FREE VIBRATION OF CENTRIFUGALLY STIFFENED UNIFORM AND TAPERED BEAMS USING THE DYNAMIC STIFFNESS METHOD

✍ Scribed by J.R. BANERJEE

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 249 KB
• Volume: 233
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2855

✦ Synopsis

Starting from the governing di!erential equations of motion in free vibration, the dynamic sti!ness matrix of a uniform rotating Bernoulli}Euler beam is derived using the Frobenius method of solution in power series. The derivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising from the rotational motion. This makes the general assembly of dynamic sti!ness matrices of several elements possible so that a non-uniform (or tapered) rotating beam can be analyzed for its free-vibration characteristics by idealizing it as an assemblage of many uniform rotating beams. The application of the derived dynamic sti!ness matrix is demonstrated by investigating the free-vibration characteristics of uniform and non-uniform (tapered) rotating beams with particular reference to the Wittrick}Williams algorithm. The results from the present theory are compared with published results. It is shown that the proposed dynamic sti!ness method o!ers an accurate and e!ective method of free-vibration analysis of rotating beams.