Suppressing self-excited vibrations of mechanical systems by impulsive force excitation

Abstract

In this contribution, self-excited mechanical systems subjected to force excitation of impulsive type are investigated. It is shown that applying force impulses which are equally spaced in time, but whose impulsive strength depends in a certain manner on the state-variables of the mechanical system, results in a periodic energy exchange between lower and higher modes of vibration. Moreover, in the theoretical case of Dirac delta impulses, it is possible that no energy crosses the system boundary while energy is transferred across modes, i.e. neither external energy is fed to the mechanical system, nor energy is extracted from the mechanical system. Shifting energy to higher modes of vibration, whose natural damping is larger compared to lower ones, results in a faster dissipation of energy. An analytical stability investigation is presented using the assumption of impulsive forcing of Dirac delta type, which allows deciding easily about the stability by evaluating the eigenvalues of the coefficient matrix of a corresponding set of difference equations. It is shown that the developed impulsive forcing concept is capable to suppress self-excited vibrations of mechanical systems. Some numerical results of a simple mechanical system with two degrees of freedom underline the presented approach.