Research On The Improvement And Application Of Rayleigh-Ritz Method On The Free Flexural Vibration Characteristics Of Complex Plate

Plate structure is widely existed in a great many engineering structures in which the dynamic performance has attracted more and more attention especially when it comes to the vibration characteristics.In this paper,an improvement on traditional Rayleigh-Ritz method was put forward so that the method could be used to calculate the free vibration characteristics of more complex plates.Then the flexural free vibration characteristics of plates in many practical projects were analyzed.Firstly,the improved Rayleigh-Ritz method was introduced.Introducing the traditional Rayleigh-Ritz method,the limitations of the traditional Rayleigh-Ritz method were pointed out;And then the improvement of the Rayleigh-Ritz method by other learners was given.Then an improved Rayleigh-Ritz method was put forward.By putting forward the idea of expanding function domain and introducing the improved Fourier series method and spring model to simulate the boundary conditions as well,the calculation range of the Rayleigh-Ritz method is greatly expanded,making it suitable for the calculation of complex plate structures in engineering application.Then some examples were given to illustrate the applicable conditions of the method.Secondly,the free vibration characteristics of the plates with complex shapes of equal thickness were analyzed.Using the improved Rayleigh-Ritz method,the dynamic model of thin plate was given,including the strain energy,kinetic energy and border spring elastic potential energy expressions of the complex shaped thin plate.The calculations of rectangular thin plate can verify the convergence of the method and at the same time get some parameter choices.Lastly,several numerical examples of thin plates with complex shapes were given to prove the accuracy of the method.Thirdly,the free vibration characteristics of the complex shaped plate with variable thickness was analyzed.In this section,the dynamic models of plates with variable thickness were presented according to the improved method.By comparing the results with others’,the effectiveness of the proposed method was demonstrated.Finally,the free vibration characteristics of the plate with cutouts were analyzed.First analyzing the plate with a single cutout.Based on the plate with a single cutout,the dynamic model of plate with multiple cutouts was established.By calculating the free vibration natural frequency of double cutouts,three cutouts,four cutouts in a single row and four cutouts in double rows,and comparing the results with the results of finite element software,the applicability of the proposed method to the free vibration calculation of multiple cutouts is demonstrated.