Fourier Transform Method in Linear Viscoelastic Analysis: The Vibrating Viscoelastic Reed

• Published in: Journal of rheology (New York : 1978) 1971-12, Vol.15 (4), p.603-626
• Main Authors: Wapner, Phillip G., Forsman, W. C.
• Format: Article
• Language: English
• ISSN: 0148-6055; 0038-0032; 1520-8516
• DOI: 10.1122/1.549216

When linear viscoelasticity is formulated in a Fourier transform space, it is not necessary to assume any specific mathematical model, such as assemblies of Voigt or Maxwell elements, or differential operator equations, to completely describe the behavior of linear viscoelastic materials under any stress‐strain history. Indeed, the Fourier transform method is quite applicable even for complex vibration problems. In this paper we apply the method to the vibrating viscoelastic reed under two modes of oscillation, fixed at one end and subjected to a sinusoidal loading at the other, and subjected to a sinusoidal force at one end with the other end left free to oscillate. Theoretical results were in excellent quantitative agreement with experiments performed on a reed of poly(t‐butyl ethylene oxide) using both modes of excitation. We expressed the results in terms of corrections to the approximate relationship tan  δ=( bandwidth ) /(resonance frequency).