DYNAMIC MODELLING AND STABILITY ANALYSIS OF AXIALLY OSCILLATING CANTILEVER BEAMS

✍ Scribed by S.H. HYUN; H.H. YOO

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 204 KB
• Volume: 228
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2427

✦ Synopsis

Dynamic stability of an axially oscillating cantilever beam is investigated in this paper. Equations of motion for the axially oscillating beam are derived and transformed into dimensionless forms. The equations include harmonically oscillating parameters which are related to the motion-induced sti!ness variation. Stability diagrams of the "rst and the second order approximate solutions are obtained by using the multiple scale perturbation method. The stability diagrams show that there exist signi"cant di!erence between the "rst and the second order approximate solutions. It is also found that relatively large unstable regions exist around the "rst bending natural frequency, twice the "rst bending natural frequency, and twice the second being natural frequency. The validity of the stability diagram is veri"ed by direct numerical integrations of the equations of motion of the system.