Resonances in Nonstationary, Nonlinear, Multidegree-of-Freedom Systems

The asymptotic method for determining resonant responses of nonstationary , nonlinear systems is presented. Resonance conditions, resonance coefficients, and higher-order resonances are discussed. The first asymptotic approximation nonstationary solution is obtained for general resonances. A gyroscopic system is analyzed for combination differential resonances v = o;2 —2co1 and v = o>2 — o}r Using the general solution, nonstationary and stationary responses and stability conditions are obtained. The numerical results indicate that the change in the rate of variation of the frequency of excitation may shift the nonstationary response from one stable mode to another stable mode.