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.

Vibrational Study of the Spinning Disc Using LDV Technique

2015 ◽  
Vol 816 ◽  
pp. 469-473 ◽  
Author(s):  
Peter Šároši ◽  
Tomáš Harčarík ◽  
Róbert Huňady
Keyword(s):  
Rotational Speed ◽  
Natural Frequencies ◽  
Rotational Velocity ◽  
Optical Methods ◽  
Mode Shapes ◽  
Vibration Behavior ◽  
Vibrational Study ◽  
Run Up ◽  
Spinning Disc

This paper reports on the application of experimental optical methods to study vibration of the centrally clamped disc. The natural frequencies and mode shapes with zero rotational speed are analyzed. Influence of rotational velocity to shifting natural frequencies was investigated with optical derotator. To evaluate shifting of natural frequencies run up analysis were measured. In run-up analysis the frequencies of centrally clamped disc considering increased rotational speed are obtained. Obtained waterfall plots show vibration behavior of spinning disc.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

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.

Mistuning Analyses of a Bladed Disk: Pole-Zero and Modal Approaches

2008 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Peak Amplitude ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Amplitude Maximum ◽  
Excitation Frequencies ◽  
Amplitude Amplification

This paper examines the fundamental aspects of amplitude amplification due to mistuning in a bladed disk. Both pole-zero and modal approaches are used to understand the effects of changes in mode shapes and the natural frequencies on the minimum and maximum values of peak amplitudes among all blades over all excitation frequencies. The nature of variation of this peak amplitude is studied, and algorithms are discussed to determine the statistics of the peak amplitude, maximum and minimum values of the peak amplitude, and corresponding mistuning patterns.

An Investigation of Dual Mode Phenomena in a Mistuned Bladed Disk

1983 ◽  
Vol 105 (3) ◽  
pp. 402-407 ◽  
Author(s):  
W. A. Stange ◽  
J. C. MacBain
Keyword(s):  
Strain Gage ◽  
Holographic Interferometry ◽  
Rotational Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Dual Mode ◽  
Disk Model ◽  
Bladed Disk ◽  
Mode Splitting ◽  
Modes Of Vibration

This paper presents the results of an investigation addressing the effects of mistuning on the lower modes of vibration of a simple bladed-disk model. The phenomena of dual modes, also known as mode splitting, is studied using holographic interferometry and strain gage measurements under nonrotating and rotating conditions. Resonant amplitudes, mode shapes, and natural frequencies of the disk model were determined, without deliberately mistuning the disk. The tests were then repeated with the disk deliberately mistuned to varying degrees, paying particular attention to the second diameter (2N) dual modes. Additionally, tests were conducted on the disk at a rotational speed of 2000 rpm, in an effort to gain insight as to the vibratory characteristics of the disk under rotating conditions.

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.

Rocking Vibration of Rotating Disk and Spindle Systems With Asymmetric Bearings

2001 ◽  
Author(s):  
Jung Seo Park ◽  
I. Y. Shen ◽  
C.-P. Roger Ku
Keyword(s):  
Numerical Simulation ◽  
Rotational Speed ◽  
Natural Frequencies ◽  
Rotating Disk ◽  
Mode Shapes ◽  
Unperturbed System ◽  
High Rotational Speed ◽  
Spindle System ◽  
Rocking Motion ◽  
Gyroscopic Effects

Abstract This paper studies how bearing asymmetry affects natural frequencies and mode shapes of a rotating disk/spindle system through a numerical simulation and a perturbation analysis. Existing literature has shown that rocking motion of a rotating disk/spindle system with symmetric bearings consists of rigid body rocking of the spindle, one-nodal-diameter modes of each disk, and deformation of spindle bearings. The rocking motion, characterized by (0,1) unbalanced modes, has repeated natural frequencies when the spindle is stationary, because the disk/spindle system is axisymmetric. For a rotating spindle, (0,1) unbalanced modes evolve into forward and backward precession with circular orbits. In this paper, the numerical simulation shows that bearing asymmetry splits a pair of repeated (0,1) unbalanced modes into two modes with distinct frequencies when the spindle is stationary. Moreover, when the rotational speed increases from zero, the (0,1) unbalanced mode with lower frequency evolves into backward precession and the (0,1) unbalanced mode with higher frequency evolves into forward precession. The precession orbits are elliptical because of the bearing asymmetry. Two perturbation schemes are developed to prove the phenomena observed in the numerical simulation. For low rotational speed, a stationary disk/spindle system with symmetric bearings serves as the unperturbed system. Both the bearing asymmetry and gyroscopic effects from rotation form the perturbation. A contraction iteration predicts the effects of bearing asymmetry on natural frequencies and mode shapes. For high rotational speed, a rotating (gyroscopic) disk/spindle system with symmetric bearings serves as the unperturbed system. The bearing asymmetry forms the perturbation. To obtain a perturbation solution, the solvability condition is first derived for the unperturbed gyroscopic system. Lindsted-Poincaré approach then predicts the effects of bearing asymmetry on natural frequencies and mode shapes of the rotating disk/spindle system.

scholarly journals Modal analysis of an aerostatic spindle system for ultra-precision machine tools at different spin speeds

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879852 ◽  
Author(s):  
Peng Chen ◽  
Hui Zhuang ◽  
Yu Chang ◽  
Jianguo Ding ◽  
Qidi Zhong ◽  
...  
Keyword(s):  
Flow Field ◽  
Rotational Speed ◽  
Machine Tools ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Spindle System ◽  
Precision Machine ◽  
Ultra Precision ◽  
Precision Machine Tools ◽  
Aerostatic Spindle

The dynamic properties of aerostatic spindle systems vary with the spindle speed and have a significant impact on the processing quality of ultra-precision machine tools. In this article, using the ICEM CFD, the structured grid model of a large-span scale gas film is built under the condition in which the ratio of the spindle gas film length to the gas film thickness is 13,100. Integral calculation model of spindle and thrust is established and CEL expressions are compiled based on dynamic meshing technique to acquire trajectory of aerostatic spindle system. The degree of freedom method is used to obtain flow field of spindle system. Considering the spindle system as an elastomer, the influence of rotational speed on natural frequencies is studied under the flow field boundary. The results indicate that the former four-order natural frequencies of the aerostatic spindle system will clearly increase as the rotational speed increases. The increase in the fifth- to seventh-order natural frequencies is small, and the eighth-order natural frequency is almost invariable. The flow field has little influence on the mode shapes of the aerostatic spindle system. The former four-order natural frequencies of spindle system decrease considering rotation effects. Rotational speed and rotation effects mainly impact the tilting motion natural frequencies of spindle and thrust.

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