Coupled Bending-torsion Flutter Research Articles

Coupled bending-torsion flutter investigation of MRE tapered sandwich blades in a turbomachinery cascade

This paper studies the effects of bending-torsion coupling on the flutter stability boundaries of a turbomachinery cascade with Magnetorheological Elastomer (MRE) based sandwich blades. The blade structure is considered as a non-uniform sandwich beam with an embedded MRE core. The governing equations of bending and torsional motions are obtained based on the classical sandwich beam theory and the unsteady Whitehead aerodynamic theory is applied for modeling of the aerodynamic flow. The equations of motion governing on the coupled aeroelastic system have been derived in a discrete form by Lagrange's equations and using the assumed modes method. The stability analysis is performed and the effects of various parameters such as coupling, magnetic field, taper ratios and different mistuning patterns on the flutter characteristics have been investigated. The results indicate that the flutter stability is clearly affected by the interaction between the bending and torsional motions which is in agreement with the results previously obtained for a typical cascade. The results also indicate that the change of blade cross sectional area has a significant effect on the flutter boundaries.

Aerodynamic and mechanical hierarchical aeroelastic analysis of composite wings

The coupled bending-torsion flutter is here investigated through Carrera Unified Formulation (CUF). The hierarchical capabilities of CUF offer a procedure to obtain refined one-dimensional models that, by going beyond the assumptions of classical theories, accurately describe the kinematics of structures. Aerodynamic loadings have been determined according to Theodorsen theory, from which the steady formulation can be easily obtained. The displacement variables over the cross section (x-z plane) are approximated by x,z polynomials of any order, N. The finite element method is used to solve the governing equations, which are derived in a weak form through the principle of virtual displacements. The equations are written in terms of “fundamental nuclei,” which do not vary with the theory order, N. Several wing configurations have been studied, giving great attention to thin-walled box beams made of orthotropic material. The effects of sweep angle and lamination scheme on flutter conditions have been investigated, and the results have been compared with solutions obtained from two-dimensional theories, experimental tests, and aeroelastic analyses carried out with the doublet lattice method (DLM). The unsteady theory, combined with advanced beam theories, represents a computationally cheap tool for preliminary aeroelastic studies of complex wing structures.

Quasi-Steady Prediction of Coupled Bending-Torsion Flutter Under Classic Surge

In this paper, a quasi-steady method is developed for predicting the coupled bending-torsion flutter in a compressor cascade during classic surge. The classic surge is one of the major compressor flow field instabilities involving pulsation of the main flow through the compressor. The primary reason for the occurrence of the classic surge is the stalling of the blade rows and if the conditions are favorable this can trigger flutter, which is a self-excited aero elastic instability. The classic surge flow is modeled by using the well-established model of Moore and Greitzer and the obtained flow condition is used to determine the aerodynamic loads of the cascade using the linearized Whitehead's theory. The cascade stability is then examined by solving the two dimensional structural model by treating it as a complex eigenvalue problem. The structural stability is analyzed for a range of values of the frequency ratio and primary emphasis is given for the frequency ratio value of 0.9 as many interesting features could be revealed. The cascade shows a bifurcation from bending flutter to the torsional one signifying that only one of the flutter modes are favored at any instant in time. The torsional flutter is found to be the dominant flutter mode for a range of frequency ratios during classic surge whereas the bending flutter is found to occur only for some values of frequency ratio very close to unity as the torsional loads acting on the blades are found to be orders of magnitude higher than the bending loads. A rapid initiation of torsional flutter is seen to occur during classic surge for frequency ratio values very close to unity and it is perceived that during blade design, frequency ratios should be kept below 0.9 to prevent the flutter possibilities. An estimate of structural energy variation with time indicates that even if the total structural energy is negative one of the modes can go unstable during classic surge.

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

Flutter Analysis of Contra-Rotating Blade Rows

To investigate the flutter characteristics of cascading blades in multiple blade rows, the computation program to calculate the unsteady blade loading based on the unsteady lifting surface theory for contra-rotating annular cascades was formulated and coded. Then a computation program to solve the coupled bending-torsion flutter equation for the contra-rotating annular cascades was also developed. Some results of the flutter analysis are presented. It is shown that the presence of the neighboring blade row gives rise to substantial change in the critical flutter condition irrespective of the blade row gap when the main acoustic duct mode is of cut-on state. The effect of the neighboring blade row is also significant irrespective of the state of the main acoustic duct mode when the blade rows are very closely placed.

二重反転環状翼列のフラッター解析

The paper studies the effect of neighboring blade rows on flutter characteristics of cascading blades. For this purpose the computation program to calculate the unsteady blade loading based on the unsteady lifting surface theory for contra-rotating annular cascades was formulated and coded. Then a computation program to solve the coupled bending-torsion flutter equation for the contra-rotating annular cascades was also developed. Some results of the flutter analysis are presented. The presence of the neighboring blade row gives rise to significant change in the critical flutter condition when the main acoustic duct mode is of cut-on state.

Achtive Control of a Blade Flutter by Means of Acoustic Excitation (2nd Report, The Case of Low Frequency Cascade Flutter and Setting Sound Source on the Wall at Blade Tip)

The paper presents theoretical and experimental studies to investigate how one can control and suppress cascade flutter through an acoustic excitation. The model considered herein is a three-dimensional linear cascade of flat plates oscillating in a low speed flow between parallel walls. An actuator consisting of loudspeakers is set on a wind tunnel wall at the blades tip side, and generates sound waves with the same frequency of the blade vibration. To determine the most suppressive condition, the dependence of the suppression effect on the width, location of actuator surface and phase difference between the blades and actuator is investigated. Experimental results show that the loudspeakers can work most effectively when the centerline of the actuator surface is located at three-quarters chord point from the leading edge of blades. Furthermore an 8% increase in the critical flutter velocity of 5.3 Hz coupled bending-torsion flutter is obtained.

Coupled mode flutter analysis using flutter derivatives

The “classical” coupled bending-torsion flutter of long-span bridges, possessing 3-dimensional vibration modes, is investigated both analytically and experimentally. In the analysis, self-excited forces are defined by using the so-called flutter derivatives. The vertical wind profile as well as the spanwise non-homogeneity of wind velocity are also incorporated. The analysis permits (i) straight forward prediction of the coupled flutter velocity by using the flutter derivatives and (ii) reasonable interpretation of 2-dimensional model tests to predict the coupled flutter behavior of bridges with 3-dimensional freedom of motion.

Coupled Bending-Torsion Flutter in a Supersonic Cascade

Coupled Bending-Torsion Flutter in a Supersonic Cascade

Coupled Bending-Torsion Flutter in Cascades

A method is presented for determining the aeroelastic stability boundaries of a cascade with aerodynamic, inertial, and structural coupling between the bending and torsional degrees of freedom. A computer program has been written to systematically investigate the effect of this coupling on cascade stability over a wide range of design parameters. Results presented illustrate that the bending-torsion interaction has a pronounced effect on the cascade flutter boundary, despite no appreciable tendency toward frequency coalescence as flutter is approached. The analysis also indicates that bending flutter is possible even in the absence of finite mean lift.