3. Experimental and Analyical determination of frquencies and modal shapes of perforated isotropic perforated plates

GRACIELA ROMERO; CARLOS MARTINEZ; ELVIO ALANÍS; LILIANA ALVAREZ; LIZ NALLIM

Sydney Australia

Congreso; International Commission for Optics ICO 21- 2008 Congress; 2008

ICO

Plates having internal holes, attached masses and different support conditions are very important in many engineering applications [1]. Particularly, internal holes are present in plates due to operational conditions, namely passage of conduits or ducts, electric conductors, etc. For these reasons this kind of plates constitutes common structural elements used in naval as well as in ocean engineering. The accurate and efficient determination of the natural vibration frequencies and mode shapes of these plates components are essentials to the design and performance evaluation of a mechanical system. The consideration of a free hole and concentrated masses in the vibrating plate formulation is the source of analytical difficulties and of complicated mathematical structures for the boundary conditions making difficult the exact analysis for even the simplest cases. Consequently, most studies on these structural elements employ approximate analytical or numerical methods. Digital Speckle Pattern Interferometry (DSPI) is a useful tool to carry out non destructive test in a variety of fields such as optical metrology. In many cases, experimental and computational methods can be combined so that the data obtained by one method can be used by the other one to verify the results [2]. Real-time Digital Speckle Pattern Interferometry (DSPI) [3] was used for tuning and visualization of natural frequencies of perforated plates with concentrated masses and elastically restrained edges. The plates where exited to resonant frequencies by sinusoidal acoustic source which provided continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plates where registered. The system was also studied analytically. The analytical approach developed is based on Rayleigh – Ritz method with the use of orthogonal polynomials as coordinate functions which allows to obtain the natural frequencies and modal shapes. A high degree of correlation between computational analysis and experimental results was observed.