Analysis of Coupled Bending-Axial Vibration of a Rotor

2013 ◽  
Vol 662 ◽  
pp. 608-611 ◽  
Author(s):  
Jian Feng Ye ◽  
Chun Long Zheng ◽  
Xue Shi Yao
Keyword(s):  
Axial Force ◽  
Vibration Frequency ◽  
Torsional Vibration ◽  
Stiffness Matrix ◽  
Tensile Force ◽  
Vibration Frequencies ◽  
Axial Vibration ◽  
Bending Vibration ◽  
Centrifugal Load ◽  
Rotor Model

Aiming at a rotor model, the coupled bending-axial vibration is being analyzed.Calculation results show that the prestress relative to rotational centrifugal load may influence bending vibration frequencies of a rotor.The bending vibration frequencies will increase when the prestress increases.The axial vibration frequency has not an influence because the direction of the spinning prestress is perpendicular to axis.When a rotor is applies axial force, a compressional force will tend to increase the axial vibration frequencies while a tensile force will decrease the axial vibration frequencies.The effects of the prestress(centrifugal load )of the spinning rotor and the axial prestress can be accounted by an adjustment of the stiffness matrix for analysis.By use of the stiffness matrix,the changed axial and bending vibration frequencies can be explained.The coupled bending-axial vibration may take place when the bending vibration frequencies have increased in the state of the changed prestress.In the end, the coupled bending-axial vibration frequency can be calculated.On the basis of prestress, the coupled lateral-torsional vibration and the coupled torsional-axial vibration frequency can be analysed,similarly.

Study on Bending-Torsional Coupling Vibration of Intermediate Axis

2012 ◽  
Vol 166-169 ◽  
pp. 3180-3183
Author(s):  
Xue Shi Yao ◽  
Chun Long Zheng
Keyword(s):  
Torsional Vibration ◽  
Dynamic Equations ◽  
Optimized Design ◽  
Modal Shape ◽  
Bending Vibration ◽  
Coupling Vibration ◽  
Centrifugal Load ◽  
Torsional Coupling ◽  
Nature Frequency ◽  
Torsional Frequency

In order to find the cause of the cracked intermediate axis in a transmission,the characteristic of the bending vibration，torsional vibration and bending-torsional coupling vibration were studied through the analysis of the nature frequency and modal shape based on prestress.The results show that the fatigue fracture of the axis is mainly due to the resonant torsional frequency and bending-torsional coupling vibration and It is basically demonstrated by experiment.It has been found that the fundamental frequency is increase with the increase in spin axis velocity because of the centrifugal load i.e.prestress.The effets can be accounted for by an adjustment of the stiffness,and the dynamic equations are derived.In the end,it is made the optimized design on the axis,the low inherent frequencies are optimized in order to avoid resonance.The problem of the cracked intermediate axis has been solved.

scholarly journals Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 126
Author(s):  
Guangwei Zhou ◽  
Changzhao Qian ◽  
Changping Chen
Keyword(s):  
Finite Element ◽  
Fundamental Frequency ◽  
Vibration Frequency ◽  
Structural Characteristics ◽  
Physical Characteristics ◽  
Parameter Analysis ◽  
Lateral Bending ◽  
Bending Vibration ◽  
Main Cable ◽  
Symmetrical Vibration

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.

scholarly journals Effect of beat frequency on the velocity of microtubule sliding in reactivated sea urchin sperm flagella under imposed head vibration.

1995 ◽  
Vol 198 (3) ◽  
pp. 645-653 ◽  
Author(s):  
C Shingyoji ◽  
K Yoshimura ◽  
D Eshel ◽  
K Takahashi ◽  
I R Gibbons
Keyword(s):  
Sea Urchin ◽  
Vibration Frequency ◽  
Beat Frequency ◽  
Distal Region ◽  
Bend Angle ◽  
Vibration Frequencies ◽  
Sliding Velocity ◽  
Flagellar Beat ◽  
Tripneustes Gratilla ◽  
Sea Urchin Sperm

The heads of demembranated spermatozoa of the sea urchin Tripneustes gratilla, reactivated at different concentrations of ATP, were held by suction in the tip of a micropipette and vibrated laterally with respect to the head axis. This imposed vibration resulted in a stable rhythmic beating of the reactivated flagella that was synchronized to the frequency of the micropipette. The reactivated flagella, which in the absence of imposed vibration had an average beat frequency of 39 Hz at 2 mmol l-1 ATP, showed stable beating synchronized to the pipette vibration over a range of 20-70 Hz. Vibration frequencies above 70 Hz caused irregular, asymmetrical beating, while those below 20 Hz induced instability of the beat plane. At ATP concentrations of 10-100 mumol l-1, the range of vibration frequency capable of maintaining stable beating was diminished; an increase in ATP concentration above 2 mmol l-1 had no effect on the range of stable beating. In flagella reactivated at ATP concentrations above 100 mumol l-1, the apparent time-averaged sliding velocity of axonemal microtubules decreased when the imposed frequency was below the undriven flagellar beat frequency, but at higher imposed frequencies it remained constant, with the higher frequency being accompanied by a decrease in bend angle. This maximal sliding velocity at 2 mmol l-1 ATP was close to the sliding velocity in the distal region of live spermatozoa, possibly indicating that it represents an inherent limit in the velocity of active sliding.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

2021 ◽  
Author(s):  
Heenkenda Jayasinghe
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Axial Force ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Compressive Force ◽  
Mode Shapes ◽  
Dynamic Finite Element ◽  
Starting Point

Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

scholarly journals Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model

2018 ◽  
Vol 38 (1) ◽  
pp. 70-87 ◽  
Author(s):  
Mustafa Ö Yayli ◽  
Suheyla Y Kandemir ◽  
Ali E Çerçevik
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Torsional Vibration ◽  
Nonlocal Boundary ◽  
Coefficient Matrix ◽  
Vibration Frequencies ◽  
Sine Series ◽  
Differential Model ◽  
Fourier Sine ◽  
Fourier Sine Series

Free torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions is studied. Eringen’s nonlocal elasticity theory is used in the analysis. Two similar rotation functions are represented by two Fourier sine series. A coefficient matrix including torsional springs and crack parameter is derived by using Stokes’ transformation and nonlocal boundary conditions. This useful coefficient matrix can be used to obtain the torsional vibration frequencies of cracked nanotubes with restrained boundary conditions. Free torsional vibration frequencies are calculated by using Fourier sine series and compared with the finite element method and analytical solutions available in the literature. The effects of various parameters such as crack parameter, geometry of nanotubes, and deformable boundary conditions are discussed in detail.

scholarly journals Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

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