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A Treatise on the Mathematical Theory of Elasticity, Volume 2

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 Excerpt: ...elastic, it is more difficult to account for the discrepancy. The consideration of the heat developed will not help us because the vibrations of Saint-Venant's theory have already absorbed too much of the kinetic energy. What we want is a theory which without assuming dissipation of energy will explain why these vibrations do not take place. 285. Voigt's Theory. Prof. Voigt1 suggested that the source of error is to be found in Saint-Venant's terminal conditions at the junction. In Mechanics it is for some purposes sufficiently exact to treat bodies as continuous and bounded by surfaces, but there are some phenomena that can only be interpreted by means of the conception of bodies as congeries of molecules. In the theories of Capillarity and of Reflexion and Refraction of Polarized Light it is necessary to treat the parts of two media near their surface of separation as having different properties from the parts more remote. Instead of a separating surface we have to consider a separating film, within which there is a rapid, but not sudden, transition from the properties of the first to those of the second medium. Prof. Voigt's theory of impact assumes the existence between two impinging bodies of a thin separating film, and his object is to attribute such properties to the film as in extreme conditions will include the Newtonian and Saint-Venant's theories as particular cases. Consider the impact of two bars, and between the two at the junction let there be a separating film. Let I be the length of this film at the instant when the impact commences, and I--SI its length at any time t during the continuance of the impact, then SI is the relative displacement towards each other of the ends of the two bars. The theory treats the film as a short massless elasti... Hide synopsis

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