Nonlinear feedback self-excitation of modal oscillations in a class of under-actuated two degrees-of-freedom mechanical systems

摘要

Recently, scientists have utilized self-excited oscillations in many mechanical and micromechanical applications and accordingly, several experimental and theoretical research activities have been undertaken with the objective of artificially inducing self-excited oscillation in mechanical systems. This paper considers some theoretical aspects of generation of self-excited oscillation in a two degrees-of-freedom under-actuated spring- mass-damper system by centralized nonlinear feedback. The control force depends on the response of both masses. The proposed control law is slightly general in nature as it entails both collocated and non-collocated control as special cases. The response of the nonlinear feedback control is studied with the help of the method of averaging. The present study shows that by appropriately selecting the control gains it is possible to excite the desired mode(s) of oscillation irrespective of initial conditions. Even it is possible to excite dual mode oscillation having the characteristics of quasiperiodic oscillations. The theoretical analysis of the dynamics of the system with the control is validated by simulation results, performed in MATLAB Simulink.