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 emerged and found their way into industrial development processes. Nowadays the TPA paradigm is largely commercialised into out-of-the-box testing products, making it difficult to articulate the differences and underlying concepts that are paramount to understanding the vibration transmission problem. The aim of this paper is to derive and review a wide repertoire of TPA techniques from their conceptual basics, liberating them from their typical field of application. A selection of historical references is provided to align methodological developments with particular milestones in science. Eleven variants of TPA are derived from a unified framework and classified into three categories, namely classical, component-based and transmissibility-based TPA. Current challenges and practical aspects are discussed and reference is made to related fields of research.
•In this paper a general framework for Transfer Path Analysis is presented.•The vibration transfer problem is derived conceptually, based on the admittances of the active and passive subsystems.•Eleven methods are derived and classified into classical, component-based and transmissibility-based TPA.•The evolution of historical developments to practical TPA methodologies is presented.•Several practicalities are discussed that may be important when conducting a TPA.
Hybrid modeling is an increasingly common procedure for predicting the structural dynamics of complex products. System equivalent model mixing (SEMM), a dynamic substructuring-based method, is a ...recent addition to the field. Its implementation within frequency-based substructuring has great potential. Therefore, it is reasonable to explore the options for implementing an equivalent substructuring framework in any of the other substructuring domains. The objective of this paper is to present M-SEMM, system equivalent model mixing in the modal domain. A theoretical derivation reveals that under certain constrained conditions, the proposed methodology is equivalent to the system equivalent reduction expansion process (SEREP), a well-established reduction/expansion technique. When considering the expansion of spatially sparse models with a high modal density, M-SEMM represents a novel expansion method, which can be seen as a potentially useful extension to SEREP. The proposed implementation offers certain advantages, the most notable being a superior ability to disregard spurious modes in the hybrid model. A study of the proposed methodology on a numerical and an experimental case demonstrates its applicability and provides a comparison with SEREP and the original implementation of SEMM in the frequency domain.
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•System equivalent model mixing in the modal domain (M-SEMM) is introduced.•Under certain constraint conditions, M-SEMM is analytically equivalent to SEREP.•For spatially sparse models, M-SEMM is a novel expansion method in the modal domain.•The advantage of modal SEMM formulation is the ability to filter out spurious peaks.
Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. ...Contrary to classical modal reduction techniques (Craig-Bampton, MacNeal) where the normal modes basis must be enriched to account for damping effects, the methodology presented here takes advantage of the Golla-Hughes-McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The Lagrange multipliers are finally employed to couple the reduced system to a host structure, as made in popular dynamic substructuring techniques. This method has two major advantages. First, substantial savings are achieved by the judicious combination of GHM and POD techniques. Second, the reduced system takes the form of a constant matrix of small size which permits to preserve confidentiality.
Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their ...theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method’s robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.
•All Degrees of Freedom (Dofs) are not required for accurate predictions provided by the Transfer Path Analysis (TPA) methods.•The required Dofs depend on the TPA method considered and on the active and passive dynamic behavior of the structures.•Component-Based TPA (CB-TPA) without Dynamic Substructuring (DS) methods only requires the consideration of the translational Dofs.•Aeronautical structures may be characterized considering only a quarter of the Dofs for accurate predictions provided by the CB-TPA methods with DS.
The dynamic properties of assembled structures are governed by the substructure dynamics as well as the dynamics of the joints that are part of the assembly. It can be challenging to describe the ...physical interactions within the joints analytically, as slight modifications, such as static preload, temperature, etc. can lead to significant changes in the assembly’s dynamic properties. Therefore, characterizing the dynamic properties of joints typically involves experimental testing and subsequent model updating. In this paper, a machine-learning-based approach to joint identification is proposed that utilizes a physics-based computational model of the joint. The idea is to combine the computational model of the joint with dynamic substructuring techniques to train the machine-learning model. The flexibility of dynamic substructuring permits the enforcement of compatibility and equilibrium conditions between the component models from the experimental and numerical domains, facilitating the development of machine-learning models that can predict the dynamic properties of joints. The proposed approach provides an accurate data-driven method for joint identification in real structures, while reducing the number of measurements needed for the identification. The approach permits the identification of a full 12-DoF joint, enabling the coupling of 3D dynamic models of substructures. Compared to the standard decoupling approach, no spurious peaks are present in the reconstructed assembly response. The proposed approach is validated numerically and experimentally by reconstructing the assembly response and comparing the results with known assembly dynamics.
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•A neural-network-based approach to joint identification is proposed.•A physics-based computational model is used to generate training dataset of joints.•Training dataset of assembly admittances are computed using dynamic substructuring.•Measuring the assembly’s interface dynamics is not required for the identification.•The proposed joint identification approach is tested in an experimental case-study.
An enhanced Craig-Bampton method Kim, Jin-Gyun; Lee, Phill-Seung
International journal for numerical methods in engineering,
13 July 2015, Volume:
103, Issue:
2
Journal Article
This paper presents a general framework for estimating the state and unknown inputs at the level of a system subdomain using a limited number of output measurements, enabling thus the component-based ...vibration monitoring or control and providing a novel approach to model updating and hybrid testing applications. Under the premise that the system subdomain dynamics are driven by the unknown (i) externally applied inputs and (ii) interface forces, with the latter representing the unmodeled system components, the problem of output-only response prediction at the substructure level can be tailored to a Bayesian input-state estimation context. As such, the solution is recursively obtained by fusing a Reduced Order Model (ROM) of the structural subdomain of interest with the available response measurements via a Bayesian filter. The proposed framework is without loss of generality established on the basis of fixed- and free-interface domain decomposition methods and verified by means of three simulated Wind Turbine (WT) structure applications of increasing complexity. The performance is assessed in terms of the achieved accuracy on the estimated unknown quantities.
•A new study on non-classical beams coupled to moving mass-spring-damper (MSD) systems.•A novel model considers arrival and departure phase of the MSD system on the beam.•A novel dynamic ...substructuring technique in state space solves the coupled system.•A generalized corresponding assumption is applied to couple the subsystems.
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In this paper a semi-analytical approach to efficiently determine the dynamic response of an Euler-Bernoulli beam with general boundary conditions crossed by a mass-spring-damper (MSD) system is presented. Based on a dynamic substructuring technique (DST), the non-classically damped beam subsystem in modal state space representation is coupled with the interacting degrees of freedom of the MSD system by applying a generalized corresponding assumption. This assumption implies equal displacements of the beam and the MSD system at the contact points. The resulting set of coupled equations of motion in state space has time-dependent system matrices. Special attention is paid to the appropriate formulation of the arrival and departure conditions of the MSD system on the beam. In an application example, the dynamic response of a viscoelastically supported beam with a lumped mass at both ends crossed by a MSD system is analyzed, examining the effect of the speed and various parameters of the viscoelastic supports. The comparison of the results of the coupled beam-MSD system and a less expensive approach, in which the MSD system is simplified by its static axle loads, shows the importance of explicitly considering the interaction between beam and MSD system for accurate response prediction.
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