Shock Waves in Anisotropic Cylinders
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We study small-amplitude longitudinal and torsional shock waves in circular cylinders consisting of an anisotropic medium such that the velocities of the longitudinal and torsional waves are close to each other. Previously, simple waves were considered in the same situation and conditions were found for these waves to overturn and for the corresponding shock waves to form. Here we present the study of shock waves: the shock adiabat and the evolutionary conditions. The results obtained can also be related to shock waves in unbounded media with quadratic nonlinearity.
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- 9.V. I. Erofeev, “Nonlinear flexural and torsional waves in rods and rod systems,” Vestn. Nauchn.-Tekh. Razvitiya, No. 4, 46–50 (2009).Google Scholar
- 10.V. I. Erofeev and N. V. Klyueva, “Propagation of nonlinear torsional waves in a beam made of a differentmodulus material,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 147–153 (2003) [Mech. Solids 38 (5), 122–126 (2003)].Google Scholar
- 11.M. F. Glushko, “Investigation of deformations and stresses in twisted ropes with real wire-contact conditions taken into account,” Izv. Vyssh. Uchebn. Zaved., Gornyi Zh., No. 11, 103–118 (1961).Google Scholar
- 12.A. Hanyga, On the Solution to the Riemann Problem for Arbitrary Hyperbolic System of Conservation Laws (Państw. Wydawn. Nauk., Warszawa, 1976), Publ. Inst. Geophys., Pol. Acad. Sci. A-1.Google Scholar
- 13.A. T. Il’ichev and A. P. Chugainova, “Spectral stability theory of heteroclinic solutions to the Korteweg–de Vries–Burgers equation with an arbitrary potential,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 295, 163–173 (2016) [Proc. Steklov Inst. Math. 295, 148–157 (2016)].MathSciNetzbMATHGoogle Scholar
- 14.A. G. Kulikovskii, “Properties of shock adiabats in the neighborhood of Jouguet points,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 184–186 (1979) [Fluid Dyn. 14, 317–320 (1979)].Google Scholar
- 17.A. G. Kulikovskii and A. P. Chugainova, “On the steady-state structure of shock waves in elastic media and dielectrics,” Zh. Eksp. Teor. Fiz. 137 (5), 973–985 (2010) [J. Exp. Theor. Phys. 110 (5), 851–862 (2010)].Google Scholar
- 22.A. G. Kulikovskii, A. P. Chugainova, and V. A. Shargatov, “Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity,” Zh. Vychisl. Mat. Mat. Fiz. 56 (7), 1363–1370 (2016) [Comput. Math. Math. Phys. 56, 1355–1362 (2016)].MathSciNetzbMATHGoogle Scholar
- 25.A. G. Kulikovskii and E. I. Sveshnikova, “Investigation of the shock adiabat of quasitransverse shock waves in a prestressed elastic medium,” Prikl. Mat. Mekh. 46 (5), 831–840 (1982) [J. Appl. Math. Mech. 46, 667–673 (1982)].Google Scholar
- 28.L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).Google Scholar
- 33.G. N. Savin, “Equations of motion of a naturally twisted thread of variable length,” Dokl. Akad. Nauk Ukr. SSR, No. 6, 726–730 (1960).Google Scholar
- 37.Yu. A. Ustinov, Saint-Venant Problems for Pseudocylinders (Fizmatlit, Moscow, 2003) [in Russian].Google Scholar