High frequency dynamics of engineering structures

This paper considers the high frequency dynamics which links vibration theory and thermodynamics. It is shown that the high frequency dynamics is the high frequency limit of vibration theory and the low frequency limit of thermodynamics. Two approaches to the high frequency dynamics of complex engineering structures are proposed. The first one is high frequency structural analysis. Its boundary value is derived from vibration theory under the assumption that the structures which have high modal overlap possess some thermodynamic properties. The second approach is the vibrational conductivity approach to high frequency dynamics which is governed by a boundary value problem of the heat conduction type. The latter has been modified to incorporate a heat sink term so that the spatial resonant absorption of vibration is taken into account. At high frequencies the structures are shown to behave like mechanical systems with a continuous spectrum of natural frequencies and considerable spatial decay. The effect of the secondary systems' vibration on the vibrational field in the structure becomes evident. The secondary systems act as dynamic absorbers on the primary structure which, in the case of high modal overlap, provides considerable spatial absorption of high frequency vibration. The secondary systems may be damaged since they absorb vibrational energy at their natural frequencies. This provides the main motivation for interest in high frequency dynamics. A comparison of the properties of high frequency vibration with those of low frequency vibration and thermal vibration is provided.