A class of synchronized nonlinear two-DOF systems with a closed-form solution

Nonlinear dynamic behavior of structural systems has a signicant role in many engineering applications. Related analysis methods are typically numerical. Accordingly, to verify and test their accuracy, availability of nonlinear systems with exact closedform solutions is important. In this paper, a three-parameter system, with an exact analytical solution, consisting of two synchronized colliding mass-spring-dashpot systems, is introduced, and the validity of the exact solutions is demonstrated. Simplicity of the system and its exact response, and the capability to control the frequency content, as well as the severity of the oscillatory behavior are addressed as the main features of the introduced system. The potential future works are outlined.