Free vibration analysis of pre-twisted rotating FGM beams
- PDF / 891,671 Bytes
- 17 Pages / 547.087 x 737.008 pts Page_size
- 77 Downloads / 261 Views
Free vibration analysis of pre-twisted rotating FGM beams M. N. V. Ramesh • N. Mohan Rao
Received: 10 April 2013 / Accepted: 24 September 2013 / Published online: 11 October 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract The natural frequencies of vibration of a rotating pre-twisted functionally graded cantilever beam are investigated. Rotating cantilever beam with pre-twist made of a functionally gradient material (FGM) consisting of metal and ceramic is considered for the study. The material properties of the FGM beam symmetrically vary continuously in thickness direction from core at mid section to the outer surfaces according to a power-law form. Equations of motion for free vibration are derived using Lagrange’s equation and the natural frequencies are determined using Rayleigh–Ritz method. The effect of parameters such as the pre-twist angle, power law index, hub radius and rotational speed on the natural frequencies of rotating functionally graded pre-twisted cantilever beams are examined through numerical studies and comparison is made with the numerical results obtained using other methods reported in literature. The effect of coupling between chordwise and flapwise bending modes on the natural frequencies has also been investigated.
M. N. V. Ramesh (&) Department of Mechanical Engineering, Nalla Malla Reddy Engineering College, Hyderabad 500088, India e-mail: [email protected] N. Mohan Rao Department of Mechanical Engineering, JNTUK College of Engineering Vizianagaram, Vizianagaram 535003, India e-mail: [email protected]
Keywords Functionally graded beam Rotating pre-twisted beam Natural frequencies Flapwise vibrations Chordwise vibrations
1 Introduction The concept of functionally graded materials (FGM) was originally introduced in the year 1984 in Japan by a group of material science scientists as ultra high temperature resistant materials. Various rotating structures, like turbo machinery, wind blades and aircraft rotary wings are pre-twisted beams that are often subjected to vibration with larger pressure loadings, temperature gradients and thermo elastically induced loadings. Due to the high potentiality of these materials, study of natural frequencies of these structures is important during design and analysis phase for estimating their dynamic behaviour. During the past decade, many researchers have focused on the vibration characteristics of stationary and rotating functionally graded beams employing various methods of analysis. Among them the salient works are presented here. Sankar (2001) found an elasticity solution for transversely loaded functionally graded beam and a simple Euler–Bernoulli beam theory was also developed with the assumption that plane sections remain plane and normal to the beam axis. Aydogdu and Taskin (2007) developed an equation of motion for functionally graded beam by
123
368
using Hamilton principle. In these the Young’s modulus is assumed to vary along the thickness. Higher order shear deformation theories and classical beam theories
Data Loading...
