EIGENVALUE ANALYSIS FOR THE OPERATOR IN PANEL FLUTTER PROBLEMS

The basic problem which is dealt with in the overwhelming majority of studies devoted to panel flutter of plates is to determine the critical flow velocity. As a rule, this problem is reduced to finding the least (in magnitude) eigenvalue of a non-self-adjoint boundary value problem. But it is noted as early as in [1] that this is not sufficient in some cases, this statement is confirmed in some subsequent publications (e.g., see [2]). However, so far the problem of properties of eigenvalues in panel flutter problems has not been staled in the general case. In the present paper, this gap is partly filled up. Some general properties of eigenvalues in flutter problems for plates and shallow spherical shells of revolution are established. Our study is based on the results of [3,4].