In this paper the vibration of a mass–spring oscillator with strong quadratic nonlinearity and one degree of freedom is analyzed. The both, strong and hard, springs are considered. The restoring force in the spring which is the function of the quadratic deformation has to satisfy the condition...

In this paper, an approximate analytic procedure is developed for solving the strong non-linear differential equations of the Duffing type with complex-valued function which describes the dynamical behavior of many real systems. The method is based on the elliptic-Krylov–Bogolubov procedure...