scholarly journals Uncertainty quantification for the Modal Phase Collinearity of complex mode shapes

2021 ◽  
Vol 152 ◽  
pp. 107436
Author(s):  
Szymon Greś ◽  
Michael Döhler ◽  
Palle Andersen ◽  
Laurent Mevel
Keyword(s):  
Uncertainty Quantification ◽  
Mode Shapes ◽  
Complex Mode

Flutter of Low Pressure Turbine Blades With Cyclic Symmetric Modes: A Preliminary Design Method

2004 ◽  
Vol 126 (2) ◽  
pp. 306-309 ◽  
Author(s):  
Robert Kielb ◽  
Jack Barter ◽  
Olga Chernycheva ◽  
Torsten Fransson
Keyword(s):  
Mode Shape ◽  
Design Method ◽  
Turbine Blades ◽  
Current Method ◽  
Low Pressure ◽  
Mode Shapes ◽  
Preliminary Design ◽  
Complex Mode ◽  
Low Pressure Turbine ◽  
Reduced Frequency

A current preliminary design method for flutter of low pressure turbine blades and vanes only requires knowledge of the reduced frequency and mode shape (real). However, many low pressure turbine (LPT) blade designs include a tip shroud that mechanically connects the blades together in a structure exhibiting cyclic symmetry. A proper vibration analysis produces a frequency and complex mode shape that represents two real modes phase shifted by 90 deg. This paper describes an extension to the current design method to consider these complex mode shapes. As in the current method, baseline unsteady aerodynamic analyses must be performed for the three fundamental motions, two translations and a rotation. Unlike the current method work matrices must be saved for a range of reduced frequencies and interblade phase angles. These work matrices are used to generate the total work for the complex mode shape. Since it still only requires knowledge of the reduced frequency and mode shape (complex), this new method is still very quick and easy to use. Theory and an example application are presented.

Identification of Coupled Mode Shapes Based on Complex Mode Indicator Function

2015 ◽  
Vol 732 ◽  
pp. 183-186
Author(s):  
Róbert Huňady ◽  
Martin Hagara ◽  
Martin Schrötter
Keyword(s):  
Modal Analysis ◽  
Correlation Method ◽  
Indicator Function ◽  
Experimental Modal Analysis ◽  
Image Correlation ◽  
Mode Shapes ◽  
Complex Mode ◽  
Coupled Mode ◽  
Value Decomposition ◽  
Function Matrix

Paper deals with the identification of coupled mode shapes by experimental modal analysis. Main attention is focused on the using of Complex Mode Indicator Function that is based on singular value decomposition of frequency response function matrix and allows to separate coupled and also closed modes. In the paper there is described experimental modal analysis at which digital image correlation method is used to measure responses of a circular plate. The measurement was evaluated in program Modan 3D that is being developed by the authors.

Flutter of Low Pressure Turbine Blades With Cyclic Symmetric Modes: A Preliminary Design Method

2003 ◽  
Author(s):  
Robert Kielb ◽  
John Barter ◽  
Olga Chernysheva ◽  
Torsten Fransson
Keyword(s):  
Mode Shape ◽  
Design Method ◽  
Turbine Blades ◽  
Current Method ◽  
Low Pressure ◽  
Mode Shapes ◽  
Preliminary Design ◽  
Complex Mode ◽  
Low Pressure Turbine ◽  
Reduced Frequency

A current preliminary design method for flutter of low pressure turbine blades and vanes only requires knowledge of the reduced frequency and mode shape (real). However, many low pressure turbine (LPT) blade designs include a tip shroud, that mechanically connects the blades together in a structure exhibiting cyclic symmetry. A proper vibration analysis produces a frequency and complex mode shape that represents two real modes phase shifted by 90 degrees. This paper describes an extension to the current design method to consider these complex mode shapes. As in the current method, baseline unsteady aerodynamic analyses must be performed for the 3 fundamental motions, two translations and a rotation. Unlike the current method work matrices must be saved for a range of reduced frequencies and interblade phase angles. These work matrices are used to generate the total work for the complex mode shape. Since it still only requires knowledge of the reduced frequency and mode shape (complex), this new method is still very quick and easy to use. Theory and an example application are presented.

Experimental Complex Modal Analysis of Machine Tool Structures

1989 ◽  
Vol 111 (2) ◽  
pp. 116-124 ◽  
Author(s):  
Y. C. Shin ◽  
K. F. Eman ◽  
S. M. Wu
Keyword(s):  
Machine Tool ◽  
Modal Analysis ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Coupled Modes ◽  
Complex Mode ◽  
Machine Tool Structure ◽  
Experimental Complex ◽  
Complex Modal Analysis ◽  
Complex Modal

Despite the well-established theories and considerable experimental research, the identification of the complex mode shapes of a real machine tool structure with general damping still remains a formidable task. Moreover, the existence of closely coupled modes with heavy damping introduces additional difficulties. This paper presents a detailed procedure for experimental complex modal analysis of a machine tool structure by the Dynamic Data System method. The accuracy and efficiency are first illustrated by numerical examples through simulation studies. It has been shown that closely coupled modes and modes with heavy damping can be successfully identified from both simulated and actual experimental data from a machine tool. Complex mode shapes were also obtained without adding any complexity or losing accuracy as compared to normal mode analysis. The experimental results obtained by the proposed method were compared with those based on the FFT algorithm.

Uncertainty Quantification in Nonlinear Resonant MEMS

2012 ◽  
Author(s):  
Rajat Goyal ◽  
Anil K. Bajaj
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Response Surface ◽  
Nonlinear Response ◽  
Linear Part ◽  
Mode Shapes ◽  
Beam Structure ◽  
Averaged Equations ◽  
Direct Sampling ◽  
Collocation Technique

This work is focused on Uncertainty Quantification (UQ) in a nonlinear MEMS T-beam structure exhibiting 1:2 autoparametric internal resonance. The study is presented by elaborating on the sources of uncertainty in fabrication and operation of the device and their quantification. Nonlinear response of the system is formulated by using a two-mode model constructed with lowest two linear modes of the structure in conjunction with the nonlinear Lagrangian representing the dynamics of the beam structure as well as the excitation mechanism. Thus UQ for the nonlinear resonant MEMS is carried out in two steps. First, propagation and quantification in linear analysis outputs namely mode shapes, natural frequencies and tuning, and secondly, UQ on nonlinear response obtained from averaged equations determined by the averaged Lagrangian. In this paper, applications of UQ techniques on linear part are presented and effects of various parameteric uncertainties on model output are brought out. Sensitivity analysis is performed to reduce the number of parameters and a comparison of sensitivity analysis with sampling is done to establish the accuracy of the method. Response surface analysis is performed using generalized polynomial chaos (gPC) to generate an analytical expression for multi-dimensional uncertainty. A detailed description of the gPC collocation method is also presented. A comparison of response surface method with direct sampling is done to illustrate the efficiency and accuracy of gPC collocation technique for up to 5 uncertain parameters.

An Investigation of Turbomachinery Shrouded Rotor Blade Flutter

2003 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chi-Chin Chen ◽  
Chih-Neng Hsu ◽  
Gwo-Chung Tsai ◽  
Kwang-Lu Koai
Keyword(s):  
Rotor Blade ◽  
Single Mode ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Blade Design ◽  
Combined System ◽  
Complex Mode ◽  
Blade Flutter ◽  
System Mode ◽  
Shrouded Rotor

Turbomachinery shrouded rotor blade design has been widely used in fans, compressors, and turbines. By using shroud design, the blade structural damping can be increased to prevent blade flutter. However, the shrouded rotor blade design will cause the blade mode shapes to be complex, and in some cases both bending and torsion mode components can be present at the same time in a single mode. Therefore, a complex mode analysis was developed to predict shrouded rotor blade flutter with these bending and torsion combined system modes. Using the blade natural frequencies and mode shapes from a finite element model, and the blade aerodynamic flow-field, the unsteady aerodynamic forces of the system mode can be calculated. A complex mode flutter analysis was then performed using a modal solution to determine the stability of the system. The analysis system was applied to two shrouded rotor blade applications. The bending and torsion combined system mode was decomposed into a real mode component and an imaginary mode component. Bending-dominated or torsion-dominated mode shapes can be analyzed using single mode approach to obtain consistent flutter stability results. However, for the bending and torsion combined mode shape cases, the single mode analysis can be misleading, and the complex mode analysis can be a useful tool.

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