Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method

Abstract

The modified decomposition method is applied to analyze the transverse vibrations of tapered rotating beams incorporating both axial centrifugal stiffening and flexible end constraints. Unlike prior analyses relying upon a power series expansion about the left end constraint, we instead expand the solution for the transverse deflection about the interval midpoint, which has significant advantages including an increased rate of convergence and readily adaptation to the Robin-type boundary conditions. The modified decomposition method facilitates systematic solution of the mathematical model including parametric simulations where the boundary conditions can be varied without resolving the original equation.

KEYWORDS:

• Rotating beams
• centrifugal stiffening
• eigenvalue problem
• mode shape
• Adomian decomposition method

Mathematics Subject Classification:

• 34B09 74K10

Disclosure statement

No potential conflict of interest was provided by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11772203).