High-resolution analysis of the complex wave spectrum in a cylindrical shell containing a viscoelastic medium. Part II. Experimental results versus theory

Abstract

The complex frequency spectrum of axisymmetric wave modes in a circular cylindrical shell containing various viscoelastic media is measured. A new measurement technique has been developed for this purpose by combining a high-resolution laser interferometer with modern spectrum estimation methods. To decompose the complex wave-number dependence, a complex spectrum estimation method has been implemented. Up to 40 dispersion curves of traveling, axisymmetric modes are decomposed simultaneously in a frequency range between 1 kHz and 2 MHz. The guided structural waves are excited by piezoelectric transducers. Linear elasticity can be considered as an extreme case of viscoelasticity (long relaxation times compared with the deformation periods). To ascertain the validity of the theory, dispersion curves are calculated for a shell containing a viscoelastic material behaving like the elastic shell and are compared with the measured curves of an isotropic aluminium rod. The phenomenon of “backward wave propagation,” in which the group velocity and the phase velocity of one mode have opposite signs, is clearly measured. Excellent agreement between experimental and theoretical results, which are also presented in a corresponding paper [J. Vollmann and J. Dual, J. Acoust. Soc. Am. 102, 896–908 (1997)], is found over a wide parameter range, including the case of a linear elastic rod.