Study On Adaptive Method For Dynamic Analysis Of Shells Of Revolution

When the transfer matrix method is used to solve the vibration characteristics of shells of revolution,the accuracy and efficiency of the calculation are determined by the adaptability of the numerical method.The study of the natural vibration,forced vibration and the adaptive method in substructure segment of the shell of revolution can provide a reliable and effective mathematical tool for the dynamic analysis of the structure,and extend the transfer matrix method to the vibration analysis in more engineering fields.For the free vibration problem,based on the basic equation of shells of revolution,this paper uses the transfer matrix method and the matrix exponential adaptive integration method to solve the natural frequency and vibration mode of conical shell.Through the comparison with the finite element results,it is found that the natural frequency error of the two methods is less than 2%,and the vibration mode is in good agreement.Therefore,the matrix exponential adaptive integration method can be applied to solve the vibration of shells of revolution with satisfactory precision.For the forced vibration problem,the Chebyshev interpolation is used to optimize the interpolation method of inhomogeneous terms based on the first order differential equation of vibration.The homogeneous high precision direct integration based on Chebyshev interpolation is proposed.The comparison of numerical examples shows that the accuracy of this method is better than that of linear interpolation and isometric polynomial interpolation.In order to achieve precision control and improve the efficiency of calculation,this paper proposes a global adaptive calculation method based on the matrix exponential adaptive integration method and Simpson formula.The numerical examples show that the method can divide the adaptive integral interval of any excitation with different degree of change according to the given tolerance requirements,and realize the precision control,while avoiding unnecessary amount of calculation.The method is applied to the harmonic response analysis of cylindrical shells under different distributed forces,and the error between the result and the finite element is less than 1%.For the problem of substructure division,the transfer matrix method is used to calculate the vibration of shells of revolution.Firstly,the shell is divided into several subsegments,and then the subsegments are connected to form the whole transfer matrix.If the coefficient matrix of the vibration differential equation is a single variable function matrix,the division interval of the substructure will directly affect the accuracy and efficiency of the overall calculation.Based on the idea of adaptive algorithm,this paper analyzes the influence of variables in coefficient matrix on the division error of substructure,puts forward the program of adaptive division of substructure,gives a span criterion,and corrects the criterion with an example to make it more reasonable and effective.The examples of conical shell with equal thickness and cylindrical shell with variable thickness show that the method can adaptively adjust the span of substructure under the condition of satisfying the span criterion,and the error between the calculation result of natural frequency and finite element is within 5%.In order to transform the above numerical method into a simple and convenient calculation tool,this paper designs a man-machine interface based on Matlab GUI to calculate the vibration characteristics of cylindrical and conical shells.By inputting the initial definition parameters and selecting the boundary condition,the corresponding solution can be realized.Through the example debugging,the interface runs smoothly and meets the expected requirements.