The Use of the Wigner Distribution to Identify Wave-Types in Multi-Element Structures

In this paper it is shown that time-frequency analysis of a transient structural response may be used to identify the wave-types carrying significant energy through a multi-element structure. The identification of various wave-types is possible since each is characterized by its own dispersion relation, with the result that each wave-type may be associated with characteristic features in the time-frequency domain representation of a structural response. For multi-element structures, propagating energy can be converted from one wave-type to another at the junction of the elements. Consequently, for those structures, the characteristic features in the time-frequency domain consist of the superposition of features associated with propagation in each element. In the work described here, the Wigner Distribution has been used to obtain time-frequency domain representations of structural transient responses. Time-frequency filtering techniques that may be used in conjunction with the Wigner Distribution are also described and it is demonstrated that they can be used to detect the presence of waves in multi-element structures.