The Influence of a Cracked Blade on Rotor’s Free Vibration

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yi-Jui Chiu ◽  
Shyh-Chin Huang
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Bending Moment ◽  
Rotor System ◽  
Coupled Modes ◽  
Mode Localization ◽  
Coupled Vibrations ◽  
Crack Location ◽  
Blade System

The influence on the coupled vibrations among shaft, disk, and blades of a rotor system due to a cracked blade was investigated analytically. On the shaft-disk-blade system, without a cracked blade, there exist three types of coupled modes, shaft disk blade (SDB), disk blade (DB), and blade-blade. A cracked blade was found to change not only the natural frequencies but also the types of coupled modes. First, the DB modes disappeared and were replaced by SDB modes. Second, in some modes the disk experienced mode localization due to the cracked blade. Numerical results showed that natural frequencies varied with the blade’s crack location and depth. At no bending moment places the crack imposed no effect. The crack affected the natural frequency slightly until its depth reached as deep as 70% then the frequency dropped abruptly.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Sensitivity Analysis and Application of Natural Frequency of Torsional Vibration of Rotor System

2008 ◽  
Author(s):  
Qing He ◽  
Dongmei Du
Keyword(s):  
Sensitivity Analysis ◽  
Electric Power ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Electric Power System ◽  
Rotor System ◽  
Analysis Method ◽  
Turbine Generator ◽  
Sensitivity Analysis Method

The disturbance of electric power system makes large-scale turbine-generator shafts generate torsional vibration. A available method to restrain the torsional vibration of turbine-generator shafts is that all the natural frequencies of torsional vibration of turbine-generator shafts must keep away from the working frequency and its harmonic frequencies as well as all the frequencies that possibly bring on interaction between turbine-generator and electric power system so that the torsional resonation of shafts may not occur. A dynamic design method for natural frequencies of torsional vibration of rotor system based on sensitivity analysis is presented. The sensitivities of natural frequency of torsional vibration to structure parameters of rotor system are obtained by means of the theory of sensitivity. After calculated the torsional vibration dynamic characteristics of original shafts of a torsional vibration stand that simulates the real shafts of 300MW turbine-generator, the dynamic modification for the torsional vibration natural frequency is carried out by the sensitivity analysis method, which makes the first-five natural frequencies of torsional vibration of the stand is very close to the design object. It is proved that the sensitivity analysis method can be used to the dynamic adjustment and optimal design of real shafts of turbine-generator.

scholarly journals The Influence of a Mistuned Blade’s Staggle Angle on the Vibration and Stability of a Shaft-Disk-Blade Assembly

2008 ◽  
Vol 15 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Yi-Jui Chiu ◽  
Shyh-Chin Huang
Keyword(s):  
Natural Frequencies ◽  
Linear Trend ◽  
Rotor System ◽  
Instability Point ◽  
Blade System ◽  
Blade Assembly ◽  
The Stability

The influence on coupling vibrations and stability among shaft-torsion, disk-transverse and blade-bending of a rotor system with a mistuned blade's staggle angle was investigated analytically. A shaft-disk-blade system has been found existing two types of coupling vibrations, disk-blade (DB), and blade-blade (BB) modes when the shaft was assumed rigid. If the shaft's torsional flexibility was taken into account, an additional type of coupling modes, shaft-disk-blade (SDB), appeared. When an angle-mistuned blade existed, the blades periodicity was destroyed and it was found to change not only the natural frequencies but also the types of modes. Due to blade's mistune, the shaft torsion had to participate to balance such that DB modes vanished and replaced by SDB modes. A mistuned staggle angle was numerically found to alter the natural frequencies in an almost linear trend. At last, the rotational effects were found to merge frequency loci and eventually reached an instability point. Very interestingly, a mistuned blade diminished the possible instability caused by blade-dominating modes, which existed in a perfect and periodic rotor. In words, the rotor might benefit from a mistuned blade from the stability viewpoint. The shaft-dominating mode, yet, was unaffected by the mistune and retained a possible instability.

Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

2007 ◽  
Author(s):  
Nikhit N. Nair ◽  
Hamid N. Hashemi ◽  
Grant M. Warner ◽  
M. Olia
Keyword(s):  
Natural Frequencies ◽  
Crack Opening ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Coupled Systems ◽  
Mode Shapes ◽  
Crack Location ◽  
Inner Region

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the natural frequencies and results in a quicker onset of instability. It is observed that the effect of the crack on the vibration characteristics of the disk is mainly a function of the crack location.

The effect of crack geometry on non-destructive fault detection of EN 8 and EN 47 cracked cantilever beam

2019 ◽  
Vol 50 (3) ◽  
pp. 92-100 ◽  
Author(s):  
V Khalkar ◽  
S Ramachandran
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Crack Location ◽  
Crack Geometry ◽  
Shaped Crack ◽  
Non Destructive

Since long it has been observed that the size of the crack in structures increases with time, and finally, it may lead to its catastrophic failure. Hence, it is crucial to do the vibration study of cracked structures with regard to vibration-based crack detection and the classification of cracks. So far, vibration-based non-destructive testing method is applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, that is, V-shaped and U-shaped, on the applicability of these methods has been overlooked. To investigate this issue, artificially cracks are made on the cantilever beam. By free vibration analysis, the effect of crack geometry, crack depth, and crack location on natural frequency is investigated. The natural frequency results obtained from V-shaped and U-shaped models for the same crack configurations are compared with each other and it is revealed that the results are not much sensitive for the change of crack geometry. Hence, it is clear that free vibration-based crack detection method approximately predicts the crack parameters, that is, crack location and crack depth, in structures irrespective of the crack geometry. It is also found that for the same configuration, results of natural frequency are comparatively on the lower side for U-shaped crack models than V-shaped crack models. In this study, the natural frequency of each cracked case is computed by a theoretical method and numerical method and shows good agreement. Finally, it is also observed that structural integrity of a cracked cantilever beam is a function of crack location.

scholarly journals Coupled Dynamic Analysis for the Riser-Conductor of Deepwater Surface BOP Drilling System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Kanhua Su ◽  
Stephen Butt ◽  
Jianming Yang ◽  
Hongyuan Qiu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Bending Moment ◽  
Equation Of Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Drilling System ◽  
Natural Frequency Analysis

Deepwater surface BOP (surface blowout prevention, SBOP) drilling differs from conventional riser drilling system. To analyze the dynamic response of this system, the riser-conductor was considered as a beam with varied cross-sections subjected to loads throughout its length; then an equation of motion and free vibration of the riser-conductor string for SBOP was developed. The finite difference method was used to solve the equation of motion in time domain and a semianalytical approach based on the concept of section division and continuation was proposed to analyze free vibration. Case simulation results show that the method established for SBOP system natural frequency analysis is reasonable. The mode shapes of the riser-conductor are different between coupled and decoupled methods. The soil types surrounding the conductor under mudline have tiny effect on the natural frequency. Given that some papers have discussed the response of the SBOP riser, this work focused on the comparison of the dynamic responses on the wellhead and conductor with variable conditions. The dynamic lateral displacement, the bending moment, and the parameters’ sensitivity of the wellhead and the conductor were analyzed.

Dynamic Response of Tubular T-Joints Under the Influence of Propagating Cracks

1996 ◽  
Vol 118 (1) ◽  
pp. 71-78 ◽  
Author(s):  
D. I. Nwosu ◽  
A. S. J. Swamidas ◽  
J. Y. Guigne´
Keyword(s):  
Natural Frequency ◽  
Crack Detection ◽  
Crack Depth ◽  
Bending Moment ◽  
Frequency Change ◽  
T Joints ◽  
Finite Element Program ◽  
Crack Location ◽  
Percent Change ◽  
Frequency Changes

This paper presents an analytical study on the vibration response of tubular T-joints for detecting the existence of cracks along their intersections. The ABAQUS finite element program was utilized for carrying out the analysis. Frequency response functions were obtained for a joint with and without cracks. The joint was modeled with 8-node degenerate shell elements having 5 degrees of freedom per node. Line spring elements were used to model the crack. The exact crack configuration (semielliptical shape, Fig. 5(b)), as observed from numerous experimental fatigue crack investigations at the critical location, has been achieved through a mapping function, that allows a crack in a planar element to be mapped on to the tube surface. The natural frequency changes with respect to crack depth show little changes, being 4.82 percent for a 83-percent crack depth for the first mode. On the other hand, significant changes have been observed for bending moment and curvature as a function of crack depth. For an 83-percent chord thickness crack, a 97-percent change in bending moment at points around the crack vicinity, and 34.15 to 78 percent change in bending moments, for those locations far away from the crack location, have been observed. Natural frequency change should be combined with other modal parameters such as “bending moment (or bending strain)” and “curvature” changes for crack detection. The presence of the crack can be detected at locations far away from the crack location using such sensors as strain gages.

scholarly journals Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Sangkyu Choi ◽  
Usik Lee
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Model ◽  
Spectral Element ◽  
Rotor System ◽  
Dynamic Responses ◽  
Disk System ◽  
Unbalanced Mass ◽  
Rotor Systems ◽  
Blade System

A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.

scholarly journals Analysis of Free Vibration of Hydraulic Opposing Cylinder Controlled by Servo Valve

2021 ◽  
Author(s):  
Xiaoming Yuan ◽  
Weiqi Wang ◽  
Xuan Zhu ◽  
Bing Du ◽  
Lijie Zhang
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Transmission System ◽  
Normal Operation ◽  
Design Parameters ◽  
Analytical Relationship ◽  
Parameter Method ◽  
Mechanical Transmission ◽  
Servo Valve

Abstract The fluid transmission medium has large compressibility and low rigidity, and its physical properties are extremely sensitive to state parameters such as flow, pressure and temperature. Therefore, compared with the mechanical transmission system, the natural frequency of the fluid transmission system is relatively low and has time-varying characteristics. After a wide frequency range changing of the load frequency and long-term operation, the excitation frequency of the fluid transmission system is more likely to approach its natural frequency and causes resonance, which seriously affects the normal operation of the system. Therefore, taking the hydraulic opposing cylinder controlled by servo valve as the research object, based on the analytical relationship between the dynamic bulk modulus and the equivalent stiffness of oil, the vibration dynamics models and equations of the system is established by using the lumped parameter method. Through the free vibration analysis, the natural frequencies and main vibration modes of the system are determined and the sensitivity changes of the natural frequencies to the design parameters are revealed. The maximum error between the theoretical modal frequency and the experimental one is 3.77%, which verifies the correctness of the dynamic model of the system. This research can provide a theoretical reference for the optimization of the dynamic performance of the hydraulic transmission system.

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