Forced response approach of a parametric vibration with a trigonometric series

A forced vibration problem with parametric stiffness is modeled by feedback structure in this manuscript, and the forced response is expressed as a special trigonometric series. The forced response of this problem is determined by algebraic equation. By applying harmonic balance and limitation operation, all coefficients of the harmonic components in the forced response solution are fully approached. The investigation result shows that the new approach has an advantage in the computational time and accuracy, and it is very significant for the theoretical research and engineering application in dealing with the problem of forced parametric vibration.