| Abstrakt: |
In the standard theory, the mode masses are multiplied by a mode shape factor to account for the energy of coupled-in-modes. This procedure represents an excellent approximation in the frequency range near the resonance peaks, but it is not exact. If, for instance, a spherical shell is driven by a point force, the stretching modes are not excited directly since the point of attack is a node for these modes; nevertheless, they all become excited because of their coupling with the transverse vibration of the shell. Because of the distributed nature of their excitation, they can be excited with a negative sign. For instance, in the case of a spherical shell at low frequencies, the stretching modes counteract the transverse motion. It is proved in network theory, that coupled systems can be represented by parallel connections of simple tuned circuits with frequency-independent elements, and that, because of the coupling, some of their signs can be negative. Similar results apply to shells. As a consequence, the driving point admittance does exhibit not only sharp antiresonance, but exhibits also some shallow minima. The deviations between the exact and the standard mode solution will be discussed and the frequency response of coupled vibrators will be illustrated by the mean-value method for cylindrical and spherical shells. [This work was sponsored by the Office of Naval Research (Code 474).] [ABSTRACT FROM AUTHOR] |
