Моделирование процесса взаимодействия ударной волны…
11
Modeling of the interaction of a shock wave
and a cylindrical shell
© V.M. Dubrovin, T.A. Butina
Bauman Moscow State Technical University, Moscow, 105005, Russia
In the work we offer
a method of calculating the pressure on the surface of the cylindrical
shell in the period of immersion and flow of it by a shock wave.
A comparative assess-
ment of the exact solution and the existing approximate solutions is carried out for weak
shock waves
. We consider two types of waves on the surface of
the rigid shell,
incident
and reflected
. As a result we obtained a pattern of presser distribution on the shell sur-
face dependent on the said types of waves.
Keywords:
incident shock wave
,
reflected shock wave
,
overpressure
,
cylindrical shell
,
integral transformation, the asymptotic representation
.
REFERENCES
[1] Karlov N.V., Kirichenko N.A.
Kolebaniya, volny, struktury
[Vibrations, waves,
structures]. Moscow, Fizmatlit, 2011, 497 p.
[2] Regirer L.S.
Shock waves
. Moscow, Nauka Publ., 1979, 542 p.
[3] Aleshkov Yu.Z.
Teoriya vzaimodeystviya voln s pregradami
[The theory of the
interaction of waves and obstacles]. Leningrad, LST Publ., 1990, 371 p.
[4] Pikovsky A., Rozenblyum M., Kurts Yu.
Sinkhronizatsiya: Fundamentalnoe
nelineynoe yavlenie
[
Synchronization: The fundamental nonlinear phenome-
non
]. Moscow, Tekhnosfera Publ., 2003, 496 p.
[5] Kubenko V.D.
Proniknovenie uprugikh obolochek v szhimaemuyu zhidkost
[
Penetration of elastic shells in compressible fluid
]. Kiev, Naukova dumka
Publ., 1984, 158 p.
[6] Dimitrienko Yu.I.
Mekhanika sploshnoy sredy. Tom 2. Universalnye zakony
mekhaniki i elektrodinamiki sploshnoy sredy
[Continuum Mechanics. Vol. 2.
Universal laws of mechanics and electrodynamics of continuous media]. Mos-
cow, BMSTU Publ., 2011, 560 p.
[7] Volmir A.S.
Obolochki v potoke zhidkosti i gaza. Zadacha aerouprugosti
[
Shells in the flow of liquid and gas. Aeroelasticity problem
]. Moscow, Nauka
Publ., 1976, 416 p.
[8] Moiseev N.N.
Asimptoticheskie metody nelineinoy mechaniki
[
Asymptotic
methods of nonlinear mechanics
]. Moscow, Nauka Publ., 1969, 379 p.
[9]
Asimptoticheskie metody v mekhanike
.
Sbornik statey
[
Asymptotic methods in
mechanics. Collection of papers]
. Novosibirsk,
Publishing House of the Siberi-
an Branch of the USSR Academy of Sciences
, 1987, 380 p.
[10] Mendlin R.P., Bleich H.H. Response of an elastic cylindrical shell to a trans-
verse step wave.
J. Appl. Mech
, 1953, vol. 20, no. 2.
[11] Glinsky M.M., Lebedev M.G., Yakubov I.R.
Modelirovanie techeniy gaza s
udarnymi volnami
[
Modeling of gas flows with shock waves
]. Moscow, Mash-
inostroenie Publ., 1984, 191 p.
[12] Landa P.S.
Nelineinye kolebaniya i volny
[
Nonlinear vibrations and waves
].
Moscow, Nauka Publ., 1997, 495 p.
Dubrovin V.M.
(b. 1934) graduated from the Faculty of Mathematics and Mechanics of
the Saratov State University in 1958. Ph.D., Assoc. Professor of the Computational
Mathematics and Mathematical Physics and of the Higher Mathematics Departments of
Bauman Moscow State Technical University. Research interests: dynamics, strength and
stability of deformable systems; creep of structural materials. He is the author of five
inventions. e-mail: dubrovinvm1934@ mail.ru
