Influence on Coupling Vibration of Rotor System with Grouped Blades due to Mistuned Lacing Wire

2011 ◽  
Vol 101-102 ◽  
pp. 1119-1125 ◽  
Author(s):  
Yi Jui Chiu ◽  
Dar Zen Chen ◽  
Chia Hao Yang
Keyword(s):  
Natural Frequencies ◽  
Rotor System ◽  
Numerical Results ◽  
Mode Shapes ◽  
Rotation Effect ◽  
Coupling Vibration ◽  
Coupling Mode ◽  
The Wire ◽  
Grouped Blades

The influence on coupling vibrations among shaft-torsion and blade-bending coupling vibrations of a rotor system with grouped blades was investigated analytically. The natural frequencies and the mode shapes of the system were solved with five- and six-blade cases used as examples. First, numerical results showed how the natural frequencies varied with the wire stiffness and the lacing wire mistuned. The diagrams of the coupling mode shapes were drawn. From the results, it was found that lacing wire did not affect the SB (shaft-blades) coupling modes, but the BB (inter-blades) modes were indeed affected by the lacing wire. At wire stiffness k*=10, the repeated BB modes split into more distinct modes. The BB modes were of (N-1) / 2 and N / 2 multiplicity for odd and even numbered blades. When the system has a mistuned lacing wire, it splits the BB modes and will once more have (N-1) frequencies. In the rotation effect, whatever tuned or mistuned, the lacing wires did not affect the instability. That means the instability preexisted due to rotation and was not induced by lacing wires.

scholarly journals The Influence of Shaft’s Bending on the Coupling Vibration of a Flexible Blade-Rotor System

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Chao-feng Li ◽  
Hou-xin She ◽  
Wen Liu ◽  
Bang-chun Wen
Keyword(s):  
Natural Frequency ◽  
Critical Speed ◽  
Vibration Mode ◽  
Rotor System ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Coupling Vibration ◽  
Mode Function ◽  
Coupling Mode ◽  
Supporting Condition

The influence of shaft bending on the coupling vibration of rotor-blades system is nonignorable. Therefore, this paper analyzed the influence of shaft bending on the coupling vibration of rotor-blades system. The vibration mode function of shaft under elastic supporting condition was also derived to ensure accuracy of the model as well. The influence of the number of blades, the position of disk, and the support stiffness of shaft on critical speed of system was analyzed. The numerical results show that there were two categories of coupling mode shapes which belong to a set where the blade’s first two modes predominate in the system: shaft-blade (SB) mode and interblade (BB) mode due to the coupling between blade and shaft. The BB mode was of repeated frequencies of (Nb-2) multiplicity for number blades, and the SB mode was of repeated frequencies of (2) multiplicity for number blades. What is more, with the increase of the number of blades, natural frequency of rotor was decreasing linearly, that of BB mode was constant, and that of SB mode was increasing linearly. Natural frequency of BB mode was not affected while that of rotor and SB mode was affected (changed symmetrically with the center of shaft) by the position of disk. In the end, vibration characteristics of coupling mode shapes were analyzed.

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

scholarly journals Vibration analysis of submerged rectangular microplates with distributed mass loading

2009 ◽  
Vol 465 (2104) ◽  
pp. 1323-1336 ◽  
Author(s):  
Zhangming Wu ◽  
Xianghong Ma ◽  
Peter N Brett ◽  
Jinwu Xu
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Numerical Results ◽  
Previous Literature ◽  
Mode Shapes ◽  
Mass Loading ◽  
Coupling System ◽  
Different Types ◽  
Loaded Structure

This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh–Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

Free Vibration Analysis of Angle-ply Laminated Shallow Cylindrical Shell with Clamped Edges

2000 ◽  
Vol 123 (2) ◽  
pp. 188-197 ◽  
Author(s):  
Kenji Hosokawa ◽  
Minehiro Murayama ◽  
Toshiyuki Sakata
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Numerical Approach ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Plastic Composite ◽  
Vibration Tests

In a previous paper, the authors proposed a numerical approach for analyzing the free vibrations of a laminated FRP (fiber reinforced plastic) composite plate. In the present paper, this approach is modified for application to a symmetrically laminated shallow cylindrical shell having a rectangular planform. First, the natural frequencies of the shell are calculated for discussion of the convergence and accuracy of the solution. Next, the effects of the curvature ratio and stacking sequence on the natural frequencies and mode shapes of the shell are studied. Furthermore, to justify the numerical results, vibration tests of the clamped symmetrically laminated shallow cylindrical shell having a square planform are carried out. These experimental results are found to agree well with the numerical results computed using the measured material properties of the lamina.

Frequencies and Mode Shapes for Axisymmetric Vibration of Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 73-80 ◽  
Author(s):  
E. W. Ross ◽  
W. T. Matthews
Keyword(s):  
Theoretical Result ◽  
General Class ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Elastic Shells ◽  
Natural Frequencies And Modes

This paper treats the axisymmetric vibration of thin elastic shells. Estimates of natural frequencies and modes are obtained for a general class of domes by applying the approximations obtained in a previous paper by one of the authors. Numerical results are obtained for ellipsoidal shells, and one new theoretical result is found.

Experiments and Calculations on the Vibrations of Rotating Radial Impellers

1988 ◽  
Vol 110 (2) ◽  
pp. 137-142 ◽  
Author(s):  
Horst Irretier
Keyword(s):  
Rotational Speed ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Rotating Waves ◽  
Excitation Frequencies ◽  
Run Up

Experimental and numerical results on the vibrations of a rotating radial impeller are presented. They show natural frequencies as a function of rotational speed, the mode shapes, the resonance excitation frequencies of the forward and backward rotating waves, and a response diagram during a run-up of the impeller.

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.

scholarly journals Tip-timing analysis of last stage steam turbine mistuned bladed disc during run-down

2018 ◽  
Vol 211 ◽  
pp. 03003
Author(s):  
Romuald Rzadkowski ◽  
Leszek Kubitz ◽  
Michał Maziarz ◽  
Pawel Troka ◽  
Leszek Piechowski ◽  
...  
Keyword(s):  
Steam Turbine ◽  
Natural Frequencies ◽  
Timing Analysis ◽  
Numerical Results ◽  
Mode Shapes ◽  
Fe Model ◽  
Numerical Studies ◽  
Last Stage

This paper presents the experimental and numerical studies of last stage LP mistuned steam turbine bladed discs during run-down. The natural frequencies and mode shapes of the turbine bladed disc were calculated using an FE model. The influence of shaft was considered. The tip-timing method was used to find the mistuned bladed disc modes and frequencies. The numerical results were compared with experimental ones.

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.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

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