Abstract
Analytical solution for spherically symmetric nonstationary oscillations of acoustic and elastic solid sphere is given. Time dependence of potential, kinetic and internal energy of a solid sphere is analyzed. The received results are of practical importance for a wide range of problems connected to testing of material dynamic strength parameters and to the problems of optimizing (minimizing) energy needed for fracture of solids.
Similar content being viewed by others
References
Pavlovskaya E E, Petrov Yu V. On some specific features of solutions of dynamic problems of elasticity. Mech Solids, 2002, 37(4): 31–36
Barzukov O P, Wiseberg L A, Semkin B V, et al. On energetic correlations under impact loading of a rod (in Russian). Izv Vuzov Phys, 1972, 7: 96–101
Berezkin A N, Krivosheev S I, Petrov Yu V, et al. Effect of delayed crack nucleation under threshold pulse loading. Doklady Phys, 2000, 45: 617–619
Bratov V A, Gruzdkov A A, Krivosheev S I, et al. Energy balance in the crack growth initiation under pulsed-load conditions. Doklady Phys, 2004, 49: 338–341
Nikiforovskiy V S, Shemyakin E I. Dynamic Fracture of Solids (in Russian). Novosibirsk: Nauka, 1979
Petrov Y V, Utkin A A. Fracture of an initially loaded solid sphere after sudden load removal (in Russian). Vestnik SPbSU, 1999, 1(2): 86–89
Bratov V, Petrov Y, Utkin A. Transient near tip fields in crack dynamics. Sci China-Phys Mech Astron, 2011, 54: 1309–1318
Smirnov V, Petrov Y V, Bratov V. Incubation time approach in rock fracture dynamics. Sci China-Phys Mech Astron, 2012, 55: 78–85
Bahrah S M, Kovalev N P, Nadykto B A, et al. Investigation of plastic and strength properties of copper under tension (in Russian). Doklady RAS, 1974, 215: 1090–1093
Zeldovich V I, et al. Quasi-spherical explosive loading of steel with a pressure of 200GPa (in Russian). Doklady RAS, 1995, 343: 621–624
Kozlov E A, Kovalenko G V, Litvinov B V, et al. Strain and fracture features of 60Kh3G8N8F austenitic steel exposed to spherical stress waves. Doklady Phys, 1998, 43: 26–29
Morozov N F, Brigadnov I A, Indeitsev D A, et al. Energy estimates for phase transitions in a ball subjected to a spherically converging compression wave. Doklady Phys, 2001, 46: 291–293
Hata T. Stress-focusing effect in a uniformly heated solid sphere. ASME J Appl Mech, 1991, 58: 58–63
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petrov, Y., Smirnov, V., Utkin, A. et al. Energy of a solid sphere under nonstationary oscillations. Sci. China Phys. Mech. Astron. 57, 469–476 (2014). https://doi.org/10.1007/s11433-013-5370-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-013-5370-4