Nonconservative Stability by Finite Element

Nonconservative stability of continuous systems has received considerable theoretical attention in recent years. This class of stability problems is examined herein by application of the finite element—Ritz method to the extended Hamilton's principle. The technique is illustrated by the detailed analysis of two examples. The first is the classical problem concerning the stability of a cantilever under follower force excitation. The principal problem is to determine the follower force at which the column will oscillate in an unstable manner (flutter). The second problem is a cantilevered tube containing an inviscid fluid in slug flow. In this example, primary interest is in the fluid velocity at which dynamic instability occurs. Results of both problems, which are presented in graphical or tabular form, or both, clearly demonstrate the power of the methods.