Frequency response functions of shape features from full-field vibration measurements using digital image correlation

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The availability of high speed digital cameras has enabled three-dimensional (3D) vibration measurement by stereography and digital image correlation (DIC). The 3D DIC technique provides non-contact full-field measurements on complex surfaces whereas conventional modal testing methods employ point-wise frequency response functions. It is proposed to identify the modal properties by utilising the domain-wise responses captured by a DIC system. This idea will be illustrated by a case study in the form a car bonnet of 3D irregular shape typical of many engineering structures. The full-field measured data are highly redundant, but the application of image processing using functional transformation enables the extraction of a small number of shape features without any significant loss of information from the raw DIC data. The complex bonnet surface on which the displacement responses are measured is essentially a 2-manifold. It is possible to apply surface parameterisation to ‘flatten’ the 3D surface to form a 2D planar domain. Well-developed image processing techniques are defined on planar domains and used to extract features from the displacement patterns on the surface of a specimen. An adaptive geometric moment descriptor (AGMD), defined on surface parametric space, is able to extract shape features from a series of full-field transient responses under random excitation. Results show the effectiveness of the AGMD and the obtained shape features are demonstrated to be succinct and efficient. Approximately 14 thousand data points of raw DIC measurement are represented by 20 shape feature terms at each time step. Shape-descriptor frequency response functions (SD-FRFs) of the response field and the loading field are derived in the shape feature space. It is seen that the SD-FRF has a similar format to the conventional receptance FRF. The usual modal identification procedure is applied to determine the natural frequencies, damping factors and eigen-shape-feature vectors from the SD-FRF. Natural frequencies and mode shapes from a finite element (FE) model are correlated with the experimental data using the cosine distance between the shape feature vectors with 20 terms. There are numerous benefits of using image decomposition to analyse 3D DIC measured data, including (1) representation of the raw measurement data with efficiency and succinctness; (2) determination of the FRF of any point on the specimen by the use of the full-field shape features; and (3) elimination of DIC measurement noise. Also, the SD-FRF is potentially ideal for cases of field excitation of structures.