A new mathematical model for resonant-column measurements including eddy-current effects

Abstract

Wave velocity and attenuation are commonly studied in the laboratory with the resonant-column device (American Society for Testing and Materials standard), which is driven by a set of coils and magnets. This paper presents a new and robust mathematical model of the electromechanical resonant-column system. The model is used to compute various transfer functions. Eddy currents, a new source of damping identified in the resonant-column device, introduce damping proportional to the velocity of the magnets. Eddy-current damping is considered in the mathematical model. A testing program is devised to calibrate the resonant column with three aluminum probes. Experimental and theoretical results show an excellent agreement (4% maximum error). Exploratory results are presented for a dry-sand specimen. A resonant-column device is modified to demonstrate the significant effect of the induced voltage (electromotive force (EMF)) on damping ratio if tests are not based on current measurements. Free-vibration tests on aluminum specimens and a dry-sand specimen show a significant effect of the induced EMF (up to 400% increase in damping for the sand specimen). The induced voltage depends on the resonant frequency and damping of the specimen. In the case of aluminum probes, eddy-current damping represents 20–150 times the material damping of the specimen. Preliminary results on dry sand show that eddy-current damping represents up to a 15% increase in damping ratio. However, the magnitude of eddy-current damping depends on the configuration and materials used in the resonant-column device. The smaller the damping ratio of the specimen is, the more important the eddy-current damping becomes.Key words: damping, eddy currents, mechanical waves, resonant-column device, shear modulus, wave velocity.