Vibration analysis of a rotating tapered Timoshenko beam using DTM

In this study, free vibration analysis of a rotating, tapered Timoshenko beam that undergoes flapwise bending vibration is performed. Derivation of the equations of motion of a rotating, uniform Timoshenko beam was made step by step in a previous work of the authors. Therefore, differential equations of motion are given directly without making any derivations in this paper. The parameters for the hub radius, rotational speed, taper ratio, rotary inertia, shear deformation and slenderness ratio are incorporated into the equations of motion. In the solution part, an efficient mathematical technique called the Differential Transform Method, DTM, is used. Finally, using the computer package Mathematica, the natural frequencies are calculated and the effects of the incorporated parameters are examined. Moreover, numerical examples are solved to make comparisons with the existing results in open literature and it is observed that the agreement between the results is very good.

[1]  Ozge Ozdemir Ozgumus,et al.  Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: Part I , 2007 .

[2]  Ozge Ozdemir Ozgumus,et al.  Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: part II. Results of flutter stability and vibration analysis of a hingeless helicopter blade in hover , 2007 .

[3]  S. Çatal.  Analysis of free vibration of beam on elastic soil using differential transform method , 2006 .

[4]  R. E. Rossi,et al.  Numerical Experiments on Vibrating, Linearly Tapered Timoshenko Beans , 1993 .

[5]  Sen-Yung Lee,et al.  Bending frequency of a rotating Timoshenko beam with general elastically restrained root , 1993 .

[6]  Metin O. Kaya,et al.  Free vibration analysis of a rotating Timoshenko beam by differential transform method , 2006 .

[7]  A. I. Martin.  Some Integrals Relating to the Vibration of a Cantilever Beam and Approximation for the Effect of Taper on Overtone Frequencies , 1956 .

[8]  Metin O. Kaya,et al.  Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method , 2006 .

[9]  N. M. Auciello,et al.  A general solution for dynamic response of axially loaded non-uniform Timoshenko beams , 2004 .

[10]  J. S. Rao.  The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper , 1965 .

[11]  Ibrahim Özkol,et al.  Solution of boundary value problems for integro-differential equations by using differential transform method , 2005, Appl. Math. Comput..

[12]  Hejun Du,et al.  A Power Series Solution For Vibration Of A Rotating Timoshenko Beam , 1994 .

[13]  Shueei Muh Lin,et al.  Bending Vibrations of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root , 1994 .

[14]  J. R. Banerjee,et al.  Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened timoshenko beams , 2001 .

[15]  R. S. Gupta,et al.  FINITE ELEMENT VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS , 2001 .

[16]  Cha'o-Kuang Chen,et al.  Application of differential transformation to transient advective-dispersive transport equation , 2004, Appl. Math. Comput..

[17]  A. Leung,et al.  Dynamic stiffness analysis of non-uniform timoshenko beams , 1995 .

[18]  Yehia A. Khulief,et al.  Further results for modal characteristics of rotating tapered Timoshenko beams , 1999 .

[19]  J. R. Banerjee,et al.  Energy Expressions for Rotating Tapered Timoshenko Beams , 2002 .

[20]  H. H. Mabie,et al.  Transverse Vibrations of Double‐Tapered Cantilever Beams , 1972 .

[21]  F. Raffa,et al.  Gyroscopic Effects Analysis in the Lagrangian Formulation of Rotating Beams , 1999 .

[22]  Furio Vatta,et al.  An analytical approach to the dynamics of rotating shafts , 1992 .

[23]  Ozge Ozdemir Ozgumus,et al.  Flapwise bending vibration analysis of double tapered rotating Euler–Bernoulli beam by using the differential transform method , 2006 .