On the Experimental Determination of the Viscosity of Vibrating Solids

Abstract

Effect of viscosity on longitudinal vibrations in bars.—The theoretical development is based on the assumption, due to Stokes, that the stress in the medium due to viscosity is proportional to the first power of the time rate of shearing strain. The equation of propagation of a plane longitudinal sound wave along a slender bar is made to include the viscous stress which arises from the shearing strain associated with this type of disturbance. Comparison with experiment. Specimen bars are excited to longitudinal vibration by means of a high frequency, sinusoidal alternating electric field impressed on a piece of piezo-electric quartz cemented to one end of the bar. The amplitude of vibration is observed by measuring the torque on a Rayleigh disk suspended in air immediately off the other end of the bar. Resonance curves are obtained showing the relation between the square of the particle velocity at the end of the bar and the frequency of excitation. The experimental curves for hard drawn copper, aluminum, and glass are in admirable agreement with those deduced from the theory. Curves for soft annealed copper and silver, however, exhibit discrepancies which indicate the presence of viscous forces varying according to higher powers of the strain velocity.