scholarly journals Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

2020 ◽  
Vol 41 (12) ◽  
pp. 1861-1880
Author(s):  
Li Ma ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Dongxing Cao
Keyword(s):  
Aerodynamic Force ◽  
Shear Deformation Theory ◽  
Phase Portraits ◽  
Cantilever Plate ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Rotating Speed ◽  
Geometric Relationship ◽  
Asymptotic Perturbation ◽  
Nonlinear Geometric

AbstractTurbo-machineries, as key components, have a wide utilization in fields of civil, aerospace, and mechanical engineering. By calculating natural frequencies and dynamical deformations, we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies. In this paper, the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed. The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations, including the centrifugal force and the aerodynamic force. In view of the first-order shear deformation theory and von-Kármán nonlinear geometric relationship, the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle. The second-order ordinary differential equations are acquired by the Galerkin approach. With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance, the averaged equation is derived by the asymptotic perturbation methodology. Bifurcation diagrams, phase portraits, waveforms, and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.

scholarly journals A Novel Aerodynamic Force and Flutter of the High-Aspect-Ratio Cantilever Plate in Subsonic Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Li Ma ◽  
Minghui Yao ◽  
Wei Zhang ◽  
Kai Lou ◽  
Dongxing Cao ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Subsonic Flow ◽  
Aerodynamic Force ◽  
Limit Cycle Oscillation ◽  
Cantilever Plate ◽  
Dynamical Equations ◽  
Ansys Fluent ◽  
Cycle Oscillation ◽  
Geometric Relationship

This paper focuses on the derivation of the aerodynamic force for the cantilever plate in subsonic flow. For the first time, a new analytical expression of the quasi-steady aerodynamic force related to the velocity and the deformation for the high-aspect-ratio cantilever plate in subsonic flow is derived by utilizing the subsonic thin airfoil theory and Kutta-Joukowski theory. Results show that aerodynamic force distribution obtained theoretically is consistent with that calculated by ANSYS FLUENT. Based on the first-order shear deformation and von Karman nonlinear geometric relationship, nonlinear partial differential dynamical equations of the high-aspect-ratio plate subjected to the aerodynamic force are established by using Hamilton’s principle. Galerkin approach is applied to discretize the governing equations to ordinary differential equations. Numerical simulation is utilized to investigate the relation between the critical flutter velocity and some parameters of the system. Results show that when the inflow velocity reaches the critical value, limit cycle oscillation occurs. The aspect ratio, the thickness, and the air damping have significant impact on the critical flutter velocity of the thin plate.

Vibration Characteristics Analysis of the Rotating Blade Based on a Polynomial Aerodynamic Force

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Li Ma ◽  
Ming Ming Zhang ◽  
Wei Zhang
Keyword(s):  
Shear Deformation ◽  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Rotating Blade ◽  
Characteristics Analysis ◽  
Method Effects ◽  
Geometric Relationship ◽  
Nonlinear Geometric

In this paper, aerodynamic expressions in forms of the series and the polynomial for a blade with low speed in low pressure compressor are deduced by numerical simulation. Considering shear deformation and cross-section warping effect, the blade is simplified as a pre-twist, pre-setting rotating cantilever plate, which subjected to the aerodynamic force and the centrifugal force. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic equation of the rotating blade is derived by using Hamilton principle. Equations of motion are converted into a series of ordinary differential equations using Galerkin method. The dynamic frequency and the dynamic deformation of the blade are explored and contrasted with results obtained by finite element method. Effects of parameters on vibration characteristics of the blade under different rotation speed are analyzed. Results show that the explicit expression of the aerodynamic force for the blade has a good applicability.

Simulation and Experiment Analyses on Resonance for a Rotor System With Elastic Supports

2007 ◽  
Author(s):  
Qingkai Han ◽  
Li Wang ◽  
Hongliang Yao ◽  
Bangchun Wen
Keyword(s):  
Rotor System ◽  
Dynamical Equations ◽  
Interesting Phenomenon ◽  
Nonlinear Dynamical ◽  
Elastic Supports ◽  
Rotating Speed ◽  
Frequency Capture ◽  
Resonance Vibrations ◽  
Simulation And Experiment ◽  
Pass Through

There exist different vibration patterns when a rotor system runs up and down through its critical speed, in one of them, is the interesting phenomenon called frequency capture. Based on a specially designed rotor system which is supported by elastic supports, the resonance vibrations of frequency capture and pass-through are discussed both in time and frequency domains. The nonlinear dynamical equations are described in details for the system. The vibrations of capture, when the rotating speed is locked, are compared with normal pass-through by numerical simulations and experiments. Also the instantaneous displacement trajectories, 3D FFT waterfalls and phase space portraits are calculated and demonstrated for the above two resonance vibrations. In addition, the periodical motions are discussed for capture motions using both amplitude spectra and pseudo-Poincare mappings of simulation and experiment data.

scholarly journals Nonlinear Dynamics of the High-Speed Rotating Plate

2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
Minghui Yao ◽  
Li Ma ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamic ◽  
Composite Plate ◽  
High Speed ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
Partial Differential ◽  
Rotating Speed ◽  
Rotating Blades

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.

scholarly journals Nonlinear and Dual-Parameter Chaotic Vibrations of Lumped Parameter Model in Blisk under Combined Aerodynamic Force and Varying Rotating Speed

2021 ◽  
Author(s):  
W. Zhang ◽  
L. Ma ◽  
Y. F. Zhang ◽  
K. Behdinan
Keyword(s):  
Multiple Scales ◽  
Aerodynamic Force ◽  
Lumped Parameter Model ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Mode Localization ◽  
Rotating Speed ◽  
Chaotic Vibrations ◽  
Lumped Parameter ◽  
Parametric And External Excitations

Abstract In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for the blisk structure with the lumped parameter model under combined the aerodynamic force and varying rotating speed. The varying rotating speed and aerodynamic force are respectively simplified to the parametric and external excitations. The nonlinear governing equations of motion for the rotating blisk are established by using Hamilton’s principle. The free vibration and mode localization phenomena are studied for the tuning and mistuning blisks. Due to the mistuning, the periodic characteristics of the blisk structure are destroyed and uniform distribution of the energy is broken. It is found that there is a positive correlation between the mistuning variable and mode localization factor to exhibit the large vibration of the blisk in a certain region. The method of multiple scales is applied to derive four-dimensional averaged equations of the blisk under 1:1 internal and principal parametric resonances. The amplitude-frequency response curves of the blisk are studied, which illustrate the influence of different parameters on the bandwidth and vibration amplitudes of the blisk. Lyapunov exponent, bifurcation diagrams, phase portraits, waveforms and Poincare maps are depicted. The dual-parameter Lyapunov exponents and bifurcation diagrams of the blisk reveal the paths leading to the chaos. The influences of different parameters on the bifurcation and chaotic vibrations are analyzed. The numerical results demonstrate that the parametric and external excitations, rotating speed and damping determine the occurrence of the chaotic vibrations and paths leading to the chaotic vibrations in the blisk.

Dynamic Loading on Turbofan Blades Due to Bird-Strike

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Sunil K. Sinha ◽  
Kevin E. Turner ◽  
Nitesh Jain
Keyword(s):  
Dynamic Loading ◽  
Time History ◽  
Material Model ◽  
Bird Strike ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
History Of ◽  
Measured Strain ◽  
Dynamic Loading Condition ◽  
Fan Blade

In the present paper, a hydrodynamic bird material model made up of water and air mixture is developed, which produces good correlation with the measured strain-gauge test data in a panel test. This parametric bird projectile model is used to generate the time-history of the transient dynamic loads on the turbofan engine blades for different size birds impacting at varying span locations of the fan blade. The problem is formulated in 3D vector dynamics equations using a nonlinear trajectory analysis approach. The analytical derivation captures the physics of the slicing process by considering the incoming bird in the shape of a cylindrical impactor as it comes into contact with the rotating fan blades modeled as a pretwisted plate with a camber. The contact-impact dynamic loading on the airfoil produced during the bird-strike is determined by solving the coupled nonlinear dynamical equations governing the movement of the bird-slice in time-domain using a sixth-order Runge-Kutta technique. The analytically predicted family of load time-history curves enables the blade designer to readily identify the critical impact location for peak dynamic loading condition during the bird-ingestion tests mandated for certification by the regulatory agencies.

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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