Free Vibration of Uniform, Flexible, Cylindrical Shell Rotors

1999 ◽  
Author(s):  
Fei-Yue Wang ◽  
Albert C. J. Luo
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Rotational Speed ◽  
Rotation Speed ◽  
Isotope Separation ◽  
Critical Speeds ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Very High ◽  
Good Agreement

Abstract The critical speeds and responses of uniform, flexible, cylindrical rotors are predicted by use of the Riccati transfer matrix method. The critical speeds are also measured experimentally. The computational and experimental results are in good agreement. The balancing of two cylindrical shell rotors is completed. For the two balanced rotors, no large amplitude vibration occur when the operating, rotational speed passes through critical speeds, and that rotation speed can arrive to a very high value to meet the requirement of isotope separation in engineering.

Vibration Analysis of a Self-Excited Vibration in a Rotor System Caused by a Ball Balancer

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Yukiko Ishida ◽  
Hideaki Niimi
Keyword(s):  
Rotational Speed ◽  
Critical Speed ◽  
Vibration Suppression ◽  
The Self ◽  
Rotor Systems ◽  
Excited Vibration ◽  
Amplitude Vibration ◽  
Speed Range ◽  
Large Amplitude Vibration ◽  
Fundamental Equations

The ball balancer has been used as a vibration suppression device in rotor systems. It has a superior characteristic that the vibration amplitude is reduced to zero theoretically at a rotational speed range higher than the critical speed. However, the ball balancer causes a self-excited vibration near the critical speed when the balls rotate in the balancer. This self-excited vibration may occur in the wide rotational speed range with a large amplitude vibration, and in such a case, escaping from it becomes difficult. In this paper, the occurrence region and the vibration characteristics of the self-excited vibration caused by the ball balancer are investigated. The nonlinear theoretical analysis is performed and a set of the fundamental equations governing the self-excited vibration is obtained. The influences of the parameters of the ball balancer, such as, the damping of the ball’s motion, the ball’s mass, and radius of the balls’ path, are explained and they are also validated experimentally.

Effects of Rotary Inertia and Shear Deformation on Nonlinear Free Vibration of Microbeams

2006 ◽  
Vol 128 (5) ◽  
pp. 611-615 ◽  
Author(s):  
Asghar Ramezani ◽  
Aria Alasty ◽  
Javad Akbari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Vibration ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Rotary Inertia ◽  
Partial Differential ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the doubly clamped microbeam. Shear deformation and rotary inertia have significant effects on the large amplitude vibration of thick and short microbeams.

scholarly journals Computational Liquid Dynamic Simulation Mixing Time from Side Inlet Mixer Tank

2021 ◽  
Vol 5 (1) ◽  
pp. 30-40
Author(s):  
Nadia Mumtazah ◽  
Ainurazis Ramadhana Putraninghadi ◽  
Ni'am Nisbatul
Keyword(s):  
Rotational Speed ◽  
Single Phase ◽  
Rotation Speed ◽  
Fluid Dynamic ◽  
Mixing Time ◽  
Flat Bottom ◽  
Geometric Size ◽  
Cfd Method ◽  
The Impact ◽  
Good Agreement

This study aims to investigate the mixing time of the side-entry mixer tank and the influence of the propeller's rotational speed on mixing time by the Computational Fluid Dynamic (CFD) method. The tank's model is a flat-bottom cylinder tank whose diameter is 40 cm with a 6 cm propeller contains three blades. The tracer, HCL 37%, was injected on the water's surface while the propeller's rotation speed is varied 100 rpm, 200 rpm, 300 rpm, and 400 rpm. The simulation process is examined using CFD FLUENT 17.1, with a turbulence model is k-ɛ RNG. Its conditions are single-phase then proceeded using species transport. Furthermore, the monitoring point's simulation is identical to the experimental data monitoring probe, which is used to inspect the mass fraction at each point. After all, this simulation contains three processes: pre-processing, solving, and post-processing. as a result, the propeller's higher rotational speed makes the mixing time shorter in the CFD method, which has a good agreement with the experimental method. Moreover, this study also examines the impact of the grid's type and the geometric size for the mixing process in the side-entry mixer tank.

Vibrational Frequencies Calculation of Fluid Conveying Pipes Based on Fluid-Structure Coupling and Acoustic-Structure Coupling Models

2014 ◽  
Vol 574 ◽  
pp. 41-47
Author(s):  
Wen Jie Guo ◽  
Tian Yun Li ◽  
Xiang Zhu ◽  
Xian Ming Zhu
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Internal Pressure ◽  
Bessel Functions ◽  
Acoustic Structure ◽  
New Approach ◽  
Fluid Structure ◽  
The Galerkin Method ◽  
Fluid Conveying Pipes ◽  
Good Agreement

Two coupling models, the fluid-structure coupling and the acoustic-structure coupling, have been studied in this paper, in order to describe the free vibration of a fluid-filled cylindrical shell under internal pressure from two different angles. For both models, a new approach to solve the characteristic equation is presented, using the Galerkin method to obtain the natural frequency of each mode. The comparison shows the results of two models are in good agreement. Although the two models are based on different mechanical theories, the mathematic essences are confirmed to be the same, both derived from Bessel functions.

Large Amplitude Vibration Analysis of Shear Deformable FGM Cylindrical Shell

2012 ◽  
Author(s):  
Davood Younesian ◽  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Cylindrical Shell ◽  
Energy Balance ◽  
Balance Method ◽  
Energy Balance Method ◽  
Dimensionless Equation ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
And Performance ◽  
Analytical Approaches ◽  
Shear Deformable

The free vibration of shear deformable FGM cylindrical shell is analyzed by means of three analytical approaches including Hamiltonian Approach (HA), Energy Balance Method (EBM) and the Modified Energy Balance Method (MEBM). Firstly, dimensionless equation of vibration of shell is derived and using the Galerkin procedure, the associating ODE is constructed. The Voight model is employed and a parametric study is provided. Effects of different parameters such as the temperature, stiffness and material properties on the natural frequencies are studies. Accuracy and performance of different approaches are analyzed. Moreover the sensitivity of frequency ratio to the different parameters is investigated.

Dislocation structures around SiO2 Particles in aged Cu-Cr-SiO2

1978 ◽  
Vol 36 (1) ◽  
pp. 594-595
Author(s):  
N.J. Long ◽  
M.H. Loretto ◽  
C.H. Lloyd
Keyword(s):  
Flow Stress ◽  
Single Crystals ◽  
Room Temperature ◽  
Thin Foil ◽  
Age Hardening ◽  
Dispersion Strengthening ◽  
Accurate Picture ◽  
The Matrix ◽  
Very High ◽  
Good Agreement

IntroductionThere have been several t.e.m. studies (1,2,3,4) of the dislocation arrangements in the matrix and around the particles in dispersion strengthened single crystals deformed in single slip. Good agreement has been obtained in general between the observed structures and the various theories for the flow stress and work hardening of this class of alloy. There has been though some difficulty in obtaining an accurate picture of these arrangements in the case when the obstacles are large (of the order of several 1000's Å). This is due to both the physical loss of dislocations from the thin foil in its preparation and to rearrangement of the structure on unloading and standing at room temperature under the influence of the very high localised stresses in the vicinity of the particles (2,3).This contribution presents part of a study of the Cu-Cr-SiO2 system where age hardening from the Cu-Cr and dispersion strengthening from Cu-Sio2 is combined.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

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