This work concerns a two stage decomposition analysis of a dynamics phenomenon due to reflection of longitudinal pulse elastic waves in long elastic rods. Elastic pulse waves are induced by impacting a miniature modal hammer at one of its free ends whereas its dynamics is recorded by a high performance piezoelectric sensor at the other end. An underlining characteristic time scale leads to a natural decomposition of experimental time series of wave acceleration into a sequence of time frames. The signals are viewed as a sequence of time frames and thus are analyzed globally and locally by further decomposing them into their intrinsic Proper Orthogonal Decomposition Modes (POD) or Principal Component Analysis (PCA) modes. It is found that experimental signals of acceleration during propagation of elastic pulse waves are governed by a small number of POD modes; one of the modes is dominant. It is conjectured that these intrinsic modes of the time frame-arranged signals represent physical modes of pulse wave propagation. The introduced method of the two-stage decomposition analysis is potentially useful for data-driven analysis in wave propagation-based damage detection.

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