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General theory for quantative evaluation of three-dimentional vibrations from time-average holographic interferograms

A procedure for calculating the amplitudes of the normal and tangential components of the displacement vector of three-dimensional vibrations of any point on the surface of mechanical wave system is proposed on the basis of experimental holographic interfrometry data and the theory of vibrations of mechanical systems The problem of determination the amplitude – frequency response characteristics of a vibrating surface, which vibrates in three dimensions in the majority of cases, is encountered in the analysis of vibrations of mechanical system. The development of methods for calculating the characteristics of three – dimensional (3D) vibrations contributes to the solution of vital problems in the investigation, design, testing, and diagnostics of systems. There are publications devoted to evaluation of deformation vector and quantitive analysis of holographic particle data in [1-11]. The papers give an instrument for interpretation and calculation component of vector deformation surface of solid bodies of the simple shapes and the use for complex forms of the links is not directly available and need to modified it. The problem is that procedure and algorithms must include into calculation relations between vibrations type and the geometry of the shapes of links. The 3-D vibrations for wave mechanical system shapes of links take part in the analysis process and its enable to find algorithms and common methods of investigation [12-15]. In the present paper a method is described for calculation of the amplitudes of the normal and tangential components of the displacement vector of 3D vibrations of the surface of deformable elements on the basis of experimental holographic-interferometry data and the theory of vibrations of mechanical systems. In contrast with previous publication on this topic, the proposed method permits a severalfold reduction in the quantity of input data for analysis of vibrations from holographic interferograms.