Input shaping for continuum beams under longitudinal vibration

The applicability of standard input shapers to continuum longitudinal beams is presented in this paper. The effectiveness of different input shapers, specifically the zero vibration, the zero vibration and derivative, and the unity magnitude-zero vibration shapers, is investigated. Also, the sensitivity of these schemes to modelling errors is presented. Through a derivation of the equation of motion of a longitudinal beam, single mode shapers are shown to have the same vibration reducing characteristics for the first mode of continuum systems as they do for lumped parameter systems. However, the contribution of higher modes is also shown to impact the response, especially when negative input shapers are employed