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

• Published in: Journal of sound and vibration Vol. 233; no. 5; pp. 857 - 875
• Main Author: BANERJEE, J.R.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 22-06-2000; Elsevier
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Structural acoustics and vibration; Stiffness matrix; Equation of motion; Differential equation; Free vibration; Axial force; Theoretical study; Centrifugal force; Angular velocity; Power series; Uniformity; Rotating beam(mechanics)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1999.2855

Starting from the governing differential equations of motion in free vibration, the dynamic stiffness 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 stiffness 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 stiffness 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 stiffness method offers an accurate and effective method of free-vibration analysis of rotating beams.