eric Pasma, Eric Pasma, M.V. van der Seijs, M.V. van der Seijs, Steven Klaassen, Steven Klaassen, Maarten van der Kooij

Frequency Based Substructuring with the Virtual Point Transformation, flexible interface modes and a transmission simulator

Conference paper - Eric Pasma, Eric Pasma, M.V. van der Seijs, M.V. van der Seijs, Steven Klaassen, Steven Klaassen, Maarten van der Kooij

Application of System Equivalent Model Mixing (SEMM) to model the structural dynamic properties of a complex vehicle component using numerical and experimental data

Conference paper - E. Pasma, S. Klaassen, L. Nieuwenhuijse, L. Nieuwenhuijse, M.V. van der Seijs, M.V. van der Seijs, D. Lennström

A popular strategy in structural dynamic modelling is breaking the structure down into separable, manageable substructures. One can choose the most efficient way of modelling the substructures, before synthesizing the full system model. System Equivalent Model Mixing (SEMM) is a ...

Validation of blocked-force transfer path analysis with compensation for test bench dynamics

Conference paper - D.D. van den Bosch, M.V. van der Seijs, D. de Klerk

Towards dynamic substructuring using measured Impulse Response Functions

Conference paper - M.V. van der Seijs, P.L.C. van der Valk, T. van der Horst, DJ Rixen

A robust Transfer Path Analysis method for steering gear vibrations on a test bench

Conference paper - M.V. van der Seijs, E. Pasma, D. de Klerk, D.J. Rixen

An improved methodology for the virtual point transformation of measured frequency response functions in dynamic substructuring

Conference paper - M.V. van der Seijs, D.D. van den Bosch, D.J. Rixen, D. de Klerk

An improved methodology for the virtual point transformation of measured frequency response functions in dynamic substructuring

Conference paper - M.V. van der Seijs, D.D. van den Bosch, D.J. Rixen, D. de Klerk

Vibration source description in substructuring: A theoretical depiction

Journal article - DJ Rixen, M.A. Boogaard, M.V. van der Seijs, G van Schothorst, T van der Poel

Vibration source description in substructuring: A theoretical depiction

Journal article - DJ Rixen, M.A. Boogaard, M.V. van der Seijs, G van Schothorst, T van der Poel

Vibration source description in substructuring: A theoretical depiction

Journal article - DJ Rixen, M.A. Boogaard, M.V. van der Seijs, G van Schothorst, T van der Poel

Contributed

2 records found

Dynamic Substructuring for Efficient Vibrational Studies in Buildings

Master thesis - V.S. van den Bosch, A. Metrikine, K.N. van Dalen, D. de Klerk, M.V. van der Seijs, Maurice Hermens

As a reaction to urban densication, light weight building is an attractive concept for optimally utilizing the capacity of the existing built environment. A common issue paired with light weight construction is the need to engage in vibrational design, in order to minimize hindrance due to human activities such as walking, that cause vibrations in buildings. The Finite Element Method (FEM) is a crucial tool for accurately predicting structural behaviour in such a context. The typical problem with FEM considering large, complex or detailed structures, is that analyses may demand intolerably large computational eort to perform design studies. As a solution, a component-wise approach called Component Mode Synthesis (CMS) is proposed. CMS technique involves separating a construction into substructures, after which Model Order Reduction (MOR) is performed on each substructure individually. With this, the substructures are eciently described by a limited amount of Degrees of Freedom (DoF), after which they are assembled by means of Dynamic Substructuring (DS) techniques. Considering the large amounts of substructure DoF to be coupled to other assembly parts (typically containing 1%-10% of the total amount), an additional measure is required for analyses to be viable: a reliable interface reduction should be performed to deal with the number of unreduced interface DoF that still exist. This research investigates interface reduction by means of Orthogonal Polynomial Series, creating an a priori determined, generic reduction basis which closely resembles the true vibration modes along substructure interfaces. Its performance is investigated with several conceptual case studies, conducting reduced order analysis in Matlab and comparing the results with a full order solution. Alterations are explored, including dierent polynomial bases (Legendre and Fourier), exible couplings and viscoelasticity at either coupled substructure boundaries or bodies. The relevance of complex modes in viscoelastic structures with lightly varying damping and stiness is examined, as well as accuracy of approximations of complex modes, with the prospect of enabling arbitrary frequency dependent material properties to be represented in an ecient manner. This involves approximation of complex modes, obtained by superposition of undamped modes, for which a strategy is developed to optimize considered inclusion of undamped modes. Ultimately, a representative building is modelled in order to relate test results of OPS interface reduction to an applicable context, and to prove the overall eectiveness of the enhanced CMS strategy for large light weight building models. OPS interface reduction using Legendre series has shown to be a reliable and ecient technique depending on the frequency range considered. Its general error trends are mostly insignicant or manageable and exible/ viscoelastic boundary couplings do not de ate this. Disproportional viscoelasticity in substructure bodies, with respect to their mass and stiness matrices, are not necessarily beneted by the use of complex vibration modes when its dynamic modulus varies lightly over frequency. Though the potential which is beyond this scope, yet remains undetermined, the presented approximation technique for complex modes also comes with additional limitations besides the amount of damping. With regards to the applicative value of CMS, the analyses of the light weight building model prove that OPS interface reduction enables signicant improvement of computational eciency, yet yielding accurate results, as a valuable solution for modern-day problems.

Equivalence in Experimental Source Characterisation

Master thesis - T.M. Spoel, P.G. Steeneken, M.V. van der Seijs

Transfer Path Analysis methods allow to describe the propagation of vibrations from an active source to a passive receiving structure. These methods are based in the experimental modelling domain, where the dynamics of the problem are described based on empirical observations from an experiment, as opposed to a numerical model based on natural and engineering laws. These methods describe the boundary conditions for the experiment, as well as how the obtained data can be used to deduce an equivalent force that describes the vibrations. Within the class of Transfer Path Analysis methods there is a specific class called the Component-based methods that are able to describe the vibrating source in such a way, that the assembled dynamical behaviour of the source attached to any other receiving structure can be predicted. This is by defining the characterisation in terms of an equivalent force on the interface. These methods are said to be a function of the source only. This is called source characterisation. In this thesis some of the assumptions of these Component-based Transfer Path Analysis are challenged. This will be done based on theoretical research as well as experiments on a numerical model. The reason this research is of interest, is that while these Component-based methods show to be valid in theory, their results in practice are not satisfactory. This is especially apparent when a characterised source is virtually assembled on a different receiving structure. Its predicted behaviour is not in line with what the real world counterpart. These Component-based Transfer Path Analysis methods involve solving an inverse problem to determine the equivalent force. Due to the experimental nature in which the data are obtained, the data has error-contamination. This happens because of interference effects causing noise on the analog sensors. This noise can have a profound effect on the solution of the inverse problem, since the problem is poorly conditioned. The main assumption of Component-based Transfer Path Analysis methods is that if an interface force can be defined that excites the interface in the same way as the source does, the interface force can be regarded as equivalent. Due to the linearity of the problem, this equivalent force can be added in negative on top of the source excitation. This would theoretically then cancel out all motion, since both the source excitation and equivalent force have the same effect on the receiving structure. This thesis proofs that it is not always possible to find an equivalent force that represents the source excitation. This is due to the position of the equivalent force, specifically that it is placed on a single point. Some dynamic modes will show a node of their motion on the interface, meaning the interface force can by definition never excite those modes. This limitation is based from the modelling choices of the interface. It will be uncovered that the modes with such nodal behaviour are the eigenfrequencies of the source for a perfectly fixed interface. The interface limitation can be expressed as a controllability measure, where the controllability defines to what extend the interface force can excite the possible modes crossing the interface from the source. This controllability is a function of the source, the receiving structure and the sensor placement, where the source determines at which frequencies the controllability problems occur and the receiving structure and sensor placement determine the size of the controllability measure. Both an upper and lower bound of controllability can be defined. It can be quantified what the effect of the incomplete interface description is on the source characterisation. This is based on comparing the motion from source excitation and the motion from the predicted dynamics from the equivalent force. It is shown that the interface motion cannot be reproduced by the equivalent force at the frequencies where there are controllability problems. This mismatch in interface motion has an effect on the motion of the receiving structure, where it will be clear that these mode occur at range of frequency bins. While a portion of the source cannot be characterised, a large part of the behaviour can be. To solve for this equivalent force, an inverse problem has to be solved. This problem is an over-determined problem with a full rank column space. Using a priori information about the levels of noise that are expected on each measurement, the problem can be altered. This makes it possible to reduce the propagation of noise from the measurement data to the solution. A set of guidelines are proposed that can help to dampen or emphasis individual modes of the inverse system. Alternatively, the entire spectrum of modes can be dampened or single modes can be truncated. The regularisation methods will all be judged on how they change the physical relevancy of the problem.