Free Vibration Analysis Of The Annular Plates Based On Improved Fourier-Bessel Method

As a basic structural element,thin annular plates have been widely used in various engineering fields due to its excellent engineering structural properties.Its performance will be affected by the various dynamic loads factors in the engineering practice,therefore,it is particularly important to analyze the free vibration characteristics of the structure.And the constraints imposed on the inner and outer edges of the annular plate play a very important role in the study of the vibration of the structure.However,the research on the free vibration features of the thin annular plate structures mainly related to several simple boundary constraints imposed on the inner and outer edges,such as completely free,simple support and fixed support.However,there is still lacking the method for analyzing the vibration behavior of the annular plate with more arbitrary elastically constraints.To do research on the free vibration features of most of them need theoretical derivation of their boundary characteristics respectively and there is still lacking united vibration analysis model.Moreover,in the process of studying the free vibration characteristics of similar structures with different boundary conditions,different geometric features or different material properties,the analysis model and related theoretical derivation of their boundary characteristics is required.Firstly,by analyzing the internal force of the isotropic annular plate structure,a mathematical model is built to satisfy the arbitrary elastic constraint,and then the displacement function of this model will be constructed.At the same time,the vibration equation of the structure will be solved based on the Rayleigh-Ritz energy theory.Finally,the accuracy of the model will be verified by comparison with the analysis results of the finite element software and the results of other research methods.Secondly,the improved Fourier-Bessel method is extended to analyze the free vibration characteristics of anisotropic annular plates and stepped variable thickness annular plate structures under arbitrary elastic boundary constraints and the correctness of the method is proved by some numerical examples.In addition,the influence of the parameters of the aperture ratio and the thickness change ratio on the free vibration characteristics of the above structure is also analyzed.Finally,the modal experiments of the annular plate under two kinds of boundaryconditions are established and carried out.The modal natural frequency and modal shape of the thin annular plate structure are obtained through the processing of experimental data.And the results will be employed to compare with the results,which are obtained by the method proposed here,so as to validate the accuracy of the proposed modeling method.