DYNAMIC STIFFNESS FORMULATION AND FREE VIBRATION ANALYSIS OF CENTRIFUGALLY STIFFENED TIMOSHENKO BEAMS

✍ Scribed by J.R. BANERJEE

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 378 KB
• Volume: 247
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.3716

✦ Synopsis

The dynamic sti!ness matrix of a centrifugally sti!ened Timoshenko beam has been developed and used to carry out a free vibration analysis. The governing di!erential equations of motion of the beam in free vibration are derived using Hamilton's principle and include the e!ect of an arbitrary hub radius. For harmonic oscillation the derivation leads to two di!erent (but of similar form) fourth-order ordinary di!erential equations with variable coe$cients that govern the amplitudes of bending displacement and bending rotation respectively. An outboard force at the end of the beam is taken into account which makes possible the free vibration analysis of rotating non-uniform or tapered Timoshenko beams. Using the Frobenius method of series solution and imposing boundary conditions, the dynamic sti!ness matrix, which relates amplitudes of harmonically varying forces with the amplitudes of harmonically varying displacements at the ends of the element, is formulated. Applying the Wittrick}Williams algorithm to the resulting dynamic sti!ness matrix the natural frequencies of a few carefully chosen illustrative examples are obtained. The results are compared with those available in the literature.