Analysis of axial waves in visco-elastic complex structural-acoustic systems: Theory and experiment

TL;DR

This paper presents a combined theoretical and experimental analysis of axial wave responses in visco-elastic coupled bars, deriving formulas that reveal how energy dissipation influences resonance envelope widths.

Contribution

It introduces novel closed-form formulas for spectral response envelopes in visco-elastic systems, explicitly showing the effect of internal friction and providing an exact alternative to fuzzy structure theory.

Findings

Formulas accurately predict laboratory measurements

Internal friction does not affect resonance envelope width

Connection established with nuclear physics strength function phenomenon

Abstract

An experimental and theoretical study of the spectral response of coupled visco-elastic bars subject to axial oscillations is done. Novel closed formulas for the envelope function and their width is derived. These formulas explicitly show the role played by energy dissipation. They show that the internal friction does not affect the width of the envelope of the individual resonances. The formulation is based on the equations of classical mechanics combined with Voigt's viscoelastic model. The systems studied consist of a sequence of one, two, or three coupled bars, with their central axes collinear. One of the bars is assumed to be much longer than the others. We discuss the connection between our results with the concept of the strength function phenomenon discovered for the first time in nuclear physics. Our formulation is an alternative and exact approach to the approximated studies based on the fuzzy structure theory that has been used by other authors to describe this type of couplings. The analytical expressions describe the measurements in the laboratory very well.