By Anatoly G. Gorshkov, Dmitry V. Tarlakovsky (auth.)
The difficulties of brief interplay of deformable our bodies with surrounding media are of significant useful and theoretical value. while fixing the issues of this type, the most hassle is within the necessity to combine together the procedure of equations which describe movement of the physique and the approach of equations which describe movement of the medium lower than the boundary stipulations predetermined on the unknown (movable) curvilinear interfaces. At that, the placement of those interfaces could be made up our minds as a part of the answer method. this is the reason, the identified certain strategies during this zone of mechanics of continuum were derived frequently for the instances of idealized inflexible our bodies. varied elements of the issues of temporary interplay of our bodies and buildings with continuum (derivation of the effective mathematical mod els for the phenomenon, improvement of the theoretical and experimental how to be used for learn of the temporary difficulties of mechanics, etc.) have been thought of within the books via S.U. Galiev, A.N. Guz, V.D. Kubenko, V.B. Poruchikov, L.L Slepyan, A.S. Volmir, and Yu.S. Yakovlev. the implications provided by way of those authors make curiosity whilst fixing an outstanding number of difficulties and express a need of joint utilization of the implications received in range ent components: aerohydrodynamics, thought of elasticity and plasticity, mechanics of soils, thought of shells and plates, utilized and computational mathemat ics, etc.
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Additional info for Transient Aerohydroelasticity of Spherical Bodies
A system of differential-difference equations with a retarded argument intended for study of dynamics of a multilayer inhomogeneous hollow sphere was derived in Molodtsov (1981); free vibrations of a thick-walled shell were analyzed. In Efimova, Stepanenko (1984), the authors applied the finite difference numerical method for solution of the problem of radial vibrations of a system which consisted of the infinitely elastic medium, thin-walled shell, and acoustic medium. A behavior of the systems of concentric thin-walled spherical shells separated by acoustic or elastic media was studied in Babaev (1983), Babaev (1984), and Babaev et al.
Ress-strain state was stated. hor employed a series expansion of the Laplace transforms in terms of the exponential functions; this method is equivalent to the one mentioned above. For one-dimensional problems, similar expansions were applied, for example, in Lurie (1950). The problem of transient radial vibrations of a thick-walled elastic or acoustic sphere was solved in Babaev (1981), Kokhmanyuk et al. (1980), and Yanyutin, Titarev (1979) by application of the inversion of the Laplace transform with respect to time by means of the Volterra integral equations; the cases of immovable and movable boundaries were considered.
1980), and Yanyutin, Titarev (1979) by application of the inversion of the Laplace transform with respect to time by means of the Volterra integral equations; the cases of immovable and movable boundaries were considered. A comparison of the results obtained when applying the linear theory of elasticity and the theory of thick-walled shells was presented in Shchipitsina (1972). Now, let us review the works devoted to propagation of radial elastic waves from a spherical cavity stiffiy joined to a thick-walled shell.