Method for solving structural vibration problem with general time-varying nonlinear boundary condition

The invention relates to a method for solving a structural vibration problem with a general time-varying nonlinear boundary condition, and solves the problem that when a boundary is nonlinear and non-homogeneous, approximate analytical solutions of the boundary and an equation are strictly met. Based on a nonlinear boundary of a structure, a linear modal superposition solution meeting a control equation is solved, a modal correction solution meeting the nonlinear boundary is constructed, the boundary serves as a part of a generalized control equation, harmonic expansion is conducted on modal coordinates and boundary generalized variables through the thought of a harmonic balance method, and then system response is obtained. According to the method, on the basis of a modal correction solution, a continuum partial differential control equation is projected into a modal space, and an ordinary differential dynamic system is formed by the continuum partial differential control equation and a boundary. According to