A Treatise On the Mathematical Theory of Elasticity
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194-196] OF A SPHERE 273 The lowest roots of this equation are — = 1-8346, 2-8950, 3-9225, 4-9385, 5-9489, 6-9563,....
7r The number Tr/ica is the ratio of the period of oscillation to the time taken by a wave of distortion* to travel over a distance equal to the diameter of the sphere. The nodal surfaces are given by the equation tan K?-=Kr, of which the roots are — = 1-4303, 2-4590, 3-4709, 4-4774, 5-4818, 6-4844,....
TT 196. Vibrations of the second class.
When the vibration is of the second... class the components of displacement are expressed by equations of the type The frequency equation (36) cannot be solved numerically until the ratio k/A is known.
We shall consider chiefly incompressible material, for which A/k = 0, and material ful- filling Poisson's condition (X=/i), for which KJh=iJ3.
Radial vibrations.
When n=0 we have radial vibrations. The normal functions are of the form «=^^o'W. «=f V'o'C^'-), w=^-^ir„' (hr), (40) and the frequency equation is 6o = 0, or which is 4 ^o{^«)+-2-2^'*^o'(^«) = 0, (41'> tan ha ha 1-J(k2/A2)^2(i2- There are, of course, no radial vibrations when the material is incompressible.
What to read after A Treatise On the Mathematical Theory of Elasticity?
You can find similar books in the "Read Also" column, or choose other free books by Love, A. E. H. (Augustus Edward Hough), 1863-1940 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
194-196] OF A SPHERE 273 The lowest roots of this equation are — = 1-8346, 2-8950, 3-9225, 4-9385, 5-9489, 6-9563,....
7r The number Tr/ica is the ratio of the period of oscillation to the time taken by a wave of distortion* to travel over a distance equal to the diameter of the sphere. The nodal surfaces are given by the equation tan K?-=Kr, of which the roots are — = 1-4303, 2-4590, 3-4709, 4-4774, 5-4818, 6-4844,....
TT 196. Vibrations of the second class.
When the vibration is of the second... class the components of displacement are expressed by equations of the type The frequency equation (36) cannot be solved numerically until the ratio k/A is known.
We shall consider chiefly incompressible material, for which A/k = 0, and material ful- filling Poisson's condition (X=/i), for which KJh=iJ3.
Radial vibrations.
When n=0 we have radial vibrations. The normal functions are of the form «=^^o'W. «=f V'o'C^'-), w=^-^ir„' (hr), (40) and the frequency equation is 6o = 0, or which is 4 ^o{^«)+-2-2^'*^o'(^«) = 0, (41'> tan ha ha 1-J(k2/A2)^2(i2- There are, of course, no radial vibrations when the material is incompressible.
What to read after A Treatise On the Mathematical Theory of Elasticity?
You can find similar books in the "Read Also" column, or choose other free books by Love, A. E. H. (Augustus Edward Hough), 1863-1940 to read onlineMoreLess
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