Analytical Solutions of a First-Order Quadratic Nonlinear System With Parametrical and Periodical Excitation

In this paper, a quadratic nonlinear dynamical system with two periodic excitation forces is discussed. Analytical period-1 motions of such dynamical system are obtained by using generalized harmonic balance method. Stability analysis is carried out via eigenvalues analysis. To verify approximate analytical solutions, numerical simulations are completed to compare analytic and numerical solutions of the dynamical system, the approximate precision is guaranteed with appropriate harmonic balance terms. More harmonic terms should be employed to guarantee good approximation of periodic motions if excitation frequency is small. Furthermore, infinite harmonic balance terms must be introduced for chaotic systems.