Application of a Correspondence Principle to the Free Vibrations of Some Viscoelastic Solids

• Published in: Geophysical Journal of the Royal Astronomical Society Vol. 86; no. 1; pp. 137 - 166
• Main Authors: Chin, R. C. Y., Hedstrom, G. W., Majda, G.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.07.1986
• Subjects: Love waves; quality factor Q; viscoelastic free vibrations
• ISSN: 0956-540X; 0016-8009; 1365-246X
• DOI: 10.1111/j.1365-246X.1986.tb01077.x

In this study we apply the correspondence principle for free vibrations of a homogeneous viscoelastic solid derived by Fisher & Leitman to obtain the torsional modes of a homogeneous viscoelastic rod. We also extend the correspondence principle, showing that it may be used to find the frequencies of Love waves in a stratified viscoelastic medium. Finally, we apply the correspondence principle to four viscoelastic materials, the Kelvin—Voigt solid, the Maxwell solid, the standard linear solid, and the Achenbach—Chao solid. We show that in each of these cases some care must be used in applying the correspondence principle because of the presence of multiple solutions. We also examine measures of dissipation of the free vibrations, and we determine the conditions under which the logarithmic decrement may be approximated by the process-independent l/Q of O'Connell & Budiansky.