Development of a method of harmonic balance for multi-periodic solutions of the nonlinear equations

The problems of implementation of the harmonic balance (HB) method for multi-periodic effects are discussed. The algorithms of optimization of fundamental frequencies set of the HB method, permitting one to reduce its number, are offered which promotes a diminution of HB set of equations size and realize the most effective HB algorithm. A new approach to the solution of the HB set of equations is offered, which allows one to exclude errors of spectrums superposition at commensurable fundamental frequencies. The effective algorithm of numerical calculation of the HB Jacobian matrix for multi-periodic effects is offered