Traditional and non-traditional active nonlinear vibration absorber with time delay combination feedback for hard excitation

Abstract

In this work, vibration suppression of a base excited nonlinear spring–mass primary system subjected to simultaneous external hard harmonic and parametric excitations is carried out by using a modified traditional and non-traditional active nonlinear vibration absorber (ANVA). The ANVA consists of a mass, time delayed damper and a PZT stack actuator in series with a linear and nonlinear spring. The ANVA utilizes various combinations of time delayed displacement, velocity and acceleration feedback gains of the primary system for vibration reduction. The governing coupled nonlinear equations of motion for the system with weighted modal matrix approach have been derived and solved by the method of multiple scales (MMS) for simultaneous superharmonic, principal parametric and primary resonance with 1:1 internal resonance conditions. The reduced equations obtained from MMS are solved using Newton’s method, which is then compared with the numerical methods, showing good agreement. The trivial state instability regions are also analyzed for various feedback gains. The parametric analyses are carried out for various system parameters, viz., variation in the nonlinear stiffness, time delay in the damper, changes in the amplitude of excitations, time delay in the feedbacks, stiffness of the absorber and various combinations of feedback gains through different feedbacks. From these parametric analyses, stable and unstable regions of operating frequencies are obtained at which the system response amplitude is minimum for a wide range of operating frequencies. Further, it is shown that 100% vibration reduction of the system can be achieved for a certain range of operating frequencies.