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This paper is a counterpart to Bousinesque's equations that have so many successful applications in the soil mechanics of a medium at rest. In the main it is a simplification to the case of an isotropic medium of “Vibrations in an Aeolotropic Medium,” a theoretical contribution by the author to a project on “Compaction of Soil by Vibration” at the California Institute of Technology, 1948–1949. Solutions are obtained for the circular and the long rectangular vibrator under various assumptions as to contact pressure. E. Reissner (2), deals with the case of a circular vibrator when the contact pressure is assumed to be uniform; the present approach is easier to comprehend, and it also succeeds in replacing Reissner's Principal Value Integrals by Definite Integrals. Apart from this case, the results obtained in this paper are made available for the first time. An experimental method is developed for determining dynamic elastic constants in situ using a dynamic oscillator. Finally, predictions based on the above theory show a fair measure of agreement when compared with experimental results.
Quinlan, Patrick M.
Professor of Mathematical PhysicsVisiting Professor of Civil Engineering, National University of IrelandCalifornia Institute of Technology, CorkPasadena, Calif.