When studying the properties of a material subject to static loading, the average stresses on the boundary of the specimen, contained by the apparatus, can be easily determined from the forces applied to the apparatus. The shape and mass of the apparatus are unimportant. For dynamic loadings where inertia forces must be considered, the measured response resulting from the application of forces to the apparatus is a function of the mass, shape, and stiffness of the apparatus as well as the properties of the specimen. The problem, then, is to interpret the response of the system, composed of the specimen and its attached apparatus, in terms of constants that will represent the properties of the material when in different surroundings (boundary conditions). To do this, it appears that some model for the material must be assumed and the analytical solution (satisfying the laws of motion and including the properties of the apparatus) for the response of the specimen-apparatus system must be obtained. The response of the system can then be interpreted in terms of the constants used to model the material. Most real materials are quite complex and no simple model will completely describe their behavior under all loading conditions. Also, the difficulty of obtaining an analytical solution for the specimen-appratus system increases rapidly with the complexity of the model for the material or model for the apparatus (i.e., certain parts of the apparatus may be assumed to be rigid or weightless,etc.). Thus, the investigator is faced with designing an apparatus that can be represented by a simple model and choosing a model for the material that is sufficiently complex to represent the material response for the desired range of loading and yet he must be able to obtain the required analytical solution. In general, the response of a real material can be best represented by the most complex model for which a solution is known. Because solutions involving more complex material models were not available for the specimen-apparatus system being used, many studies of the dynamic properties of soils have been based on the assumption that the material was Hookean. The dissipative properties have been reported in terms of the logarithmic decrement calculated from the observation of the decay of free vibration of a specimen-apparatus system. The general steady-state solution, for the forced vibration of a cylindrical shaft of material represented by the generalized Kelvin-Voigt model, is presented. This solution can be used, together with the boundary conditions and properties of the various types of apparatus (i.e., apparatus involving vibration of cylindrical specimens), to obtain the analytical solutions for these specimen- apparatus systems. The use of the general solution is also illustrated by showing how it can be applied to a boundary value problem that is typical for some of the specimen- apparatus systems previously used; and, the measured response for a cylindrical specimen of sand obtained with such an apparatus is compared with the computed results obtained from the analytical solutions. It was possible to choose the parameters in the analytical solution such that relatively good agreement with the measured response for sand was obtained.

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  • Accession Number: 00095053
  • Record Type: Publication
  • Files: TRIS
  • Created Date: May 29 1975 12:00AM