Abstract
The question of the natural motion density in dynamics problems of elastic shells is considered. Motions are studied for which an exponential growth in amplitude with time occurs. The number of natural motions incident in a given range of variation of the exponent is computed by using an idea of R. Courant. The governing natural motions and condensation points at which the natural motion density tends to infinity are found. The condensation points and governing motions are compared in specific examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
M. A. Lavrent'ev and A. Yu. Ishlinskii, “Dynamic buckling modes of elastic systems,” Dokl. Akad. Nauk SSSR,64, No. 6 (1949).
A. S. Vol'mir, Stability of Deformable Systems [in Russian], Fizmatgiz, Moscow (1967).
V. M. Kornev, “Development of dynamic buckling modes of elastic systems under intensive loading in a finite time segment,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4 (1972).
V. M. Kornev, “On the buckling modes of elastic shells under intensive loading,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2 (1969).
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2, Wiley.
V. V. Bolotin, “Theory of natural frequency distribution of elastic bodies and its application to problems of random vibrations,” Prikl. Mekh.,8, No. 4 (1972).
D. L. Anderson and H. E. Lindberg, “Dynamic pulse buckling of cylindrical shells under transient lateral pressures,” AIAA J.,6, No. 4 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 173–178, September–October, 1975.
Rights and permissions
About this article
Cite this article
Kornev, V.M., Markin, A.V. Natural motion density of elastic shells under intensive dynamic loading. J Appl Mech Tech Phys 16, 821–825 (1975). https://doi.org/10.1007/BF00854098
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00854098