Mid-frequency transient vibration analysis of flexible structures has been widely seen in a variety of engineering applications. In the mid-frequency region, neither low-frequency methods like the Finite Element Analysis (FEA) nor high-frequency methods like the Statistical Energy Analysis (SEA) are directly applicable to transient vibration analysis. For optimal design of multi-body structures, a mid-frequency transient vibration analysis tool with a good balance of accuracy and efficiency in computation is in demand.To address the aforementioned issue, a new model reduction method is developed for mid-frequency transient vibration analysis of beam structures. The method is based on the augmented Distributed Transfer Function Method (augmented DTFM). From our previous work, it is illustrated that the augmented DTFM is capable of solving both steady-state and transient responses of complex beam frames vibrating at medium and high frequencies. The augmented formulation has been shown to be consistent in different frequency regions, from low to high, and does not rely on spatial discretization.In this work, the augmented DTFM is modified for model reduction in mid-frequency analysis of beam structures, which is an extension of our previous effort.&nbsp; The idea behind this new approach is to properly select several modes in the low-frequency region and a number of modes in a mid-frequency region that encompasses the excitation frequency spectrum, from the infinite series given by the augmented DTFM. This way, a reduced model of a beam structure for mid-frequency transient analysis is systematically obtained.A highlight of the new model reduction method is that the mid-frequency transient vibration solutions of a beam structure can be determined through direct solution of the time-domain governing equations for the selected modes of vibration. Some existing methods usually rely on energy-based frequency-domain governing equations that are formulated under certain assumptions. Another special feature is that the proposed method provides detailed local information about system response at mid and high frequencies, such as bending moment and shear force at any point. The existing energy-based methods usually can only predict the smoothed energetics. Furthermore, with the proposed method, the selection of modes of vibration in a model reduction process is physically intuitive and straightforward.&nbsp;The proposed model reduction method is validated in numerical examples, where the augmented method is compared with other methods, including the FEA. The accuracy and efficiency of the mew method on computation of transient displacement and shear force is demonstrated. As shown in the simulation results, a proper balance between accuracy and efficiency in model reduction can be achieved by the augmented-DTFM. The computation savings (computer storage and computation time) by the proposed method, compared with the traditional numerical methods, can be of several orders of magnitude.

Model Reduction for Mid-Frequency Transient Vibration Analysis  of Beam Structures by the Augmented DTFM

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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