Vibration of Flexibly Mounted Gyroscopes

1973 ◽  
Vol 15 (3) ◽  
pp. 225-231
Author(s):  
L. Maunder
Keyword(s):  
Natural Frequencies ◽  
Critical Speeds ◽  
Supporting Structure ◽  
Vibrational Characteristics

Flexibility in the supporting structure of two-axis or single-axis gyroscopes is shown to have a radical effect on vibrational characteristics. The analysis determines the ensuing natural frequencies and critical speeds.

Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems

1979 ◽  
Vol 101 (2) ◽  
pp. 210-223 ◽  
Author(s):  
S. Kalaycioglu ◽  
C. Bagci
Keyword(s):  
Dynamic Systems ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Large Error ◽  
Free Vibrations ◽  
Lumped Mass ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Line Elements ◽  
Kinematic Motion

It has been a well-established fact that dynamic systems in motion experience critical speeds, such as rotating shafts and geared systems whose undeformed reference geometry remain the same at all times. Their critical speeds are determined by their natural frequencies of considered type of free vibrations. Linkage mechanisms as dynamic systems in motion change their undeformed geometries as function of time during the cycle of kinematic motion. They do also experience critical operating speeds as rotating shafts and geared systems do, and their critical speeds are determined by the minima of their natural frequencies during a cycle of kinematic motion. Such a minimum occurs at the critical geometry of a mechanism, which is the position at which the maximum of the input power is required to maintain the instantaneous dynamic equilibrium of the mechanism. Actual finite line elements are used to form the global generalized coordinate flexibility matrix. The natural frequencies of the mechanism and the corresponding mode vectors (mode deflections) are determined as the eigen values and eigen vectors of the equations of instantaneous-position-free-motion of the mechanism. Method is formulated to include or exclude the link axial deformations, and apply to any number of loops having any type of planar pair. Critical speeds of planar four-bar, slider-crank, and Stephenson’s six-bar mechanisms are determined. Experimental results for the four-bar mechanism are given. Effect of axial deformations and link rotary inertias are investigated. Inclusion of link axial deformations in mechanisms having pairs with sliding freedoms is seen to predict critical speeds with large error.

Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

2007 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Valerie J. Lease
Keyword(s):  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Rotor Dynamics ◽  
Axial Position ◽  
Disk System ◽  
Apparent Contradiction ◽  
Critical Speeds ◽  
Shaft Flexibility ◽  
Gyroscopic Effects ◽  
Lumped Masses

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.

Vibrational characteristics of an earth dam

1966 ◽  
Vol 56 (6) ◽  
pp. 1207-1226
Author(s):  
W. O. Keightley
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Forced Vibrations ◽  
Earth Dam ◽  
Mode Shapes ◽  
Modal Damping ◽  
Vibrational Characteristics ◽  
Good Agreement ◽  
Lower Frequencies

Abstract An earth dam was excited into vibrations, in the upstream-downstream direction, by four rotating eccentric-mass vibration generators which were operated on the crest. Natural frequencies, mode shapes, and equivalent viscous modal damping constants of the dam were revealed by the forced vibrations. A theoretical analysis of the dam, based on consideration of shearing deformations only, shows moderately good agreement with the behavior which was observed at the lower frequencies.

Finite element investigation of the vibrational behavior of concentric multi-walled boron nitride and carbon nanotubes

2017 ◽  
Vol 31 (04) ◽  
pp. 1750018 ◽  
Author(s):  
R. Ansari ◽  
S. Rouhi ◽  
A. Nikkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boron Nitride ◽  
Natural Frequencies ◽  
Vacancy Defect ◽  
Boron Nitride Nanotubes ◽  
The Finite Element Method ◽  
Zigzag Nanotubes ◽  
Vibrational Behavior ◽  
Vibrational Characteristics

This paper concerns the vibrational behavior of concentric double-walled and triple-walled carbon and boron nitride nanotubes using the finite element method. Armchair and zigzag nanotubes with different lengths and diameters are considered. Moreover, different boundary conditions are applied on the nanotubes. It is observed that in double-walled nanotubes, when the inner and outer layers are respectively from boron nitride and carbon, the frequencies are larger than those in the reverse arrangement. Investigating the effect of diameter on the first 10 natural frequencies of double-walled and triple-walled nanotubes showed that nanotubes with larger diameters possess smaller frequencies. The effect of diameter is more significant for higher modes. Finally, comparisons are made between the vibrational behavior of concentric carbon and boron nitride double-walled and triple-walled nanotubes. Considering the effect of vacancy defect on the vibrational characteristics of the nanotubes revealed that when all of the walls of the nanotubes are defective, the largest diminish occurs for the fundamental natural frequencies.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part I: The Rotor Mass—Elastic Model

1987 ◽  
Vol 109 (1) ◽  
pp. 1-7 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Research Program ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Computer Programs ◽  
Elastic Model ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Improve Accuracy ◽  
Speed Computer ◽  
Rotor Mass

This is the first part (Part I) of two papers describing results of a research program directed at verifying computer programs used to calculate critical speeds of turbomachinery. This research program was undertaken since questions existed about the accuracy of calculations for the second and higher critical speeds. Part I describes improvements in computer programs and data modeling that resulted from comparing measured and calculated “free-free” natural frequencies of several shafts and rotors. Program modifications to improve accuracy include consideration of the effect of disk/shaft attachment stiffness, revised treatment of the end masses, and an improved convergence. Modifications resulting from the study are applicable to many other damped and undamped critical speed computer programs.

Analysis Behavior of a Rig Shafting Vibration Set Changes Bearing Parameters

2013 ◽  
Vol 437 ◽  
pp. 98-101 ◽  
Author(s):  
Van Thanh Ngo ◽  
Dan Mei Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Lateral Vibration ◽  
Eigenvalues And Eigenvectors ◽  
Fem Model ◽  
Critical Speeds ◽  
Bearing Stiffness

Frequently, in the design of machines, some of parameters that directly affect the rotordynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using finite element method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior.

Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams

1965 ◽  
Vol 32 (4) ◽  
pp. 881-886 ◽  
Author(s):  
R. A. DiTaranto
Keyword(s):  
Differential Equation ◽  
Finite Length ◽  
Loss Factor ◽  
Natural Frequencies ◽  
Auxiliary Equation ◽  
Order Complex ◽  
Laminated Beam ◽  
Vibrational Characteristics ◽  
Bending Problems ◽  
Viscoelastic Layers

The vibrational characteristics, natural frequencies, and associated composite loss factor of a finite-length laminated beam having alternate elastic and viscoelastic layers, are investigated. An auxiliary equation which accounts for the effect of the viscoelastic layers is derived. The use of this equation in conjunction with the ordinary bending equations encountered for homogeneous beams, allows one to solve static and dynamic bending problems for laminated beams in the same manner as for homogeneous beams. The resulting equations are complex expressions since the shear modulus of the viscoelastic material is a complex quantity. The use of the auxiliary equation in conjunction with the loading equation for a freely vibrating beam yields a sixth-order, complex, homogeneous differential equation. The solution of this equation, subject to satisfying the boundary conditions, yields the desired natural frequencies and associated composite loss-factors.

Vibrations of Twisted Cantilevered Plates—Experimental Investigation

1985 ◽  
Vol 107 (1) ◽  
pp. 187-196 ◽  
Author(s):  
J. C. MacBain ◽  
R. E. Kielb ◽  
A. W. Leissa
Keyword(s):  
Research Study ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Mode Shapes ◽  
Turbine Engine ◽  
Aspect Ratios ◽  
Engine Blade ◽  
Vibrational Characteristics ◽  
Cantilevered Plates ◽  
Effect Of Support

The experimental portion of a joint government/industry/university research study on the vibrational characteristics of twisted cantilevered plates is presented. The overall purpose of the research study was to assess the capabilities and limitations of existing analytical methods in predicting the vibratory characteristics of twisted plates. Thirty cantilevered plates were precision machined at the Air Force’s Aero Propulsion Laboratory. These plates, having five different degrees of twist, two thicknesses, and three aspect ratios representative of turbine engine blade geometries, were tested for their vibration mode shapes and frequencies. The resulting nondimensional frequencies and selected mode shapes are presented as a function of plate tip twist. The trends of the plate natural frequencies as a function of the governing geometric parameters are discussed. The effect of support compliance on the plate natural frequency and its impact on numerically modeling twisted plates is also presented.

scholarly journals Modal analysis of spindles while accounting for system decay and its application to machine tool chatter prevention

2021 ◽  
Author(s):  
Seyed M. Hashemi ◽  
Omar Gaber
Keyword(s):  
Life Span ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Advanced Manufacturing ◽  
Machining Parameters ◽  
Fundamental Frequencies ◽  
Stability Lobes ◽  
Machine Tool Chatter ◽  
Vibrational Characteristics ◽  
The Stability

This paper investigates the vibrational characteristics of a machining spindle over its life span. The experimental investigation was carried out using tap testing, where the fundamental frequencies of the spindle system were recorded for different spindle categories, namely, ‘production’ and ‘prove-out’ spindles. Focussing on production spindles, the system ageing translated through a reduction in the system’s natural frequency is modelled as changes in the bearings’ stiffness. The experimentally evaluated natural frequencies were then used to calculate the equivalent bearings’ stiffness within the spindle by means of a calibrated dynamic stiffness method (CDSM) at various stages of spindle’s life. A comparison between the stability lobes generated for two different instances in time, in a full slotting cuts process, shows that over the life span of a spindle, the stability lobes would shift sufficiently to cause chatter after initially being stable. Therefore, as the spindle ages, the presented methodology can be exploited to predict the updated machining parameters necessary to avoid unstable chatter conditions.<div><br></div><div>This is a post-peer-review, pre-copyedit version of an article published in The International Journal of Advanced Manufacturing Technology. The final authenticated version is available online at: https://doi.org/10.1007/s00170-015-6979-4 <br></div>

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