Study On Vibration Characteristic Of Thin-walled Cylindrical Shells Based On Flügge Theory

The thin-walled cylindrical shell is widely used in practice and is a lightweight,high-efficiency thin-walled structure.In the actual engineering,in order to obtain more accurate mechanical properties of the cylindrical shell structure,many researchers have studied this,but now Some theories and methods have certain limitations and precisions in practical applications.Therefore,based on the analysis of the existing classical shell theory,the semi-analytical differential quadrature finite element method is used to analyze its dynamic characteristics,and the cylindrical shell structure is obtained.An exact solution of higher precision.In this paper,the dynamic characteristics of thin-walled cylindrical shells are used to further improve the calculation accuracy of free-vibration of thin-walled cylindrical shells.In this paper,the semi-analytical differential quadrature method is used to establish the free vibration differential equation of thin-walled cylindrical shell based on Flügge shell theory,and the vibration equation is solved.The obtained results are compared with the existing literature,analytical solution and finite element method.On this basis,the main research contents of this paper are as follows:(1)Analysis of different classical shell theory: Donnell shell theory,Soedel shell theory and Flügge shell theory,the establishment of thin-walled cylindrical shell freedom through the expression of curvature,the expression of non-middle surface strain and the expression of internal force and internal moment The vibration differential equation is analyzed by using the exact solution and the approximate beam function method.The free vibration characteristics of the structure are analyzed and compared with the finite element method and related literature to verify the accuracy and application range of the theoretical calculation of different basic shells.(2)Based on Fl ü gge shell theory,the differential equation of free vibration of thin-walled cylindrical shell is established.For the simple-supported and simply supported ends,the two ends are fixed-fixed,the two ends are free-free and one end is fixed and the one end is free-bound.The thin-walled cylindrical shell model is based on the free vibration differential equation.By analyzing the differential quadrature finite element method,the natural frequency equation of thin-walled cylindrical shell is obtained,and its frequency value is solved.The analysis and verification are carried out with relevant literature and analytical methods to prove the accuracy and convergence of the method.(3)Considering the influence of material parameters on the vibration characteristics of thin-walled cylindrical shell structures,based on Flügge shell theory,the differential vibration equations of orthotropic cylindrical shells are established,and the orthotropic cylinders under various combined boundary conditions are established.The shell model is used to analyze the free vibration characteristics of orthotropic cylindrical shell structures.The accuracy of the method is proved by numerical examples.Moreover,this paper also analyzes the effects of different length-diameter ratio,aspect ratio and material properties on the free vibration characteristics of the structure.