Session: 02-01-02: Dynamic Loads, Response, Vibration and Alleviation of Aerospace Structures - II

Paper Number: 108468

108468 - Free Vibration Analysis of Rotating Rayleigh Cantilever Beam Using P-Type Finite Element Method 

Rotating elastic beams are widely used for modelling various mechanical structural elements like turbine blades, helicopter blades, propellers, satellite solar panel frame, etc. In this paper we investigate the free vibration of rotating non-uniform cantilever beams by incorporating Rayleigh beam theory. Rayleigh beam theory considers the rotating inertia term which is neglected in Euler-Bernoulli beam theory (EBT), thus providing more accurate results. Moreover, the fact that Rayleigh beam theory does not consider shear deformation effect, makes it computationally cheaper than Timoshenko beam theory which produces two coupled second order differential equations. In this paper, the governing equation for rotating Rayleigh beams has been solved numerically with the help of polynomial type finite element method (p-FEM). The p-FEM is a special type of finite element analysis which uses the whole beam as one element and that makes it perfect for analysing non-uniformity. In conventional Hermite cubic polynomial type FEM (h-FEM) elements, the mass and stiffness matrix are considered uniform over the element. Hence, analysing non-uniform beam takes a large number of elements for convergence of result. The finite element code has been written in the Mathematica. This code takes the mass per unit length and flexural stiffness distributions as a function of the length of the beam as the input, and determines the natural frequencies and mode shapes. We have compared the results of free vibrational analysis for Euler Bernoulli beam and Rayleigh beam, and significant variations are found for shorter and thicker beams. To account for the effect of damping, a factor known as Rayleigh damping has been introduced in the solution. The following cases such as gravity loaded beam, axially loaded beam has also been incorporated in the code. The Abaqus modelling has also been done to match with our results.

Presenting Author: Korak Sarkar Indian Institute of Technology, Kharagpur

Presenting Author Biography: Dr. Korak Sarkar is an Assistant Professor in the Department of Mechanical Engineering at Indian Institute of Technology, Kharagpur, India. He earned his PhD degree from the Department of Aerospace Engineering at Indian Institute of Science, Bangalore. His dissertation was on inverse problems in free vibration analysis of rotating and non-rotating beams and its application to random eigenvalue characterization. He also worked as a SERB Indo-US Postdoctoral Research Fellow in the Aerospace Engineering Department at Georgia Tech, USA, working with Professor Dewey Hodges. His research interests are in structural dynamics, solid mechanics, vibration of rotor blades and mechanics of metamaterials.

Authors:

Dipannoy Dhar Indian Institute of Technology, Kharagpur
Korak Sarkar Indian Institute of Technology, Kharagpur