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

nonlinear dynamic behaviour of structural systems has a significant role in many engineering applications. the analysis methods are typically numerical. accordingly, for verification and test of accuracies, availability of nonlinear systems with exact closed form solutions is important. in this paper, a three-parameter system, with exact analytical solution, consisted of two synchronized colliding mass-spring-dashpot systems, is introduced and the validity of the exact solutions is demonstrated. simplicity of the exact response, and the capability to control the frequency content, are addressed as the main features of the introduced system. selection of appropriate values of the parameters entailing desired response features is discussed, and practical implementations of the model are described.