ON THE DYNAMICS OF VIBRO-IMPACTING TAPERED CANTILEVER WITH TIP MASS

Vibro-impact situations in beams arise in several applications including turbine blades, vibration energy harvesting, etc This paper presents dynamic analysis of vibro-impacting tapered beam having tip mass and impacting against two stops. It is well known in the literature that typical frequency response of a uniform cantilever impacting against single stop shows resonance frequency shift along with hysteretic jump and drop phenomena. This paper investigates interesting perturbations in the frequency response curves on account of addition of another stop for a tapered counterpart. A piecewise linear modeling is used to consider spring-damper model for impact and tapered beam mode shapes are obtained using differential transform method. It is demonstrated both experimentally and theoretically that more taper in the beam in general increases the peak amplitude ratio and two stops play important role in enhancement of peak amplitude ratio while keeping the frequency shift the same.