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

Paper Number: 108413

108413 - Slope-Inertia Model for Rotating Timoshenko-Ehrenfest Beams 

The classical Euler-Bernoulli beam theory (EBT) is not adequate in providing accurate bending, buckling, and vibration results when the thickness-to-length ratio of the beam is relatively large. This is because the effect of transverse shear strains, neglected in the classical theory, becomes significant in short and thick beams, and for higher vibration frequencies. In such cases, shear deformation theories provide much more accurate solutions compared to the classical theory. So, for the accurate prediction of the mechanical behaviour of beams, application of Timoshenko-Ehrenfest beam theory is essential. The area of research pertaining to this paper is to study the effect on the beam when it is rotated. Rotating beams are used to model various aerospace and mechanical structures like helicopter blades, wind turbine, gas turbine blades, propeller blades, etc. This paper focuses on the free vibration analysis of axially inhomogeneous and nonuniform rotating beams considering the Timoshenko-Ehrenfest slope-inertia model (TESIM) as the governing equation. The TESIM governing equation is obtained by modifying the rotational term in the kinetic energy expression of the original Timoshenko beam theory. To solve the TESIM equation analytically, it is reduced to an uncoupled second-order differential equation of Sturm-Liouville type with respect to rotation angle due to bending. This simplified equation is then solved to obtain closed-form solutions for some allowable variation of properties along the beam axis. Natural frequencies are then calculated for different material and geometric non-uniformities along the beam axis, using cantilever boundary conditions. A comparison between the results obtained for the reduced equation and the finite element method is carried out. The effect of changing the kinetic energy expression is shown by comparing the natural frequencies obtained from the original TBT and TESIM model.

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, inverse problems and mechanics of metamaterials.

Authors:

Apurva Sunil Rangari Indian Institute of Technology, Kharagpur
Isaac Elishakoff Florida Atlantic University
Korak Sarkar Indian Institute of Technology, Kharagpur