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

Mid-frequency transient vibration analysis of flexible structures plays an important role in a variety of engineering applications. In a 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. In this paper, to address the aforementioned issue, a 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). In this work, the augmented DTFM is modified for model reduction in mid-frequency analysis of beam structures, which is an extension of the authors’ previous effort. The idea behind this 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. 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 new method on the 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 by the proposed method, compared with the traditional numerical methods, can be of several orders of magnitude.