Based on the Silnikov criterion, the chaotic properties of mechanically and electrically coupled nonlinear dynamical systems were discussed. Using Cardano formula and series solution of differential equation, the eigenvalue problem and existence of homoclinic orbit were studied respectively. A rigorous proof of the existence of Silnikov-sense Smale horseshoe chaos was presented and some conditions leading to chaos were obtained. The space trajectory, Lyapunov exponent and Lyapunov dimension were investigated via numerical simulation, which showed that chaotic attractors exist in the non-linear dynamical systems.