scholarly journals Crack identification in cyclic symmetric structures based on relative indicators of frequency separation

2021 ◽  
Vol 12 (1) ◽  
pp. 173-184
Author(s):  
Shuai Wang ◽  
Menghui Liang
Keyword(s):  
Natural Frequencies ◽  
Frequency Separation ◽  
Mode Shapes ◽  
Crack Identification ◽  
Sector Model ◽  
Symmetric Structure ◽  
Cyclic Symmetric ◽  
Small Cracks ◽  
Rotation Transformation ◽  
Symmetric Structures

Abstract. Cyclic symmetric structures are an important class of structures in the fields of civil and mechanical engineering. In order to avoid accidents due to cracks in such structures, an effective method for crack identification is presented in this paper. First, the dynamic model of cyclic symmetric structures with gapless cracks is developed using a structure's sector model and rotation transformation. Then, the effects of cracks on the free vibration characteristics of a cracked cyclic symmetric structure are addressed, with particular interests in the distortion of mode shapes and the shift and split of natural frequencies. On the basis of crack-induced phenomena, an effective method based on relative indicators of frequency separation is developed for quantitative crack identification. Numerical results illustrate that the relative indicators are sensitive to small cracks and insensitive to the predicting model used during analysis. Finally, the method is validated by experiments conducted on an impeller-shaft assembly. The results show the effectiveness of the frequency separation indicators in crack identification in cyclically symmetric structures.

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Discs

2003 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Nonlinear Structure ◽  
Sector Model ◽  
Symmetry Properties ◽  
Symmetric Structures

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disc using a periodic sector model without any loss of accuracy in calculations and modelling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disc forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disc model: (i) using sector finite element matrices; (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disc with shrouds have demonstrated the high efficiency of the method.

Detection of Cracks in Stationary Rotors via the Modal Frequency Changes Induced by a Roving Disc

2014 ◽  
Author(s):  
Z. N. Haji ◽  
S. O. Oyadiji
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Mode Shapes ◽  
Crack Identification ◽  
Open Crack ◽  
Suggested Approach ◽  
Rotor Systems ◽  
Crack Location ◽  
High Crack ◽  
Frequency Changes

In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

Development of a Multi-Shaker-Control to Investigate the Influence of the Interblade Phase Angle on Frictionally Damped Turbine Blades

2021 ◽  
Author(s):  
Florian Jäger ◽  
Ferhat Kaptan ◽  
Lars Panning-Von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Phase Angle ◽  
Phase Difference ◽  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Mode Shapes ◽  
Nodal Diameter ◽  
Cyclic Symmetric ◽  
Symmetric Structures ◽  
Interblade Phase Angle ◽  
Experimental Effort

Abstract Constructive damper concepts are developed and integrated in turbomachinery to reduce vibration amplitudes generated by dynamic loads. The potential damping effectiveness of friction-based damper concepts is strongly dependent on the relative motion between adjacent blades, besides other factors such as normal force. In cyclic symmetric structures the phase difference is determined by the excited nodal diameter, which leads to different damper movements and efficiencies for given mode shapes. Several studies on the investigation of the damper performance of different underplatform damper geometries have been carried out on non-rotating test stands consisting usually of two blades in order to reduce the experimental effort before setting up rotational tests. Based on the existing modes of the two blades and the application of commonly just one shaker, the investigations are limited to the in-phase and out-of-phase modes. In this paper an experimental approach is developed to reduce the gap of transferability between non-rotating and rotational tests to analyze the effects of a variable interblade phase angle on the damping effect of underplatform dampers. For this purpose, a cascaded control system using two shakers is being developed to control the force amplitudes and the phase difference between the response of the two blades. The control algorithm is designed in a model-based way by using a two degrees of freedom oscillator with friction contact and is subsequently integrated in the non-rotating test stand.

On the Use of Higher-Order Frequencies in Crack Identification in Columns Subjected to Important Tip Mass

2015 ◽  
Vol 801 ◽  
pp. 148-153
Author(s):  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Codrin Nistor Nitescu ◽  
Vasile Iancu ◽  
Zeno Iosif Praisach ◽  
...  
Keyword(s):  
Evaluation Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Crack Identification ◽  
Structural Elements ◽  
Axial Loads ◽  
Damage Location ◽  
Tip Mass ◽  
Non Destructive ◽  
Top Mass

The paper present a novel non-destructive evaluation method designed to assess damage in structural elements subjected to important axial loads, as columns are. In the prior research a reliable damage detection method was developed for beams subjected to own mass, that consider the relation existing between the energy stored in the beam in certain vibration modes and the related natural frequencies. First we found the mathematical relations expressing the healthy pillar mode shapes and frequencies with respect to the top mass. Afterward, by means of FEM, we derived the natural frequencies for the numerous damage cases, in order to define the frequency shift curves. Analogous to the case of beams, the damage location is characterized by patterns that are derived from the mode shape curvatures square of the healthy beam. The damage location becomes an inverse problem while the damage position is found by interpreting frequency measurements made on the healthy and damaged beam.

Modal Analysis of Mistuned Turbine Blade Packet Due to Combined Blade and Lacing Wire Damage

2019 ◽  
Vol 24 (3) ◽  
pp. 546-557
Author(s):  
Mangesh S. Kotambkar
Keyword(s):  
Material Properties ◽  
Natural Frequencies ◽  
Cyclic Symmetry ◽  
Vibration Localization ◽  
Symmetric Structure ◽  
Blade System ◽  
Cyclic Symmetric ◽  
Drastic Effect ◽  
Grouped Blades ◽  
Geometric Variation

The turbine disk blade system is a cyclic symmetric structure, initially tuned with all its blades perfectly identical in geometry and material properties; similarly interconnecting lacing wires are of equal stiffness. The cyclic symmetry of the bladed disks gets destroyed due to small differences in material properties or geometric variation between individual blades or lacing wires causing mistuning. Although mistuning is typically small, it can have a drastic effect on the dynamic response of the system. In particular, mistuning can also cause vibration localization for a few blades and the associated concentration of vibration energy can lead to an increase in blade amplitude and stress levels. Numerical simulations are performed with the characteristic equations of the simplified continuum model. Two different damage severity indices are included in the model to study the combined effect of cracked blades and damaged lacing wires on the natural frequencies of grouped blades. This study highlights the characteristic changes in the sub modal frequencies under combined damage in a stand still position. Although the major cause of mistuning is blade damage, lacing wire damage is more frequent and often acts as a precursor to blade damage and thus the present study focuses on mistuning due to combined damage.

Study of the Effect of Multi-Stage Cyclic Symmetric Modeling on the Natural Frequencies of Bladed Disks of an Aero Engine Rotor System

2015 ◽  
Author(s):  
Siva Srinivas ◽  
Hardik Roy ◽  
Esakki Muthu Shanmugam
Keyword(s):  
Modal Analysis ◽  
Gas Turbine ◽  
Natural Frequencies ◽  
Rotor System ◽  
Mode Shapes ◽  
Computational Time ◽  
Cyclic Symmetry ◽  
Multi Stage ◽  
Cyclic Symmetric ◽  
Multiple Stages

Majority of the failures in Gas turbine Blades are caused by High Cycle Fatigue induced by the vibratory stresses in the rotor blades. The first step in blade design is the prevention of coincidence of natural frequencies of the blades with the frequencies of the fluctuating Gas loads. The forcing frequency is a function of number of upstream and downstream stator blades, and rotational speed. In gas turbines with multiple stages, modal analysis of bladed-disks is individually performed i.e. stage by stage. As the structure is rotationally periodic, cyclic symmetric boundary conditions can be utilized, over 360 degree modeling. The advantage of cyclic symmetry over full model lies in reduced degrees of freedom and hence reduced computational time. In most of the available tools, cyclic symmetry for modal analysis is limited to single stage. As such there is no provision to model and analyze multiple stages at the same time. This leads to inaccurate values of natural frequencies as the flexibility introduced by the adjacent stages is not being taken into consideration. An alternative to this is full 3D modeling and analysis of all the combined stages. Bladh et al. (2003) [1] have shown that interstage coupling can significantly affect the dynamics of the multi-stage assembly and in some cases lead to an underestimation of vibratory levels. Sokolowski et al [2] studied the influence of inclusion of shaft in the model on the natural frequencies and mode shapes of the shrouded bladed discs up to four nodal diameters for first two frequency series (mode shapes). Rzadkowski and Drewczynski (2006) [3] have used full 360 degrees models to study the free and forced dynamics of multi-stage systems. However this method is avoided as the computational cost is prohibitive. Multi stage cyclic symmetry overcomes this obstacle in which each stage is cyclically modeled and an inter-stage coupling is introduced between adjacent stages. The advantage of multi stage cyclic symmetry lies in the significant reduction in the number of elements and therefore computational time. Laxalde et al. (2007) [4] were the first to come up with the method of dynamic analysis of turbo machinery rotors with multi stage cyclic symmetry using interstage coupling. They considered an example of two-stage High Pressure compressor. The results were validated against a complete 360 degrees reference model. Forced response analysis of rotor stages to fluctuating gas loads with and without interstage coupling definition was also presented and compared. In the present work a complete Gas Turbine rotor system with multiple stages of Compressor, Shaft and Turbine were analyzed together.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

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