Nonlinear Vibration Analysis Of Rectangular Thin Plate And Stiffened Plate Structure

Rectangular plates and stiffened plate structures are widely used in various fields,such as aerospace,marine vessels,etc.Under the action of external excitation,nonlinear vibration will occur in the structure,which will bring very adverse effects to the equipment and devices in the project,and even cause serious damage.Therefore,it has very important theoretical significance and application value for the study of nonlinear vibration of the plate structure.However,the current nonlinear vibration analysis modeling method mainly focuses on the classical boundary conditions,and the numerical method is used to solve the problem,which is not conducive to the unified study of the influence of boundary conditions and other factors on the nonlinear vibration of the structure.Therefore,this paper proposes a method combining energy method and improved Fourier series method,aiming to construct a general nonlinear vibration analysis model of rectangular plate and stiffened plate under arbitrary elastic boundary conditions.In this paper,the following research work is carried out around the nonlinear vibration of rectangular plates and stiffened plates:Firstly,the nonlinear vibration analysis of rectangular thin plate structures under arbitrary boundary conditions is carried out in combination with the improved Fourier series method and energy method.In this paper,the modified Fourier series method is used to represent the displacement function of a rectangular thin plate under arbitrary elastic boundary conditions,which overcomes the discontinuity of the traditional Fourier series and is carried into the nonlinear vibration differential equation to solve the nonlinear vibration control of the rectangular thin plate.equation.Numerical examples show that the proposed method has good convergence.Compared with the literature and simulation results,it can be seen that it has high accuracy,and the influence of geometrical dimensions,loads and other parameters on nonlinear vibration is analyzed..Secondly,based on the study of single plate structure,the nonlinear vibration analysis modeling of stiffened plate structure under arbitrary boundary conditions is carried out.The model effectively processes the rectangular plate domain and satisfies the arbitrary elastic boundary conditions.The coupling relationship of the ribs.The specific details are that the rectangular plate domain displacement function adopts the improved Fourier series,and the rib displacement function uses the orthogonal polynomial beam function.According to the energy method and the displacement matching condition,the energy equation and characteristic equation of the nonlinear vibration of the stiffened plate are derived.Through the numerical examples of nonlinear vibration analysis of stiffened plate structure,the accuracy of the modeling method is verified,and the position of the stiffener,the cross-sectional area ratio of the stiffener and the plate,the number of stiffeners and other factors are added to the reinforcement.The influence of the large deflection dynamic behavior of the plate structure.Finally,the nonlinear vibration analysis experiments of rectangular thin plates and stiffened plates were designed and carried out.The experimental scheme of nonlinear vibration of rectangular plate and stiffened plate structure under the condition of fixed boundary is designed.The vibration characteristics and dynamic response parameters are obtained through experiments.The different thicknesses,different excitation amplitudes,cross-sectional area ratios of different ribs,etc.are analyzed.By analyzing the nonlinear vibration of the plate structure,the correctness of the modeling method is further verified by analyzing and comparing the data.