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Longitudinal Vibrations of High-Elastic Gels as a Method for Determining Viscoelastic Constants

A one-dimensional equation of motion for the longitudinal vibrations of a viscoelastic cylinder is analyzed under boundary conditions that the upper end is free and the lower end is fixed on a vibrating horizontal plane. The amplitude of the free end is calculated as a function of the frequency for given viscoelastic constants. It is shown that all the resonance curves of the amplitude have the same shape for the same value of the mechanical loss tangent. A simplified resonance method is proposed, which enables us to determine the viscoelastic constants by measuring only the resonance frequency and half-value width of the amplitude. In order to study the viscoelastic properties for a wider range of frequencies (10-2∼103 Hz), measurements of the longitudinal vibrations are made in the lower frequency range for an agar-agar cylinder with the upper end fixed to a strain gauge.