Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams; a mechanical solution

This paper deals with enhancing the existing Finite Element formulations through employing basic principles of structural mechanics accompanied with mathematical techniques. Introducing the concept of Basic Displacement Functions (BDFs), the free vibration analysis of rotating tapered beams is studied from a mechanical point of view. It is shown that exact shape functions could be derived in terms of BDFs. The new shape functions turn out to be dependent on the rotational speed, circular frequency, the position of element along the beam and variation of cross-sectional dimensions along the element. Dynamic BDFs are obtained by applying Adomian Modified Decomposition Method (AMDM) to the governing differential equation of motion. Carrying out numerical examples, the competency of the method is verified.

[1]  Richard H. Gallagher,et al.  Matrix dynamic and instability analysis with non-uniform elements , 1970 .

[2]  B. Downs,et al.  Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers , 1977 .

[3]  C.H.J. Fox,et al.  The natural frequencies of a thin rotating cantilever with offset root , 1979 .

[4]  Dewey H. Hodges,et al.  Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method , 1981 .

[5]  Charles E. Smith,et al.  Vibration Modes of Centrifugally Stiffened Beams , 1982 .

[6]  K. B. Subrahmanyam,et al.  Non-linear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects , 1987 .

[7]  A. G. Ulsoy,et al.  Flexural motion of a radially rotating beam attached to a rigid body , 1988 .

[8]  Takashi Yokoyama,et al.  Free vibration characteristics of rotating Timoshenko beams , 1988 .

[9]  T. K. Varadan,et al.  Hierarchical finite element method for rotating beams , 1990 .

[10]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[11]  J. R. Banerjee,et al.  FREE VIBRATION OF CENTRIFUGALLY STIFFENED UNIFORM AND TAPERED BEAMS USING THE DYNAMIC STIFFNESS METHOD , 2000 .

[12]  R. Ganguli.  A Fuzzy Logic System for Ground Based Structural Health Monitoring of a Helicopter Rotor Using Modal Data , 2001 .

[13]  J. R. Banerjee,et al.  Free vibration of sandwich beams using the dynamic stiffness method , 2001 .

[14]  S. Naguleswaran,et al.  Natural frequencies, sensitivity and mode shape details of an Euler-Bernoulli beam with one-step change in cross-section and with ends on classical supports , 2002 .

[15]  Hong Hee Yoo,et al.  DYNAMIC ANALYSIS OF A ROTATING CANTILEVER BEAM BY USING THE FINITE ELEMENT METHOD , 2002 .

[16]  Gang Wang,et al.  Free Vibration Analysis of Rotating Blades With Uniform Tapers , 2004 .

[17]  Ranjan Ganguli,et al.  Helicopter vibration reduction in forward flight with induced-shear based piezoceramic actuation , 2004 .

[18]  Ranjan Ganguli,et al.  Helicopter rotor blade frequency evolution with damage growth and signal processing , 2005 .

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

[20]  J. R. Banerjee,et al.  Free vibration of rotating tapered beams using the dynamic stiffness method , 2006 .

[21]  R. Ganguli,et al.  Wave Propogation Characteristics of Rotating Uniform Euler-Bernoulli Beams , 2006 .

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

[23]  Saudi Arabia,et al.  Effect of tapering on natural frequencies of rotating beams , 2007 .

[24]  Ranjan Ganguli,et al.  Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements , 2007 .

[25]  Ranjan Ganguli,et al.  Free vibration analysis of rotating tapered blades using Fourier-p superelement , 2007 .

[26]  C. Mei,et al.  Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam , 2008 .

[27]  Ranjan Ganguli,et al.  Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams , 2008 .

[28]  Reza Attarnejad,et al.  Application of Differential Transform Method in Free Vibration Analysis of Rotating Non-Prismatic Beams , 2008 .

[29]  Ranjan Ganguli,et al.  New rational interpolation functions for finite element analysis of rotating beams , 2008 .

[30]  Ranjan Ganguli,et al.  Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams , 2009 .

[31]  Reza Attarnejad,et al.  Basic displacement functions in analysis of nonprismatic beams , 2010 .

[32]  M. O. Kaya,et al.  Vibration analysis of a rotating tapered Timoshenko beam using DTM , 2010 .

[33]  Reza Attarnejad,et al.  Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams , 2010 .

[34]  Reza Attarnejad,et al.  Basic displacement functions for centrifugally stiffened tapered beams , 2011 .

[35]  Reza Attarnejad,et al.  Analysis of Non-Prismatic Timoshenko Beams Using Basic Displacement Functions , 2011 .

[36]  R. Attarnejad,et al.  Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams , 2011 .

[37]  Reza Attarnejad,et al.  Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams , 2011 .