Transmission of waves through elastic and viscoelastic junctions

Abstract: Transmission of extensional waves through elastic and viscoelastic junctions between elastic and collinear bars have been studied theoretically and experimentally. The models used can be interpreted also for other types of waves (e.g. dilatational waves, shear waves, electromagnetic waves) and systems.Five different problems of particular interest were considered.All junctions with the transmission properties of a given junction were synthesized. For a junction which consists of a finite number N of segments such transmission-equivalent junctions can be obtained through manipulations of a polynomial of degree N. Experimental tests showed that the degree of transmission equivalence between original and synthesized junctions was high.Optimum junctions with given material and length which maximize the energy transmission for a given incident wave of finite duration were determined for elastic and viscoelastic junctions. Optimum elastic junctions for a class of incident waves with piece-wise constant amplitudes have a finite number of plateaus with constant characteristic impedances and equal transit times. The optimum viscoelastic junctions can be viewed as displaced and deformed versions of their elastic counterparts.The optimum incident wave of given duration which maximizes the energy transmission through a given viscoelastic junction was determined. The optimum waves are characterized by being symmetric or anti-symmetric, by having alternating or constant sign, and by showing abrupt changes or being smooth. The optimum waves are unique, which they are not for elastic junctions.The dependence of the energy reflection, transmission and dissipation on the transmission direction was studied for non-uniform viscoelastic junctions. The theoretical and experimental results show that when the transmission direction through the junction is reversed the transmission properties are preserved while those with regard to dissipation are generally modified.

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