TOEPLITZ JACOBIAN METHOD FOR NONLINEAR DOUBLE-PERIODIC EXCITATIONS

The Toeplitz Jacobian matrix method is an efficient algorithm for comp uting the steady state solutions of nonlinear periodic vibration. In t his paper the method is generalized by using multiple time scales to d ouble-periodic solutions in a multi-frequency excited system. The meth od is combined with a standard multi-dimensional FFT algorithm to accu rately simulate the nonlinear oscillators with widely separated freque ncies. The continuation technique can also be incorporated with the Ne wton-Raphson iteration to further increase its efficiency and to achie ve the complete frequency response characteristics.