Analysis Of Fundamental Frequency And Experimental Modal Analysis On Elastic Plate With Multi-concentrated Mass

The elastic plate with multi-concentrated mass is widely used in many fields. Dynamic parameters are determined through the dynamic characteristic analysis, which can provide important design parameters for fault diagnose, reliability analysis and identification, structure optimal design and dynamic model modification of the system respectively, In the paper, combining analytical modal analysis with experimental modal analysis, the dynamic parameters and vibrating behavior of the complicated elastic plate with multi-concentrated mass would be analyzed as follows:Firstly, with the help of conformal mapping theory, conformal mapping function between complicated region and the unit dish region is achieved by adopting trigonometric interpolation and normal convergence method, so as to provide a mathematical method for describing vibrating differential function of elastic plate with multi-concentrated mass in unit dish region instead of complicated region.Secondly, based on the small deflection theory, the structural characteristics and boundary conditions are analized for the elastic plate with multi-concentrated mass. And vibrating differential function is created according to the conformal mapping function described in the unit dish region instead of the complicated region. Also the vibrating differential function for citing the rectangle with arc elastic clamped plates is deduced.Thirdly, combined with Galerkin method, fundamental frequency can be obtained, and the varietied in fundamental frequency caused by changing location and mass of concentrated substance described in polar coordinates is analyzed. The method is determined for the solution of fundamental frequency of elastic plate with multi-concentrated mass, according to the location of concentrated mass described in rectangular coordinates in complicated region, in order to provide designing basis for distributing concentrated mass logically so as to improve the capacity against vibrating for the system.Finally, the testing method of the hammer multiple-inputs and single-output for the accelerometer is applied in experimental modal analysis, regarding elastic plates which the concentrated mass is placed on different locations as the experimental objects respectively. With the help of DASP (Data Acquisition and Signal Processing) modal analysis software, both the fundamental frequency and high-order frequencies are realized to fix up mode orders and analyze mode shapes while the concentrated mass is placed on different locations. And comparing with the result of analytical modal analysis, the analytical method is proved to be correct.