Open AccessThe lateral vibrations of sharply-pointed bars
Author(s) -
J. W. G. Nicholson
Publication year - 1920
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1920.0022
Subject(s) - conical surface , tangent , vibration , geometry , physics , surface of revolution , parabola , mathematics , quantum mechanics , surface (topology)
In a preceding paper, a discussion was given of the lateral vibrations of bars of circular cross-section formed by the revolution of the curvey = Axn —whenn is between the values zero and unity—about the axis ofx . The matter arose in connection with the siliceous deposits found upon a certain type of sponge spicule, as discussed in a joint paper by Prof. Dendy and the present author. It is of some interest to obtain a more extended knowledge of the vibrations of solids belonging to this class, with a view to further applications. The phenomena presented change in a curious manner with the value ofn , and, in certain respects, could not be foreseen in an elementary way. A discussion of the subject, in numerical terms, for an exponentn between 1 and 2 is very laborious, and in the present paper we confine attention to the casen = 2. This is a limiting case, which presents very exceptional features, and gives rise to a period equation of an unusual type. It illustrates clearly, at the same time, the effect of sharpening the ends of the rod beyond the point at which they are conical (n = 1). The rod is a free-free bar, symmetrical about its axis, and each half is obtained by the revolution of a portion of a parabola about the tangent at its vertex.