Although I would agree that the book by Wowk is useful for beginners to understand the nature of vibration analysis, I think it is of very small help in any analysis of vibration of machine tools.
There are a number of known attempts to study static and dynamic stability of machine tools. There are a number of different centers in the USA and Canada dealing with this problem. However, when one tries to use their results in practice he/she realizes: “Huston, we have a problem.” The problem is with understanding the sources of vibration in machining. This is a long story starting with Prof Tobias (S.A.Tobias, Machine Tool Vibration, Blackie, 1965. The history and state of the art on machine tool vibrations can be found in a book:
Y.Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge Univ., 2000.
However, in my opinion, the real assessment, control and used of machine tool vibrations are not known. Ideally, it should be the DYNAMIC SIGNATURE of any machine tools which contains all the info on its quality. The results of any improvement, retrofitting, adding some fixtures, maintenance etc should compared against this signature to see what has been done in reality. Is it feasible? Oh yes, it is. Unfortunately, leading machine tool producers afraid this signature (by ignoring any further studies and blocking funds at any levels for this studies) because it will rank their machines so that they could not sell those really bad (70%). Because today, there is no any meaningful dynamic acceptance test during runoff of a machine tool, you still buy whatever they sell you. Apparent rigidity of the modern machine tools and excess of power do not guarantee their dynamic stability.
Regards
Viktor