A duality in a non-conservative system

✍ Scribed by G.L. Anderson

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 365 KB
• Volume: 41
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(75)80093-9

✦ Synopsis

A mathematical connection between two physically distinct non-conservative stability problems is described. It is shown by means of the principle of complementary energy that the stability problem associated with a uniform cantilever beam subjected to a tangential force and carrying a tip mass at its free end is the dual problem for a uniform beam subjected to a tangential force at its free end and having transverse and torsional spring constraints at its supported end. Both systems are proved to possess exactly the same eigenfrequencies and critical flutter loads upon proper interpretation of the transverse and rotary inertia parameters for the former and the torsional and transverse spring compliance parameters for the latter.