Divergence instability of multiple-parameter circulatory systems

Abstract

The free vibrations and stability of a discrete linear non-dissipative system subjected to the combined effect of several independent circulatory and conservative loads are studied. Attention is restricted to systems which exhibit only divergence-type instability and are incapable of flutter. Two theorems concerning the basic properties of the characteristic surfaces (loading-frequency relationship) and the stability boundary are established. One of the several other theorems insures that the stability boundary of the corresponding conservative system will always provide a lower bound for the actual stability boundary of the non-conservative system. This particular result is valid for all types of divergence-instability problems, including those which can exhibit flutter after divergence. The theorems established are quite general in the sense that they are valid for all systems in the class considered, without further analytical conditions. Practical implications of the general results are briefly discussed.