L.B.Lerman Joint non-stationary vibrations of mechanical systems having the shape of spherical cupolas on basic cylindrical shells |
Acoustic bulletin, Vol. 4 ¹ 2, (2001) |
| Within the frameworks of the theory of shells the problems of determination of the stress-strain state for the elastic deformable systems, non-stationary oscillating under the impulsive distributed surface loadings action, are considered. The dynamic problem solutions are presented as decompositions of the desired values to series with respect to special systems of the orthogonal vector-functions. These functions describe the stationary states, arising under the harmonic system elements oscillations of a general frequency in absence of the external and boundary loadings, and are built as the solutions of the so called "non-classic problems on the eigen-values". In doing so, the last determine the eigen-oscillation frequency spectrum for the system as a whole. Such an approach allows to account within the single algorithm the diverse nature of the physical system elements interaction during the joint non-stationary deformation. The general convergence estimations of decompositions with respect to systems of the vector-functions are represented, and the particular computation examples are offered, allowing to put together a conception of their convergence speed. On the basis of the general representation of the motion equations solutions the asymptotic estimations are obtained for big and small (with respect to the basic oscillations period of mechanical system) time intervals under the impulsive loadings of long and short duration. The general problem solution scheme is shown for mechanical systems, consisting of the shells of revolution with common axis. The potentials of developed algorithms are illustrated by numerical examples for the flat spherical cupolas, connected with supporting cylindrical shells of the smaller radius. |
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KEY WORDS: transient oscillation, pulse load, the elastic deformable systems, thin-walled shells, deformable supports |
| TEXT LANGUAGE: Russian |