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This article is cited in 3 scientific papers (total in 3 papers)
Scattering of plane longitudinal elastic waves by a slender cavity of revolution. The case of axial incidence
G. V. Zhdanova
Abstract:
The system of equations of elasticity theory
$$
A(\partial_x)\overline u+\omega^2\rho\overline u=0,\quad x\in D_\varepsilon;\qquad T\overline u=0,\quad x\in S_\varepsilon,
$$
is solved in a homogeneous isotropic medium. Here $A(\partial_x)$ is a matrix differential operator, $T$ is the stress operator, $x\in R^3$, $\varepsilon>0$ is a small parameter, $S_\varepsilon$ is a smooth bounded closed surface of revolution, and $D_\varepsilon$ is the exterior of $S_\varepsilon$. The case where
$$
\overline u(x)=A_le^{ik_lz}\overline i_z+\overline u^{(s)}(x),\qquad A_l=\mathrm{const},
$$
is considered. The reflected wave $\overline u^{(s)}(x)$ satisfies the radiation condition. The asymptotics of $\overline u^{(s)}(x)$ is constructed with $O(\varepsilon^{(m)})$ precision as $\varepsilon\to+0$, where $m>0$ is arbitrary.
The formulas obtained are useful everywhere near $S_\varepsilon$, including its endpoints, and at a distance. The asymptotics of the scattering amplitudes of the reflected waves is found.
Figures: 1.
Bibliography: 16 titles.
Received: 05.01.1982
Citation:
G. V. Zhdanova, “Scattering of plane longitudinal elastic waves by a slender cavity of revolution. The case of axial incidence”, Mat. Sb. (N.S.), 121(163):3(7) (1983), 310–326; Math. USSR-Sb., 49:2 (1984), 305–323
Linking options:
https://www.mathnet.ru/eng/sm2195https://doi.org/10.1070/SM1984v049n02ABEH002712 https://www.mathnet.ru/eng/sm/v163/i3/p310
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Abstract page: | 377 | Russian version PDF: | 100 | English version PDF: | 4 | References: | 51 |
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