Nonlinear vibrations of blade with varying rotating speed

Nonlinear behaviors of thin-walled Euler-Bernoulli beams with varying rotating speed which are attached to a rigid hub are investigated. Centrifugal force, aerodynamic load and the perturbed angular speed due to the inconstant air velocity are considered. The nonlinear factors are involved in displacement-strain relationships. The nonlinear governing partial differential equations of high-speed rotating thin-walled beam are established by using Hamiltonian Principle. Then, the ordinary differential equations of the rotating thin-walled beam are obtained by employing Galekin's approach during which Galekin's modes satisfy corresponding boundary conditions. The four-dimensional nonlinear averaged equations are obtained by applying the method of multiple scales. In this paper, the case of 1∶1 internal resonance is only considered. The results of the numerical simulation show that there exits complicated nonlinear behaviors in thin-walled Euler-Bernoulli beams with varying rotating speed.

[1]  K. M. Liew,et al.  A global continuum Ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in , 1994 .

[2]  Chung-Yi Lin,et al.  Dynamic stability of rotating pre-twisted blades with a constrained damping layer , 2003 .

[3]  H. Yoo,et al.  Flapwise bending vibration analysis of rotating multi-layered composite beams , 2005 .

[4]  Wei Zhang,et al.  Chaotic motion and its control for nonlinear nonplanar oscillations of a parametrically excited cantilever beam , 2005 .

[5]  J. H. Wang,et al.  The influence of a variable friction coefficient on the dynamic behavior of a blade with a friction damper , 1991 .

[6]  M. Yao,et al.  THEORIES OF MULTI-PULSE GLOBAL BIFURCATIONS FOR HIGH-DIMENSIONAL SYSTEMS AND APPLICATION TO CANTILEVER BEAM , 2008 .

[7]  William Carnegie,et al.  Vibrations of Rotating Cantilever Blading: Theoretical Approaches to the Frequency Problem Based on Energy Methods , 1959 .

[8]  Wei Zhang,et al.  Multipulse Shilnikov orbits and Chaotic Dynamics for Nonlinear Nonplanar Motion of a Cantilever Beam , 2005, Int. J. Bifurc. Chaos.

[9]  J. S. Rao,et al.  Vibrations of rotating, pretwisted and tapered blades , 1977 .

[10]  Hong Hee Yoo,et al.  Vibration Analysis of Rotating Pre-Twisted Blades with a Concentrated Mass , 2001 .

[11]  G. L. Anderson,et al.  On the extensional and flexural vibrations of rotating bars , 1975 .

[12]  Lien-Wen Chen,et al.  Vibrational analyses of cracked pre-twisted blades , 1993 .

[13]  Ebrahim Esmailzadeh,et al.  Vibration suppression of rotating beams using time-varying internal tensile force , 2011 .

[14]  M. N. Hamdan,et al.  On the non-linear vibrations of an inextensible rotating arm with setting angle and flexible hub , 2005 .

[15]  T. H. Young,et al.  Dynamic resppnse of a pretwisted, tapered beam with non-constant rotating speed , 1991 .

[16]  L. Librescu,et al.  Thin-Walled Composite Beams: Theory and Application , 2006 .

[17]  Zhang Lin,et al.  Analytical analysis for large-amplitude oscillation of a rotational pendulum system , 2011, Appl. Math. Comput..

[18]  K. M. Liew,et al.  Vibration of pretwisted cantilever trapezoidal symmetric laminates , 1995 .

[19]  Ji-Hwan Kim,et al.  Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectric fiber composites , 2007 .

[20]  M. N. Hamdan,et al.  Nonlinear vibrations and buckling of a flexible rotating beam: A prescribed torque approach , 2007 .

[21]  Ohseop Song,et al.  Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability , 2004 .

[22]  Lien-Wen Chen,et al.  Dynamic Stability of Rotating Blades with Geometric Non-Linearity , 1995 .

[23]  C. W. Lim,et al.  A spiral model for bending of non-linearly pretwisted helicoidal structures with lateral loading , 2003 .

[24]  Ting Rui Liu,et al.  Vibration of Wind Turbine Blade Modeled as Composite Thin-Walled Closed-Section Structure , 2010 .

[25]  Shueei-Muh Lin,et al.  PD control of a rotating smart beam with an elastic root , 2008 .

[26]  J. S. Rao,et al.  Coupled bending-torsion vibrations of rotating blades of asymmetric aerofoil cross section with allowance for shear deflection and rotary inertia by use of the Reissner method , 1981 .

[27]  Liviu Librescu,et al.  Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams , 2003 .

[28]  Chen Lien-Wen,et al.  Vibration and stability of cracked thick rotating blades , 1988 .

[29]  S. P. Machado.  Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation , 2008 .

[30]  J. S. Rao,et al.  Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method , 1981 .

[31]  J. B. Yang,et al.  Dynamic modelling and control of a rotating Euler–Bernoulli beam , 2004 .

[32]  J. S. Rao,et al.  Solution of the equations of motion of coupled-bending bending torsion vibrations of turbine blades by the method of ritz-galerkin , 1970 .

[33]  N. K. Chandiramani.  Active control of a piezo-composite rotating beam using coupled plant dynamics , 2010 .

[34]  W. Zhang,et al.  Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed , 2010 .

[35]  M. Seetharama Bhat,et al.  A new super convergent thin walled composite beam element for analysis of box beam structures , 2004 .

[36]  R. Sampaio,et al.  A study on the dynamics of rotating beams with functionally graded properties , 2009 .

[37]  J. S. Rao,et al.  Coupled bending-torsional vibrations of rotating cantilever blades—method of polynomial frequency equation , 1977 .

[38]  Sunil K. Sinha,et al.  Dynamic characteristics of a flexible bladed-rotor with Coulomb damping due to tip-rub , 2004 .

[39]  W. Zhang,et al.  Using the extended Melnikov method to study the multi-pulse global bifurcations and chaos of a cantilever beam , 2009 .

[40]  Evgeny V. Morozov,et al.  Thin-walled composite beams , 2013 .

[41]  Josip Brnić,et al.  Large rotation analysis of elastic thin-walled beam-type structures using ESA approach , 2003 .

[42]  A. D. Sahasrabudhe,et al.  Vibration analysis and optimal control of rotating pre-twisted thin-walled beams using MFC actuators and sensors , 2009 .

[43]  Mohammad Hosseini,et al.  Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method , 2007 .