Closed-form solutions for rotating cantilever non-uniform Rayleigh beams
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Conference Proceeding
Publication/Event/Conference Title
American Helicopter Society International 3rd Asian Australian Rotorcraft Forum and the 8th Australian Pacific Vertiflite Conference on Helicopter Technology 2014
Publication Status
Version of Record
Abstract
In this paper, we investigate the free vibration of non-uniform rotating Rayleigh cantilever beams. Rayleigh beam accounts for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. We show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for rotating Rayleigh beams. An inverse problem approach is used to find an infinite number of rotating Rayleigh beams with various mass per unit length variations and flexural stiffness distributions, which share the same fundamental frequency. The derived flexural stiffness and mass polynomial functions can serve as test functions for numerical methods. The functions can also be used to design Rayleigh beams having a pre-specified fundamental natural frequency. Examples of such beams with rectangular cross section are presented and have been compared with those derived using the Euler-Bernoulli beam theory.
First Page
90
Last Page
97
Publication Date
1-1-2014
Recommended Citation
Sarkar, Korak; Ganguli, Ranjan; and Elishakoff, Isaac, "Closed-form solutions for rotating cantilever non-uniform Rayleigh beams" (2014). Faculty Scholarship. 327.
https://digitalcommons.fau.edu/faculty_papers/327