Theory of Elasticity, Volume 7"This present volume of our Theoretical Physics deals with the theory of elasticity. Being written by physicists, and primarily for physicists, it naturally includes not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subjects, such as thermal conduction and viscosity in solids, and various problems in the theory of elastic vibration and waves."--Authors, 'Preface to the First English Edition. |
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Page 69
... angle 7 , which is the angle of rotation per unit length of the rod . This means that two neighbouring cross - sections at a distance da will rotate through a relative angle dø = 7 dz ( so that 7 = do / dx ) . The torsional deformation ...
... angle 7 , which is the angle of rotation per unit length of the rod . This means that two neighbouring cross - sections at a distance da will rotate through a relative angle dø = 7 dz ( so that 7 = do / dx ) . The torsional deformation ...
Page 79
... angle . Let do be the vector of the angle of relative rotation of two systems at a distance d / apart along the rod ( we know that an infinitesimal angle of rotation can be regarded as a vector parallel to the axis of rotation ; its ...
... angle . Let do be the vector of the angle of relative rotation of two systems at a distance d / apart along the rod ( we know that an infinitesimal angle of rotation can be regarded as a vector parallel to the axis of rotation ; its ...
Page 104
... angle ) . The relations giving the directions of the reflected and refracted waves can be obtained immediately from ... angle of incidence is equal to the angle of reflection . For the longitudinal reflected wave , however , c ' = c ...
... angle ) . The relations giving the directions of the reflected and refracted waves can be obtained immediately from ... angle of incidence is equal to the angle of reflection . For the longitudinal reflected wave , however , c ' = c ...
Contents
FUNDAMENTAL EQUATIONS | 1 |
2 The stress tensor | 11 |
8 Equilibrium of an elastic medium bounded by a plane | 29 |
Copyright | |
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Common terms and phrases
angle arbitrary axis bending biharmonic equation boundary conditions Burgers vector centre clamped coefficient components constant contour corresponding cross-section crystal crystallites curvature deflection denote derivatives Determine the deformation dislocation line displacement vector edge elastic wave element equations of equilibrium equations of motion expression external forces fluid force F forces acting forces applied formula free energy frequency function given gives grad div Hence HOOKE's law integral internal stresses isotropic isotropic body Let us consider longitudinal longitudinal waves medium moduli non-zero obtain parallel perpendicular plate PROBLEM quantities radius relation result rotation shear shell small compared SOLUTION strain tensor stress tensor stretching Substituting suffixes symmetry temperature thermal thermal conduction torsion transverse transverse waves two-dimensional undeformed unit length unit volume values velocity of propagation vibrations wave vector x-axis xy-plane z-axis zero σικ ди дхду дхк