Routes to Synchronization in a pitch-plunge aeroelastic system with coupled structural and aerodynamic nonlinearities

2021 ◽  
pp. 103766
Author(s):  
Sai Vishal ◽  
Ashwad Raaj ◽  
Chandan Bose ◽  
Venkatramani J.
Keyword(s):  
Aeroelastic System

scholarly journals A Combined Energy Method for Flutter Instability Analysis of Weakly Damped Panels in Supersonic Airflow

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1090
Author(s):  
Xiaochen Wang ◽  
Zhichun Yang ◽  
Guiwei Zhang ◽  
Xinwei Xu
Keyword(s):  
Energy Balance ◽  
Energy Method ◽  
Plate Theory ◽  
Dynamic Pressure ◽  
Physical Nature ◽  
Aeroelastic System ◽  
Dissipation Energy ◽  
Supersonic Airflow ◽  
Flutter Instability ◽  
Modal Damping

A combined energy method is proposed to investigate the flutter instability characteristics of weakly damped panels in the supersonic airflow. Based on the small damping assumption, the motion governing partial differential equation (PDE) of the panel aeroelastic system, is built by adopting the first-order piston theory and von Karman large deflection plate theory. Then by applying the Galerkin procedure, the PDE is discretized into a set of coupled ordinary differential equations, and the system reduced order model (ROM) with two degrees of freedom is obtained. Considering that the panel aeroelastic system is non-conservative in the physical nature, and assuming that the panel exhibits a single period oscillation on the flutter occurrence, the non-conservative energy balance principle is applied to the linearized ROM within one single oscillation period. The obtained result shows that the ROM modal coordinate amplitudes ratio is regulated by the modal damping coefficients ratio, though each modal damping coefficient is small. Furthermore, as the total damping dissipation energy can be eliminated due to its smallness, the He’s energy balance method is applied to the undamped ROM, therefore the critical non-dimensional dynamic pressure on the flutter instability occurrence, and the oscillation circular frequency amplitude relationship (linear and nonlinear form) are derived. In addition, the damping destabilization paradoxical influence on the system flutter instability is investigated. The accuracy and efficiency of the proposed method are validated by comparing the results with that obtained by using Routh Hurwitz criteria.

scholarly journals Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

2016 ◽  
Author(s):  
L. Salles ◽  
M. Vahdati
Keyword(s):  
Numerical Models ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Mode Shapes ◽  
Minimal Amount ◽  
Aeroelastic System ◽  
Cpu Time ◽  
Influence Coefficients ◽  
Non Linear ◽  
The Time Domain

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Licai Wang ◽  
Yudong Chen ◽  
Chunyan Pei ◽  
Lina Liu ◽  
Suhuan Chen
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Critical Point ◽  
Control Parameter ◽  
Eigenvalue Problems ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
State Matrix ◽  
Aeroelastic System ◽  
Center Manifold Reduction

Abstract The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presented methods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.

Investigating amplitude death in a coupled nonlinear aeroelastic system

2021 ◽  
Vol 129 ◽  
pp. 103659
Author(s):  
Ashwad Raaj ◽  
Sirshendu Mondal ◽  
Venkatramani Jagdish
Keyword(s):  
Amplitude Death ◽  
Aeroelastic System

Propagation of Parametric Uncertainties in a Nonlinear Aeroelastic System Using an Improved Adaptive Sparse Grid Quadrature Routine

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Harshini Devathi ◽  
Sunetra Sarkar
Keyword(s):  
Basis Functions ◽  
Sparse Grid ◽  
Parametric Uncertainties ◽  
Relative Importance ◽  
Stochastic Response ◽  
Aeroelastic System ◽  
Accelerated Convergence ◽  
Aerodynamic Parameters ◽  
Stall Flutter ◽  
Sparse Grid Quadrature

A novel uncertainty quantification routine in the genre of adaptive sparse grid stochastic collocation (SC) has been proposed in this study to investigate the propagation of parametric uncertainties in a stall flutter aeroelastic system. In a hypercube stochastic domain, presence of strong nonlinearities can give way to steep solution gradients that can adversely affect the convergence of nonadaptive sparse grid collocation schemes. A new adaptive scheme is proposed here that allows for accelerated convergence by clustering more discretization points in regimes characterized by steep fronts, using hat-like basis functions with nonequidistant nodes. The proposed technique has been applied on a nonlinear stall flutter aeroelastic system to quantify the propagation of multiparametric uncertainty from both structural and aerodynamic parameters. Their relative importance on the stochastic response is presented through a sensitivity analysis.

Instability of Heated Panels in Supersonic Air Flow

2008 ◽  
Vol 33-37 ◽  
pp. 1101-1108
Author(s):  
Zhi Chun Yang ◽  
Wei Xia
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Static Stability ◽  
Static Deformation ◽  
Limit Cycle Oscillation ◽  
Aerodynamic Load ◽  
Aeroelastic System ◽  
Aerodynamic Pressure ◽  
The Stability

An investigation on the stability of heated panels in supersonic airflow is performed. The nonlinear aeroelastic model for a two-dimensional panel is established using Galerkin method and the thermal effect on the panel stiffness is also considered. The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel. The static and dynamic stabilities for flat panels are studied using Lyapunov indirect method and the stability boundary curve is obtained. The static deformation of a post-buckled panel is then calculated and the local stability of the post-buckling equilibrium is analyzed. The limit cycle oscillation of the post-buckled panel is simulated in time domain. The results show that a two-mode model is suitable for panel static stability analysis and static deformation calculation; but more than four modes are required for dynamic stability analysis. The effects of temperature elevation and dimensionless parameters related to panel length/thickness ratio, material density and Mach number on the stability of heated panel are studied. It is found that panel flutter may occur at relatively low aerodynamic pressure when several stable equilibria exist for the aeroelastic system of heated panel.

Aeroelastic Properties of Closely Spaced Modes for a Highly Loaded Transonic Fan

2008 ◽  
Author(s):  
Hans Ma˚rtensson ◽  
Ste´fan Sturla Gunnsteinsson ◽  
Damian M. Vogt
Keyword(s):  
Rotational Speed ◽  
Pressure Ratio ◽  
Stability Margin ◽  
Frequency Separation ◽  
Mode Shapes ◽  
Compressor Blades ◽  
Aeroelastic System ◽  
High Pressure Ratio ◽  
Mode Separation ◽  
Centrifugal Stiffening

In the design of modern compressor blades of wide chord (low aspect ratio) type it is often hard to avoid having modes that are close to each other in frequency. Modes which are closely spaced can interact dynamically. Mistuning and localization of stresses are known problems with this. A potential problem with this is also the possibility of coalescence flutter of the modes. Even if the modes are frequency separated at zero rotational speed, the centrifugal stiffening may cause the modes to attract and even cross (or veer) at some rotational speed. In design, mode separation criteria are sometimes applied in order to minimize the risk of encountering unknown dynamic phenomena. This study is performed to better understand the dynamics of closely spaced modes with respect to risk for coalescence flutter. A reduced order aeroelastic system is then constructed that describes the interaction between the different modes. The aeroelastic couplings are then calculated for the 2 mode system. The method is general in terms of mode shapes and number of interacting modes. A parametrical study is performed in order to study how strongly the modes interact when the frequency separation is decreased and if there is a risk of destructive coalescence flutter. The investigation is performed on a high pressure ratio front stage fan blade. The tendency of the modes to interact depends on the strength of the coupling compared to the strength of the pure structural modes. The tendency towards instability was increased in cases where the stability margin was smaller of the single modes. The results can be considered to support a separation criterion of 2% for the lower. A re-evaluation should be considered if lighter blade material and increased loads are to be used.

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

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