The Effect of Circumferential Aerodynamic Detuning on Coupled Bending-Torsion Unstalled Supersonic Flutter

1986 ◽  
Vol 108 (2) ◽  
pp. 253-260 ◽  
Author(s):  
D. Hoyniak ◽  
S. Fleeter
Keyword(s):  
Stability Analysis ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Center Of Gravity ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unsteady Aerodynamic ◽  
Supersonic Flutter

A mathematical model is developed to predict the enhanced coupled bending-torsion unstalled supersonic flutter stability due to alternate circumferential spacing aerodynamic detuning of a turbomachine rotor. The translational and torsional unsteady aerodynamic coefficients are developed in terms of influence coefficients, with the coupled bending-torsion stability analysis developed by considering the coupled equations of motion together with the unsteady aerodynamic loading. The effect of this aerodynamic detuning on coupled bending-torsion unstalled supersonic flutter as well as the verification of the modeling are then demonstrated by considering an unstable twelve-bladed rotor, with Verdon’s uniformly spaced Cascade B flow geometry as a baseline. It was found that with the elastic axis and center of gravity at or forward of the airfoil midchord, 10 percent aerodynamic detuning results in a lower critical reduced frequency value as compared to the baseline rotor, thereby demonstrating the aerodynamic detuning stability enhancement. However, with the elastic axis and center of gravity at 60 percent of the chord, this type of aerodynamic detuning has a minimal effect on stability. For both uniform and nonuniform circumferentially spaced rotors, a single degree of freedom torsion mode analysis was shown to be appropriate for values of the bending-torsion natural frequency ratio lower than 0.6 and higher than 1.2. However, for values of this natural frequency ratio between 0.6 and 1.2, a coupled flutter stability analysis is required. When the elastic axis and center of gravity are not coincident, the effect of detuning on cascade stability was found to be very sensitive to the location of the center of gravity with respect to the elastic axis. In addition, it was determined that when the center of gravity was forward of an elastic axis located at midchord, a single degree of freedom torsion model did not accurately predict cascade stability.

The Response of Nonlinear Systems to Modulated High-Frequency Input

1993 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Systems ◽  
Natural Frequency ◽  
Amplitude Modulation ◽  
Carrier Frequency ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Resonant Excitation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

Demonstrator to show the effects of negative stiffness on the natural frequency of a simple oscillator

2008 ◽  
Vol 222 (7) ◽  
pp. 1189-1192 ◽  
Author(s):  
A Carrella ◽  
M J Brennan ◽  
T P Waters
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Test Rig ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Horizontal Beam ◽  
Additional Correction

This article describes a demonstrator to show the effects of negative stiffness on the free vibration of a simple oscillator. The test rig consists of a horizontal beam that is hinged at one end and is supported by two coil springs to form a single-degree-of-freedom system. Additional correction springs, which provide negative stiffness, can be attached to lower the natural frequency of the system. The effect of the change in natural frequency can be easily seen visually, and it is shown that for one of the configurations of correction springs, the natural frequency can be reduced by a factor of about 4.

Effectiveness of neoprene pad vibration isolators at high frequencies

2021 ◽  
Vol 263 (4) ◽  
pp. 2172-2183
Author(s):  
Jerry Lilly
Keyword(s):  
Natural Frequency ◽  
Insertion Loss ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Frequency Wave ◽  
Single Degree Of Freedom ◽  
High Frequencies ◽  
Vibration Isolators ◽  
Single Degree ◽  
Wide Range

The natural frequency, dynamic stiffness, and insertion loss of commercially available neoprene pad vibration isolators have been measured in a simple, single degree of freedom system over a wide range of pad loadings out to a maximum frequency of 10 kHz. The results reveal that dynamic stiffness can vary significantly with pad loading as well as the durometer of the material. It will also be shown that insertion loss follows the theoretical single degree of freedom curve only out to a frequency that is about 5 to 10 times the natural frequency, depending upon the pad durometer rating. Above that frequency wave resonances in the material cause the insertion loss to deteriorate significantly out to a frequency near 1 kHz, above which the insertion loss maintains a relatively constant value, again depending upon the pad durometer rating. In some instances the insertion loss values can approach 0 dB or even become negative at specific frequencies in the frequency region that is 10 to 20 times the natural frequency of the system.

scholarly journals On the Estimation of the Moving Mass of a TMD Installed on a Lively Structure

2021 ◽  
Vol 11 (10) ◽  
pp. 4712
Author(s):  
Alvaro Magdaleno ◽  
Cesar Pelaez ◽  
Alvaro Iglesias-Pordomingo ◽  
Antolin Lorenzana
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Structural Response ◽  
Degree Of Freedom ◽  
Moving Mass ◽  
Tuned Mass Dampers ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Modification Technique ◽  
One Step

Tuned Mass Dampers are devices which can be assimilated to single-degree-of-freedom systems with a certain amount of moving mass, a natural frequency and a damping ratio intended to be installed on lively structures to reduce the contribution of a certain mode to their response. Once placed on the structure, the movement of the mass damper couples to the structural response and determines its properties as an isolated system becomes challenging. The authors have previously presented a methodology to estimate the natural frequency and damping ratio of an SDOF system installed on a structure and not necessarily tuned to a certain mode. It was based on a transmissibility function and, thus, the moving mass could not be estimated. With this work, the authors go one step further and present a novel procedure to estimate the moving mass value by means of the same transmissibility function and two well selected frequency response functions. The methodology is applied to estimate the properties of a real single-degree-of-freedom system placed on a lively timber platform. The results are compared with the mass modification technique to show that the proposed methodology provides better estimations in a more efficient way.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part II — Multi-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Time Integration ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Friction Damper ◽  
Compressor Blades ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damping Characteristics

Abstract A multi-mode analysis of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent friction force is conducted. The level of displacement-dependence is governed by a ramp angle and spring arrangement as discussed in Part I. The system is studied by using harmonic balance as an approximate analytical solution and then by using a time integration method. The damping characteristics of the system are studied in detail. The results qualitatively agree with those obtained using a single-degree-of-freedom analysis of this system reported in Part I. Interesting findings include the appearance of internal resonance peaks when multiple modes are considered. Also, as with the earlier single-degree-of-freedom study, two dynamic response solutions exist at certain parameter values. It is found that the ability to control the amplitude of the response is a function of the frequency range considered. In general, near modal resonance peaks, the amplitude of the response decreases with increasing ramp angle. However, in an “overlapping” region between resonance peaks, the amplitude of the response actually increases with increasing ramp angle. Detailed analysis of the damping characteristics indicate that the dry friction damper is most effective in damping the fundamental mode. The other critical observation is that the damping contribution from the displacement-dependent dry friction damper is “viscous-like” in nature and relatively insensitive to the amplitude of the response. This result suggests that in the case of turbine or compressor blades, this type of damping arrangement may be effective in the suppression of flutter.

Resonance Classification in a Cubic System

1971 ◽  
Vol 38 (3) ◽  
pp. 585-590 ◽  
Author(s):  
D. J. Ness
Keyword(s):  
Stability Analysis ◽  
Parametric Excitation ◽  
Degree Of Freedom ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Resonance Phenomena ◽  
Cubic System

A weakly nonlinear, single-degree-of-freedom cubic system subject simultaneously to a time-varying force and parametric excitation is considered. The various types of resonance phenomena exhibited by the system are classified and a detailed stability analysis is presented for one case of particular interest.

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