Application of energy criteria to vibration isolation

Abstract

An extended analysis is provided into the fundamental relationship between the global stationary vibration of a structure expressed by its energy and the supplied complex mechanical power. The relationship contains a dimensionless quantity, the apparent loss factor, which depends on the spatial-frequency distribution of damping and potential energy within the structure. A large number of multi degree-of-freedom systems of the type “source-isolators-receiver” are analyzed statistically with the objective of checking out whether the apparent loss factor can be substituted by the averaged physical loss factor. The substitution was found to be statistically unbiased and of relatively modest error. Based on mobility approach an isolation strategy is provided which enables the selection of vibration isolators aimed at minimising the entire kinetic energy of the isolated structure. This strategy can be applied to already existing mechanical components by using mobility measurements at the coupling points. The apparent loss factor can then be estimated from the same measurements using a specific energy relationship. The proposed isolation strategy is tested through a case study where the selection of isolators is done using three indicators: (a) the estimate of global kinetic energy herein developed, (b) its simplified substitute – the frequency-weighted net input power and (c) the RMS force transmitted to the isolated structure. The indicators (a) and (b) are both found suitable for the selection of isolators which minimise the global vibration.