Controlled motion of a two-module vibration-driven system induced by internal acceleration-controlled masses

The rectilinear motion of a vibration-driven mechanical system composed of two identical modules connected by an elastic element is considered in this paper. Each module consists of a main body and an internal mass that can move inside the main body. Anisotropic linear resistance is assumed to act between each module and the resistant medium. The motion of the system is excited by two acceleration-controlled masses inside the respective main bodies. The primary resonance situation that the excitation frequency is close to the natural frequency of the system is considered, and the steady-state motion of the system as a whole is mainly investigated. Both the internal excitation force and the external resistance force contain non-smooth factors and are assumed to be small quantities of the same order when compared with the maximum value of the force developed in the elastic element during the motion. With this assumption, method of averaging can be employed and an approximate value of the average steady-state velocity of the entire system is derived through a set of algebraic equations. The analytical results show that the magnitude of the average steady-state velocity can be controlled by varying the time shift between the excitations in the modules. The optimal value of the time shift that corresponds to the maximal average steady-state velocity exists and is unchanging with the external coefficients of resistance. For a system with specific parameters, numerical simulations are carried out to verify the correctness of the analytical results. The optimal value of the time shift is numerically obtained, and the optimal situation is studied to show the advantages of the control.