Nonlinear vibrations of a linkage mechanism: theory and experiment

Linkage mechanisms have a wide range of applications in truck-mounted cranes, folding mechanical arms of transport vehicles and so on due to their simple and effective design. Vibration problems in the linkage mechanisms seriously affect the stability and reliability of crane machines or transport vehicles. Therefore, in this study, an effective nonlinear dynamic model of a linkage mechanism with spring-damping systems is developed and experimentally validated to explore the nonlinear vibration properties. The geometric nonlinearity of the linkage mechanism is considered and the Lagrange equation is employed to establish the nonlinear dynamic equations. Based on the harmonic balance method (HBM), the nonlinear vibration properties of the structural system are analyzed. The nonlinear primary resonance response of the linkage mechanism calculated from the HBM is compared with those of the Runge–Kutta method and the experimental result, which validates the effectiveness and accuracy of the proposed nonlinear dynamic model. The influences of some parameters, such as the spring stiffness, the lengths of connecting rods, and the installation positions of the spring-damping system, on the nonlinear vibration characteristic of the linkage mechanism are analyzed. Based on the numerical results, the folding mechanical arms or truck-mounted cranes can be conveniently designed to avoid irreparable damage to the structure caused by nonlinear primary resonance and instability phenomena, which provides new insight into the stability analysis and design of various linkage mechanisms required in engineering applications.