Nonlinear Dynamics of the High-Speed Rotating Plate

High speed rotating blades are crucial components of modern large aircraft engines. The rotating blades under working condition frequently suffer from the aerodynamic, elastic and inertia loads, which may lead to large amplitude nonlinear oscillations. This paper investigates nonlinear dynamic responses of the blade with varying rotating speed in supersonic airflow. The blade is simplified as a pre-twist and presetting cantilever composite plate. Warping effect of the rectangular cross-section of the plate is considered. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic equations of motion for the plate are derived by using Hamilton’s principle. Galerkin approach is applied to discretize the partial differential governing equations of motion to ordinary differential equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom averaged equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. Based on the averaged equation, numerical simulation is used to analyze the influence of the perturbation rotating speed on nonlinear dynamic responses of the blade. Bifurcation diagram, phase portraits, waveforms and power spectrum prove that periodic motion and chaotic motion exist in nonlinear vibration of the rotating cantilever composite plate.

[1]  H. Yoo,et al.  Free Vibration Analysis of Rotating Cantilever Plates , 2002 .

[2]  Tai-Yan Kam,et al.  Quasi-static buckling and first-ply failure loads of shear web reinforced glass-fabric composite wind blades , 2017 .

[3]  Paul M. Weaver,et al.  A zero torsional stiffness twist morphing blade as a wind turbine load alleviation device , 2013 .

[4]  Wen Rong Wang,et al.  The dynamic analysis of nonuniformly pretwisted Timoshenko beams with elastic boundary conditions , 2001 .

[5]  Joachim Belz,et al.  Numerical investigation of nonlinear fluid-structure interaction in vibrating compressor blades , 2001 .

[6]  Liqun Chen,et al.  Nonlinear free transverse vibrations of in-plane moving plates: Without and with internal resonances , 2011 .

[7]  Dingguo Zhang,et al.  Free vibration analysis of rotating functionally graded rectangular plates , 2016 .

[8]  Yueming Li,et al.  Nonlinear vibration of rotating pre-deformed blade with thermal gradient , 2016 .

[9]  Mauro Hugo Mathias,et al.  The dynamic analysis of rotors mounted on composite shafts with internal damping , 2017 .

[10]  T. H. Young,et al.  Coriolis Effect on the Vibration of a Cantilever Plate With Time-Varying Rotating Speed , 1992 .

[11]  P. Neittaanmäki,et al.  On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability , 2016 .

[12]  Wenhu Huang,et al.  Nonlinear coupled dynamics of flexible blade–rotor–bearing systems , 2010 .

[13]  Hassan Haddadpour,et al.  Aero-thermoelastic stability of functionally graded plates , 2007 .

[14]  Sunil K. Sinha,et al.  Vibration analysis of composite airfoil blade using orthotropic thin shell bending theory , 2017 .

[15]  Holt Ashley,et al.  Piston Theory-A New Aerodynamic Tool for the Aeroelastician , 1956 .

[16]  M. Shariyat,et al.  Enhanced model for nonlinear dynamic analysis of rectangular composite plates with embedded SMA wires, considering the instantaneous local phase changes , 2014 .

[17]  R. Ganguli,et al.  Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams , 2014 .

[18]  Earl H. Dowell,et al.  Limit Cycle Oscillations of a Cantilevered Wing in Low Subsonic Flow , 1999 .

[19]  Arthur W. Leissa,et al.  Rotating Blade Vibration Analysis Using Shells , 1982 .

[20]  M. Yao,et al.  Nonlinear vibrations of blade with varying rotating speed , 2012 .

[21]  Zhiping Qiu,et al.  Nonlinear flutter analysis of stiffened composite panels in supersonic flow , 2010 .

[22]  Ji-Hwan Kim,et al.  Vibration characteristics of initially twisted rotating shell type composite blades , 2004 .

[23]  Hui Ma,et al.  Vibration characteristics analysis of rotating shrouded blades with impacts , 2016 .

[24]  Kivanc Ekici,et al.  Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery , 2008 .

[25]  Jerzy Warminski,et al.  Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle , 2014 .

[26]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[27]  Jian Zhou,et al.  Integrated analysis on static/dynamic aeroelasticity of curved panels based on a modified local piston theory , 2014 .

[28]  M. A. Kouchakzadeh,et al.  Panel flutter analysis of general laminated composite plates , 2010 .

[29]  Jao-Hwa Kuang,et al.  Variation in the stability of a rotating blade disk with a local crack defect , 2006 .

[30]  S. Hosseini-Hashemi,et al.  Aeroelastic behavior of cantilevered rotating rectangular plates , 2011 .

[31]  Jia Sun,et al.  Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory , 2013 .

[32]  Hui Ma,et al.  Vibration response comparison of twisted shrouded blades using different impact models , 2017 .

[33]  Earl H. Dowell,et al.  Limit cycle oscillation of a fluttering cantilever plate , 1991 .

[34]  H. Al-Qahtani,et al.  Vibration Control of Rotating Blades Using Root-Embedded Piezoelectric Materials , 2015 .

[35]  Jia Sun,et al.  General shell model for a rotating pretwisted blade , 2013 .

[36]  Fangqi Chen,et al.  Local bifurcation analysis of a rotating blade , 2016 .

[37]  Sunil K. Sinha,et al.  Natural frequencies of a pre-twisted blade in a centrifugal force field , 2011 .