Abstract: For a beam with one end clamped and the other end connected by a sleeve joint subjected to distributed force and with a gap, the nonlinear frequency response is studied, under conditons with and without pre-load. The improved mode transfer method and the continuous amplitude method are both adopted to model the system, Galerkin’s approximation is applied to the beam’s equations of motion. Then for a study case, Runge-Kutta method is used to carry out the numerical analysis. The nonlinear amplitude-frequency respose is obtained. The results can be used for studying the frequncy-shift phenomenon in the spacecraft ground test.