关键词: 振动与波, 拉索, 模态分析, 有限元, 离散法, 无量纲化

Abstract:

In order to study the influence of the strength of geometric nonlinearity on the applicability of Galerkin discretization method under the background of single horizontal cable. Two kinds of different non-dimensional parameters are introduced to dimensionless the nonlinear equations of motion in the cable plane, and it was transformed into an ordinary differential equation using Galerkin method. Using the method of multiple scale to get perturbation solution, the corresponding frequency response equations are derived, and draw the amplitude-frequency response curve; Then MATLAB is used to obtain the time history curve of the system. Finally, ABAQUS software is used to carry out finite element simulation, and the results are compared with the numerical solutions of the method. While the time history curve of the system is obtained by numerical simulation, the two dimensionless methods are also compared. The results show that the Galerkin discrete method is more suitable for systems with weak geometric non-linearity. Dimensionless will lead to the increase of the nonlinear term coefficient of the system. system.The?numerical?solutions?obtained?by?the?two?dimensionless?methods?are?more?similar?with?the?increase?of?Irvine?coefficient. The research results may provide a basis for the numerical solution of nonlinear vibration of cables and contribute to the perfection of the theory.