Conformal Analysis Of Fundamental Frequency And Experimental Modal Analysis Of Vibration On Complicated Elastic Clamped Plates

The vibrating response widely occurs in electro-mechanical equipments, which affects the component service life seriously. In order to ensure the stabilization, reliability and safety for the systemic operation, it is important that both dynamic analysis and parameter identification are determined. The elastic plate used broadly as a component of the system, above two aspects analysis, is also vital for the systemic high-reliability to be guaranteed. At present, many numerical methods, for examples, Finite Element Method and boundary Element Method can complete modal analysis, but their calculating methods have deficiencies in preprocessing modeling, post-processing analysis and the low result precision etc. Moreover, the experimental modal analysis lacking perfect theatrical support, its result is only regarded as useful supplement for the dynamic design.Analysis theory of vibrating model to analyze vibrating question accurately lacks of mathematical theory basis. As a result, its calculating modeling is difficult in this field, and is seldom reported systemically now. The key reason is that mathematical models of the plate region and its geometrical boundary cannot be depicted to analyze vibrating differential equation.Aimed at the problem above, taking the thin elastic plate for example, the paper combines the analysis method and experimental modal- analysis, and its vibrating fundamental frequency analysis and experimental model are studied. The main research conclusions are gotten as follows:Firstly, by the elastic plate theories, vibrating differential function in the complicated clamped plates is analyzed. With the help of Conformal Mapping theory, mapping function is solved between given complicated region and unit dish region, as a result, plate vibrating mode function is depicted with unit dish region.Secondly, aimed at modeling of vibrating differential function, taking the ellipse region and rectangle region for instances, its vibrating mode differential functions are analyzed. Meanwhile, a kind of significant method is provided for analysis of complicated plate fundamental frequency.Thirdly, range of the first rank natural frequency is estimated in experimental mode analysis by calculating plate fundamental frequency with analysis method. Then, testing method of multiple-inputs and single-output is applied in experimental model research. With the with modal analysis software—data acquisition and signal processing (DASP), by varied-time-based signal processing technology, analysis of mode shape and property parameters are realized on vibrating elastic plate.Finally, Taking experimental mode analysis of the thin elastic plate for instance, the fundamental frequency of analysis method is compared with the first rank natural frequency of the experimental mode. Thus, analogy conclusions prove the experimental mode correct.