Vibrational characteristics of a long and very flexible rotating fixed-free beam

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to digital@library.tamu.edu, referencing the URI of the item.Includes bibliographical references (leaves 37-38).Issued also on microfiche from Lange Micrographics.The differential eigenvalue problem of a long and very flexible rotating fixed-free beam is studied. This kind of system produces a singular perturbation equation with a turning point. The perturbation factor arises because of the division of the small bending stiffness value by the large value of the length to the power of four. A translation of the beam along one of the rotating axis was required in order to solve the reduced problem, in which the perturbing factor is set to zero. A formal composite solution is proposed and the eigenvalue problem is solved complementing the asymptotic method with a numerical method. The eigenfunctions are found to depend upon even integer Legendre polynomials and the Airy functions. The assumed modes method is used in order to compare the approximate solutions