By Professor Dr. Vladimir B. Poruchikov (auth.)
"Methods of the Classical concept of Elastodynamics" offers not just with classical tools as constructed some time past many years, yet offers additionally very fresh ways. purposes and strategies to express difficulties serve to demonstrate the theoretical presentation. key phrases: Smirnov-Sobolev approach with additional advancements; critical transforms; Wiener-Hopf method; combined boundary-value difficulties; time-dependent obstacles; ideas for unisotropic media (Willis method); 3D dynamical difficulties for combined boundary conditions.
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Additional info for Methods of the Classical Theory of Elastodynamics
Therefore, transverse waves propagating with the phase speed C2 are also called equivoluminal waves (or rotational waves, distortional waves, shear waves, secondary waves, S-waves). The vector potential 1/1 is called the transverse displacement potential. 1-4). If an elastic body is subject to plane deformation in the plane XIX2, then (u· e3) = 0, and == f(Xl,x2,t), == if! (X 1, X2, t) , cP == cp(Xl, X2, t) , f If! if! 11 cp = C1 cp ~ - ->. 3,7), with U3 == 0, 0"13 == 0"23 == O. 1], transition from the plane-strain equations to those of the generalized plane-stress state is implemented by replacement of the Lame constant >.
1B = O. 15) Taking into account that curl grad == 0, the displacement vector in the form 'U may be written 28 2. Formulation of EJastodynamic Problems. 14)]. 1-4). 8). ) grad div 1£ - P. curlcurl1/J-u-ib+'Ii] . 75) for the function 1/J, as well as the identity curl grad == 0, one may rewrite the latter tenn on the right-hand side in the fonn curl [- p. Ll1/J - e-ib + 'Ii] . 18) vanishes. 1-4), this condition is unimportant. 20), since curl grad == O. 3) will remain unchanged for 1/Jo, too, but now div 1/Jo = LlX = ci2 x =t 0 .
Hence, the presence of the instantaneous concentrated forces Ii = i5(t)i5(:v - :VO)i5i k' I? = i5(to - t)i5(:v - yo)i5i/ 26 2. Fonnulation of Elastodynamic Problems. 12) results in the equality U,k(YO, ilJO, to) = Ukl(ilJO, Yo, to) . 16) remains valid in the case of an unbounded elastic space, too. 7 Various Representations of Solutions to the Equations of Motion of a Homogeneous Isotropic Medium In this section we consider the main representations of solutions to elastodynamic equations for a homogeneous isotropic medium.