The aim of this paper is to present the basic theory and preliminary applications of a newly developed formulation for the modal analysis of vibrating structures. This is based on the statistical processing of the data extracted from a holographic shot of the vibrating object. Specifically, the elastic displacement field is obtained through digital processing of two holographic shots (generated by laser beams in quadrature), and the Proper Orthogonal Decomposition (POD) technique is used to extract from the data basis functions, which are optimal in the sense of maximum energy content. The use of holographic images as data source has two advantages: i) the optical data acquisition is a non-invasive technique, which allows an accurate analysis of certain phenomena (such as aeroelastic and acoustoelastic problems) for which instrumentation of the experimental models represents a critical issue; ii) holographic shots contain three-dimensional information, and can be effectively used to estimate the elastic displacement vector of a three-dimensional structure. In the present work, the optical holographic process has been simulated through a dedicated, in-house developed, computer program. The displacement field has been evaluated analytically for simple structures, such as thin plates and membranes. Preliminary numerical results reveal that the empirical basis functions given by the POD predict, within plotting accuracy, with the fundamental modes of vibration of the structure.
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