An Elementary Treatise on the Mathematical Theory of Perfectly Elastic Solids: With a Short Account of Viscous FluidsMacmillan and Company, 1887 - 515 Seiten |
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amount angle anticlastic Applied Forces arbitrary beam boundary conditions bounding surface Central Axis centre coefficients components conjugate constant coördinates curvature curves cylinder deduce direction direction-cosines displacement dxdydz elastic elastic limits element ellipse ellipsoid elongation equal equilibrium external forces finite flexion formulæ functions given h₁ h₂ Hence homogeneous Hooke's law integral irrotational length limit longitudinal molecules N₁ natural orthogonal P₁ parallel to Ox perpendicular plane of yz plate portion positive potential energy principal axes produce Quadric radius represent rotation satisfied shearing stress simple shear small strain solid solid harmonics solution straight line Substituting suppose Surface Tractions surfaces of revolution symmetry tangent temperature tion torsion uniform unstrained values vanish vibrations viscosity wire Young's modulus zero ΟΔ ди дх Эф
Beliebte Passagen
Seite 162 - ... the power of any spring is in the same proportion with the tension thereof: that is, if one power stretch or bend it one space, two will bend it two, and three will bend it three, and so forward.
Seite 457 - ... that there is no oscillation. When it is left to itself it turns slowly towards the right, gradually undoing part of the effect of the more recent twist, then stops, and twists still more slowly to the left, thus undoing part of the quasi-permanent effect of the earlier twist. Thus the behaviour of such a wire, strictly speaking, is an excessively complex one, depending, as it were, upon its whole previous history ; though, of course, the trace left by each stage of its treatment is less marked...
Seite 14 - The four lines of argument which I have now indicated lead all to substantially the same estimate of the dimensions of molecular structure. Jointly they establish with what we cannot but regard as a very high degree of probability the conclusion that, in any ordinary liquid, transparent solid, or seemingly opaque solid, the mean distance between the centres of contiguous molecules is less than the hundred-millionth, and greater than the two thousand-millionth of a centimetre.
Seite 165 - The capability which solids possess of being put into a state of isochronous vibration shews that the pressures called into action by small displacements depend on homogeneous functions of those displacements of one dimension. I shall suppose moreover, according to the general principle of the superposition of small quantities, that the pressures due to different displacements are superimposed, and consequently that the pressures are linear functions of the displacements.
Seite 15 - To form some conception of the degree of coarse-grainedness indicated by this conclusion, imagine a rain drop, or a globe of glass as large as a pea, to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be coarser grained than a heap of small shot, but probably less coarse grained than a heap of cricketballs.
Seite 162 - About two years since I printed this theory in an anagram at the end of my book of the descriptions of helioscopes, viz. ceiiinosssttuu, id est, ut tensio sic vis; that is, the power of any spring is in the same proportion with the tension thereof...
Seite 15 - To form some conception of the degree of coarsegrainedness indicated by this conclusion, imagine a globe of water or glass, as large as a football,3 to be magnified up to the size of the earth, each constituent molecule being magnified in the same proportion. The magnified structure would be more coarse-grained than a heap of small shot, but probably less coarse-grained than a heap of footballs.
Seite 450 - ... 4. An elastic wire, indefinitely extended in one direction, is firmly held in a clamp at the other end. If a series of simple transverse waves travelling along the wire be reflected at the clamp ; show that the reflected waves will have the same amplitude as the incident waves, but that their phase is accelerated by one quarter of a wave length.
Seite 33 - Let p be the perpendicular from the centre on the tangent plane at...
Seite 162 - The true Theory of Elasticity or Springiness, and a particular Explication thereof in several Subjects in which it is to be found: And the way of computing the velocity of Bodies moved by them. ceiiinosssttuu.