An improved model for the frequency estimate of mass-loaded plates by a combined use of equivalent center mass and stiffness factors

In this paper, an improved model is developed to determine the frequency of vibrating plates carrying multiple masses at various positions. By virtue of an equivalent-center method, the frequencies of the plates carrying multiple masses can be predicted by using merely the data obtained earlier for the same plate with each corresponding mass component. Further accounting the change of the strain energy into the model and by introducing respective stiffness ratios, one can obtain a quick and better estimation of the loaded plates with various boundary conditions. The proposed model is validated through experimentation of a rectangular clamped plate carrying concentrated masses. Analytical and experimental results for the plate system are compared and discussed. It is found that the change in the strain energy should be incorporated in the model, especially for cases of large masses placed on a thin plate, in order to predict well the natural frequency of the amalgamated system from those of the component systems. The excellent performance of the proposed model is due to the fact that the effects of both the different masses and their locations on the frequency have been accounted for, implicitly, in the respective equivalent center mass and stiffness factors. Although the model considered is rather simple, the proposed methodology can be extended to plates with other geometry and configurations.