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 101
... motion occurs in a deformed body , its temperature is not in general constant , but varies in both time and space . This considerably complicates the exact equations of motion in the general case of arbitrary motions . Usually , however ...
... motion occurs in a deformed body , its temperature is not in general constant , but varies in both time and space . This considerably complicates the exact equations of motion in the general case of arbitrary motions . Usually , however ...
Page 107
... equations of motion are püt = λικιν- a2um дхидх ( 23.1 ) Let us consider a monochromatic elastic wave in a crystal . We can seek a solution of the equations of motion in the form μ1 = uote ( kr - wt ) , where the uot are constants , the ...
... equations of motion are püt = λικιν- a2um дхидх ( 23.1 ) Let us consider a monochromatic elastic wave in a crystal . We can seek a solution of the equations of motion in the form μ1 = uote ( kr - wt ) , where the uot are constants , the ...
Page 119
... equations of motion are linear . The most characteristic property of elastic waves in this approximation is that any wave can be obtained by simple superposition ( i.e. as a linear com- bination ) of separate monochromatic waves . Each ...
... equations of motion are linear . The most characteristic property of elastic waves in this approximation is that any wave can be obtained by simple superposition ( i.e. as a linear com- bination ) of separate monochromatic waves . Each ...
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