Trillo Cristina, Doval Angel F, Mendoza-Santoyo Fernando, Pérez-López Carlos, de la Torre-Ibarra Manuel, Deán J Luis
Departamento de Física Aplicada, E. T. S. E. Industriais, Universidade de Vigo. 36310 Vigo, Spain.
Opt Express. 2009 Sep 28;17(20):18014-25. doi: 10.1364/OE.17.018014.
The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.
本文提出了一种将高速电视全息系统与三维傅里叶变换数据处理相结合的方法，用于分析平板中的多模振动。在一般振动激励下，物体的面外位移通过高速摄像机的快速采集速率在时间上进行分辨，并记录在一系列带有空间载波的干涉图中。由此获得了多模振动的全场时间历程。提取干涉图的光学相位并从参考状态的相位中减去，以生成一系列光学相位变化图。每张图表示物体在任何给定状态与参考状态之间所经历的变化。该图序列是一个三维数据阵列（两个空间维度加时间），用三维傅里叶变换算法进行处理。由于各振动模式的振动频率不同，且在较小程度上由于振型的空间频率不同，各振动模式在三维频率空间中被分离。然后可以通过一个或多个带通滤波器分离每个单独模式（或几个模式的叠加）对物体动态行为的贡献。最终输出是一系列复值图，其中包含所选模式在机械振幅和相位方面的全场时间历程。通过一个矩形、完全夹紧的薄金属板在白噪声激励下同时以其几个固有共振频率振动，验证了该技术的原理。
