Size Effects in Dynamics of Dipolar Planar Nanosystems

2004 ◽  
Vol 99-100 ◽  
pp. 223-226
Author(s):  
H. Puszkarski ◽  
J.-C.S. Lévy ◽  
M. Krawczyk
Keyword(s):  
Size Effects ◽  
Equations Of Motion ◽  
Sample Surface ◽  
Dipolar Field ◽  
Dipolar Interactions ◽  
Planar System ◽  
Frequency Spectra ◽  
Magnetostatic Waves ◽  
Dynamic Components ◽  
Field Static

The equations of motion are derived for a magnetic planar system with dipolar interactions taken into account. Magnetostatic waves propagating perpendicularly to the sample surface and dipolar field static and dynamic components are calculated for the case when saturating field is applied perpendicularly to the sample surface. The corresponding frequency spectra and mode profiles are computed numerically with emphasis laid on size effects. It is established that two lowest-frequency modes are surface-localized modes. These modes preserve their surface-localized character with growing sample dimensions.

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

2014 ◽  
Author(s):  
T. N. Shiau ◽  
C. R. Wang ◽  
D. S. Liu ◽  
W. C. Hsu ◽  
T. H. Young
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Rotor System ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Frequency Spectra ◽  
Squeeze Film Damper ◽  
Assumed Mode Method ◽  
Nonlinear Dynamic Behavior

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincaré maps, and bifurcation diagrams are investigated. Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.

FREQUENCY SPECTRA OF FREE LATTICES AND PARTICLE SIZE EFFECTS ON THE HEAT CAPACITY OF SOLIDS

1955 ◽  
Vol 33 (6) ◽  
pp. 1079-1087 ◽  
Author(s):  
D. Patterson
Keyword(s):  
Particle Size ◽  
Heat Capacity ◽  
Low Temperature ◽  
Temperature Effect ◽  
Size Effects ◽  
Continuum Model ◽  
Free Boundaries ◽  
Frequency Spectra ◽  
Optical Modes ◽  
Effect Of Particle Size

The effect of particle size on the heat capacity of solids has been investigated using lattices with free boundaries as models. A monatomic lattice shows a low temperature effect associated with the acoustic modes. This can be compared with results obtained from a continuum model. With a diatomic lattice, however, an effect is also associated with the optical modes and is apparent at higher temperatures. The possibility that this latter effect can explain some recent experimental results is examined.

Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses

1991 ◽  
Vol 113 (1) ◽  
pp. 74-78 ◽  
Author(s):  
K. R. Collins ◽  
R. H. Plaut ◽  
J. Wauer
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Effective Means ◽  
Linear Equations ◽  
Free Vibrations ◽  
Frequency Spectra ◽  
Time Histories ◽  
Rotating Shafts ◽  
Linear Equations Of Motion

A rotating Timoshenko shaft with a single transverse crack is considered. The crack opens and closes during motion and is represented by generalized forces and moments. The shaft has simply supported ends, and the six coupled, piecewise-linear equations of motion (including longitudinal, transverse, and torsional displacements) are integrated numerically after application of Galerkin’s method with two-term approximations for each of the six displacements. Time histories and frequency spectra are compared for shafts with no crack and with a crack for which the crack depth is one-fifth of the shaft diameter. Free vibrations and the responses to a single axial impulse and periodic axial impulses are analyzed. The last case appears to provide an effective means for detecting cracks in rotating shafts.

An Investigation of Rolling Element Vibrations Caused by Local Defects

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
H. Arslan ◽  
N. Aktürk
Keyword(s):  
Equations Of Motion ◽  
Angular Contact Ball Bearing ◽  
Frequency Spectra ◽  
Rolling Element ◽  
Rolling Elements ◽  
Computer Simulation Program ◽  
Localized Defects ◽  
Spring System ◽  
Mass Spring ◽  
Local Defects

In this paper, a shaft-bearing model is developed in order to investigate the rolling element vibrations for an angular contact ball bearing with and without defects. The shaft-bearing assembly is considered as a mass-spring system. The system shows a nonlinear characteristic under dynamic conditions. The equations of motion in radial and axial directions were obtained for shaft and rolling elements, and they were solved simultaneously with a computer simulation program. Additionally, the effect of localized defects on running surfaces (i.e., inner ring, outer ring, and ball) on the vibration of the balls is investigated. Vibration of rolling elements in the radial direction is analyzed in time and frequency domains. Characteristic defect frequencies and their components can be seen in the frequency spectra of rolling element vibrations. Comparison of the obtained results with similar studies available in literature showed reasonable qualitative agreement.

scholarly journals The Dynamic Modeling of Multiple Pairs of Spur Gears in Mesh, Including Friction and Geometrical Errors

2003 ◽  
Vol 9 (6) ◽  
pp. 437-442 ◽  
Author(s):  
Shengxiang Jia ◽  
Ian Howard ◽  
Jiande Wang
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Frequency Spectra ◽  
Gear Teeth ◽  
Geometrical Errors ◽  
Tooth Stiffness ◽  
The Common ◽  
Profile Errors

This article presents a dynamic model of three shafts and two pair of gears in mesh, with 26 degrees of freedom, including the effects of variable tooth stiffness, pitch and profile errors, friction, and a localized tooth crack on one of the gears. The article also details howgeometrical errors in teeth can be included in a model. The model incorporates the effects of variations in torsional mesh stiffness in gear teeth by using a common formula to describe stiffness that occurs as the gears mesh together. The comparison between the presence and absence of geometrical errors in teeth was made by using Matlab and Simulink models, which were developed from the equations of motion. The effects of pitch and profile errors on the resultant input pinion angular velocity coherent-signal of the input pinion's average are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results.

Coupling of In-Plane Flexural, Tangential, and Shear Wave Modes of a Curved Beam

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
B. Kang ◽  
C. H. Riedel
Keyword(s):  
Shear Wave ◽  
Equations Of Motion ◽  
High Order ◽  
Curved Beam ◽  
Beam Model ◽  
Elastic Coupling ◽  
Dynamic Coupling ◽  
Frequency Spectra ◽  
Coupling Terms ◽  
Wave Modes

In this paper, the coupling effects among three elastic wave modes, flexural, tangential, and radial shear, on the dynamics of a planar curved beam are assessed. Two sets of equations of motion governing the in-plane motion of a curved beam are derived, in a consistent manner, based on the theory of elasticity and Hamilton’s principle. The first set of equations retains all resulting linear coupling terms that includes both static and dynamic coupling among the three wave modes. In the derivation of the second set of equations, the effects of Coriolis acceleration and high-order elastic coupling terms are neglected, which leads to a set of equations without dynamic coupling terms between the tangential and shear wave modes. This second set of equations of motion is the one most commonly used in studies on thick curved beams that include the effects of centerline extensibility, rotary inertia, and shear deformation. The assessment is carried out by comparing the dynamic behavior predicted by each curved beam model in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and mode shapes, and frequency responses. In order to ensure the comparison is based on accurate results, the wave propagation technique is applied to obtain exact wave solutions. The results suggest that the contributions of the dynamic and high-order elastic coupling terms to the response of a thick curved beam are quite significant and that these coupling terms should not be neglected for an accurate analysis of a thick curved beam with a large curvature parameter.

Modeling and Analysis of a Multi Degree of Freedom Point Absorber Wave Energy Converter

2014 ◽  
Author(s):  
Andrew F. Davis ◽  
Jim Thomson ◽  
Tim R. Mundon ◽  
Brian C. Fabien
Keyword(s):  
Time Series ◽  
Wave Energy ◽  
Equations Of Motion ◽  
Field Testing ◽  
Wave Energy Converter ◽  
System Response ◽  
Model Parameters ◽  
Energy Converter ◽  
Frequency Spectra ◽  
Modeling And Analysis

This paper illustrates an approach to the modeling of a point absorbing Wave Energy Converter (WEC) with the intent of analyzing the sensitivity of the system response to variation in the model parameters. Using first principles, the nonlinear equations of motion are formed to describe the heave motion of a 3 body system. A linearized model is developed and used to simulate the system in both the time and frequency domains. The input to the model is a time series displacement and a time series velocity that describes the incident waves. A sensitivity analysis is then performed on the system parameters to show how the characteristics of the heave plate, the component masses, and the mass of the entrained fluid affect the performance of the system. The model is validated by numerically modeling a generation 1 device produced by Oscilla Power Inc., which is compared against experimental data from a field test on Lake Washington. The WEC is designed to provide tension along a series of tethers with connected power take off units. The wave input is specified using frequency spectra measured with a nearby Datawell Waverider MK III buoy during the field testing, from which time domain waves are reconstructed.

Multi-Physics Modeling of an Electro-Thermally Actuated Micro-Cantilever for Scanning Probe Microscopy

2010 ◽  
Author(s):  
Thomas Sattel ◽  
Dennis Roeser ◽  
Stefanie Gutschmidt
Keyword(s):  
Equations Of Motion ◽  
Real Life ◽  
Sample Surface ◽  
Dynamical Analysis ◽  
Atomic Force ◽  
First Results ◽  
Physics Modeling ◽  
Thermally Actuated ◽  
Micro Cantilever ◽  
Nonlinear Equations Of Motion

This article presents the nonlinear equations of motion and analysis of a smart micro-cantilever which was designed and fabricated for AFM (atomic force microscopy) technology. The model is derived from the mechanical continuum expressions and includes thermo-visco-elastic damping as well as the localized atomic force interaction between the tip and sample surface, which in turn is deduced from the Lennard-Jones potential. The modal dynamical system obtained from the continuum model and by means of the Galerkin decomposition is then numerically analyzed. The analysis begins with the study of equilibria and natural frequencies under the influence of the selected parameters, such as the direct current and gap between tip and sample. This is complemented by a brief dynamical analysis of the system in selected parameter domains. The multi-physics micro-cantilever exists in real life and these first results of work in progress serve our intentions of systematically investigating the static and dynamic behavior of the same experimentally in the future.

scholarly journals Investigation of a spatial double pendulum: an engineering approach

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
S. Bendersky ◽  
B. Sandler
Keyword(s):  
Fourier Transformation ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Double Pendulum ◽  
Kutta Method ◽  
Free Oscillations ◽  
Frequency Spectra ◽  
Runge Kutta Method ◽  
Dynamic Investigation

The behavior of a spatial double pendulum (SDP), comprising two pendulums that swing in different planes, was investigated. Movement equations (i.e., mathematical model) were derived for this SDP, and oscillations of the system were computed and compared with experimental results. Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. Solutions for free oscillations of the pendulums and graphic descriptions of changes in the frequency spectra were used for the dynamic investigation of the pendulums for different initial conditions of motion. The value of the friction constant was estimated experimentally and incorporated into the equations of motion of the pendulums. This step facilitated the comparison between the computed and measured oscillations.

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