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An averaging theorem for distributed conservative systems and its application to von Kármán’s equations. (English. Russian original) Zbl 0722.73039

J. Appl. Math. Mech. 53, No. 2, 150-157 (1989); translation from Prikl. Mat. Mekh. 53, No. 2, 196-205 (1989).
Summary: An averaging theorem, of the Krylov-Bogolyubov-Mitropols’kij type, is proved for oscillatory processes in spatially-multidimensional conservative systems. Von Kármán’s equations are considered as an example.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
34C29 Averaging method for ordinary differential equations
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