ABSTRACT
Precision mechanical instruments are rarely highly stressed through dynamical effects and so the methods of statics can be used for most of their design. They are very susceptible to small scale oscillatory behaviour that can limit their ability to function accurately in the presence of unwanted disturbances or to follow a signal Consequently system dynamics is discussed here in the context of response and vibration isolation. The first part of the chapter examines basic analytical techniques, concentrating on the readily generalized combination of Lagrangian mechanics and transfer function (frequency response) descriptions. The dynamic response of linear second order, single degree of freedom systems is used to illustrate characteristic behaviours. Particular emphasis is placed on viscous damping in the system, expressed by the critical damping factor, ξ, and the related quality factor, Q. Connecting these elements in series results in higher order systems which are briefly considered because of their importance in vibration isolation. The practical measurement of damping is then examined, particularly the ‘hammer test’ and logarithmic decrement method. This is followed by a discussion of parameter selection, especially damping coefficients, for a variety of applications, mainly noise and vibration isolation. Finally, there is a review of methods of damping suitable for small amplitude applications, including acoustic chambers, rubber and air suspensions and high damping factor materials. Case studies cover aspects of scanning tip microscope and gravity wave antenna designs.
