By Ivan V Andronov

Provides the assumption of zero-range potentials and exhibits the restrictions of the purpose types utilized in structural mechanics. bargains particular examples from the speculation of generalized features, regularization of super-singular imperative equations and different specifics of the boundary price difficulties.

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**Example text**

The Green's function for the isolated plate can be expressed in terms of Bessel functions of the third kind 9o(p,Po) = g ^ p (H^ikolp- p 0 |) - H£\ik0\p-p0\j) . 3 the solution of the problem for isolated plate can be expressed in the form of convolution with the Green's function w =- l | wWg0 + -7^-Mgo - go^w + -p-Mw ) ds. 47) Applying operator A — &Q to this formula yields the far field asymptotics for the function £(x,y). 47) with the far field amplitude V'clv) = — 2^oV'o(y)- Noting also that C(x,y) satisfies the twodimensional Helmholtz equation with the wavenumber &o a n d thus Sommerfeld formula is valid for it one concludes that £ = 0.

DX + - Res . . — - Res .. 2 X—K, 2 X——K For |A| > k the integrated functions in the above integrals are real and imaginary parts of Dt are only due to the integrals form — k to Ar and Classical Point Models 41 residues. t[ N_ f Vk2 - A2A*rfA 1 ImDt = iM T - / „ ,2 , J,,2 < 92W W4 , 4X 4 , + T 2^ J AT + (k - A )(A - fc )2 (K2 - U 5 K 4 k2)^ - 4K 2 k 2 - *4 This formula shows that the two expressions derived above for the effective cross-section coincide. Analogously one can check the optical theorem for the case of incident surface wave.

14). 26) is valid for the field U. 35) one can check the validity of similar formula for t h e field U U(r) = - J J exp (ik(x cos d sin

z* = m a x s z. Under this condition the integral by a exponentially converges in the nonshaded in Fig. 2 semi-strips. For the derivation of similar formula in two dimensions see [17]. 33) can be written for the case when S coincides with the surface of the obstacle.