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.

最近，科学家们在许多机械和微机械应用中利用了自激振荡，因此，已经进行了一些实验和理论研究活动，目的是在机械系统中人为地诱导自激振荡。本文考虑了通过集中非线性反馈在两个自由度欠驱动弹簧-质量-阻尼器系统中产生自激振荡的一些理论方面。控制力取决于两个质量的响应。拟议的控制法在性质上略显笼统，因为它需要作为特殊情况的并置和非并置控制。借助平均法研究非线性反馈控制的响应。本研究表明，通过适当地选择控制增益，无论初始条件如何，都可以激发所需的振荡模式。甚至可以激发具有准周期振荡特性的双模振荡。通过在 MATLAB Simulink 中执行的仿真结果验证了系统动力学的理论分析与控制。