Abstract:Because the conventional method of natural vibration analysis fails to make full use of the inherent symmetry of the structure, the calculation cost increases significantly when the degree of freedom of the structure increases. Based on group theory, an efficient method for analyzing the dynamic characteristics of symmetrical prestressed structures is presented in this paper. Firstly, the generalized characteristic equation of the prestressed structure is established by combining the uniform mass matrix and tangential stiffness matrix, and the influence of the initial prestress on the structure is considered to solve the natural vibration frequency and mode of the structure. Then, a symmetric coordinate system is established to decompose the stiffness matrix and mass matrix into a series of partitioned diagonalized matrices. Because each submatrix is independent of each other, the difficulty of solving the generalized eigenvalue problem is significantly reduced, and the natural frequency and corresponding mode of the structure can be efficiently solved. Numerical examples illustrate the basic calculation process and significant advantages of the proposed method. Compared with the results of finite element method and conventional method, the symmetry method based on group theory is accurate and efficient.