Vibration of a Boring Bar System
I am investigating the design of boring bar systems for deep hollowing of wooden objects on a wood lathe. The bar rests upon two supports with one end overhanging. The cantilevered end has a scraping bit on the end that bores into a rotating wood work piece. The characteristics of the the tool bar (the cantilever) may or may not be the same as those of the support bar. The boring bar rests freely on the supports. I want to calculate the the resonance frequencies of the tool bar which will be excited by the scraping action. I am familiar with the various formulas for transverse vibration frequencies of a uniformly loaded cantilever. However, they do not apply directly here, because the effective stiffness of the cantilever will be reduced by the bending of the support bar, and (I believe) the mass of the support section will be reflected as a change of the effective mass of the cantilever. It seems to me that this problem ought to be a standard one, bit I have not found any references. Can anyone help?