Forced Torsional Vibrations With Damping: An Extension of Holzer’s Method
J. P. Den Hartog, J. P. Li · Journal of Applied Mechanics · 1946
Abstract An extension of Holzer’s method is given for the case of damped systems of discreet as well as of uniformly distributed inertias and flexibilities. For discreet systems the modification in the Holzer table consists of replacing I by I − jc0/ω, and of replacing k by k + jωci, whereby most numbers in the tables become complex. The meaning of the real part of any complex number is that quantity which is in time-phase with the motion at the free end, while the imaginary part is 90 deg out of time-phase with that motion. For distributed systems the results are given by Equations [12] and [12a] for a free forward end; by Equations [13] and [13a] for a damped forward end, while the letters a and b appearing in these results are defined by Equations [8] and [8a].