Three-dimensional oscillation characteristics of electrostatically deformed drops

1991 ◽  
Vol 227 ◽  
pp. 429-447 ◽  
Author(s):  
James Q. Feng ◽  
Kenneth V. Beard
Keyword(s):  
Electric Field ◽  
Three Dimensional ◽  
Normal Modes ◽  
Oscillation Mode ◽  
Mode Shapes ◽  
Physical Factors ◽  
Mathematical Framework ◽  
Drop Shape ◽  
Oscillation Modes ◽  
Oscillation Characteristics

A three-dimensional asymptotic analysis of the oscillations of electrically charged drops in an external electric field is carried out by means of the multiple-parameter perturbation method. The mathematical framework allows separate treatments of the quiescent deformation due to the electric field and the oscillatory motions caused by other physical factors. Without oscillations, the solution for the quiescent drop shape exhibits a prolate deformation with a slight asymmetry about the drop's equatorial plane. This axisymmetric quiescent deformation of the equilibrium drop shape is shown to modify the oscillation characteristics of axisymmetric as well as asymmetric modes. The expression of the characteristic frequency modification is derived for the oscillation modes, manifesting fine structure in the frequency spectrum so the degeneracy of Rayleigh's normal modes for charged drops is removed in the presence of an electric field. Physical reasoning indicates that the degeneracy of the oscillation modes is associated with the spherical symmetry of the system, so the removal of the degeneracy may be regarded as a consequence of the symmetry breaking caused by the electric field. In addition, the small-amplitude oscillation mode shapes are also modified as a result of the coupling between the oscillatory motions and the electric field as well as the quiescent deformation.

AXISYMMETRIC VIBRATION OF POLAR ORTHOTROPIC CIRCULAR PLATES OF QUADRATICALLY VARYING THICKNESS RESTING ON ELASTIC FOUNDATION

2005 ◽  
Vol 05 (03) ◽  
pp. 387-408 ◽  
Author(s):  
N. BHARDWAJ ◽  
A. P. GUPTA
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Three Dimensional ◽  
Normal Modes ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Varying Thickness ◽  
Edge Conditions ◽  
Polar Orthotropic

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

scholarly journals Inside-wind-farm/Wind-farm-grid sub-synchronous oscillation characteristics analysis in grid-connected system of multiple DFIGs

2021 ◽  
Vol 2076 (1) ◽  
pp. 012116
Author(s):  
Mengxue Sun ◽  
Ruixin Gao ◽  
Yuhui Ji ◽  
Xin Long ◽  
Changzhi Yao ◽  
...  
Keyword(s):  
Oscillation Frequency ◽  
Wind Farm ◽  
Oscillation Mode ◽  
Time Domain Simulation ◽  
Synchronous Oscillation ◽  
Machine Model ◽  
Oscillation Modes ◽  
Characteristics Analysis ◽  
The Stability ◽  
Oscillation Characteristics

Abstract Aiming at the sub-synchronous oscillation (SSO) problem of the grid-connected system of multiple DFIGs, most of the existing theoretical studies take the entire wind farm as a single-machine model, the stand-alone model cannot reflect the inside-wind-farm oscillation mode produced by the interactions among DFIGs in the wind farm. Therefore, this paper takes the equivalent value of DFIG-based wind farm to three DFIGs, establishes a mathematical model of the grid-connected system of three DFIGs, and studies the sub-synchronous oscillation modes existing in the system through eigenvalue analysis and participation factor analysis. The results show: When the length of transmission line increases, the oscillation frequency of the inside-wind-farm/wind-farm-grid sub-synchronous oscillation mode increases, the damping decreases and the stability weakens; when the number of grid-connected DFIGs increases, the oscillation frequency of the inside-wind-farm/wind-farm-grid sub-synchronous oscillation mode decreases, the damping increases and the stability enhances. Finally, a time-domain simulation model of the grid-connected system of multiple DFIGs was built in PSCAD/EMTDC to verify the correctness of the theoretical analysis results.

Predicting the onset of high-frequency self-excited oscillations in elastic-walled tubes

2010 ◽  
Vol 466 (2124) ◽  
pp. 3635-3657 ◽  
Author(s):  
Robert J. Whittaker ◽  
Matthias Heil ◽  
Oliver E. Jensen ◽  
Sarah L. Waters
Keyword(s):  
High Frequency ◽  
Solid Mechanics ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Normal Modes ◽  
Theoretical Description ◽  
Elastic Tube ◽  
Mode Shapes ◽  
Navier Stokes ◽  
Navier Stokes Equations

We present a theoretical description of flow-induced self-excited oscillations in the Starling resistor—a pre-stretched thin-walled elastic tube that is mounted on two rigid tubes and enclosed in a pressure chamber. Assuming that the flow through the elastic tube is driven by imposing the flow rate at the downstream end, we study the development of small-amplitude long-wavelength high-frequency oscillations, combining the results of two previous studies in which we analysed the fluid and solid mechanics of the problem in isolation. We derive a one-dimensional eigenvalue problem for the frequencies and mode shapes of the oscillations, and determine the slow growth or decay of the normal modes by considering the system’s energy budget. We compare the theoretical predictions for the mode shapes, frequencies and growth rates with the results of direct numerical simulations, based on the solution of the three-dimensional Navier–Stokes equations, coupled to the equations of shell theory, and find good agreement between the results. Our results provide the first asymptotic predictions for the onset of self-excited oscillations in three-dimensional collapsible tube flows.

Natural Frequencies and Normal Modes for Externally Damped Spinning Timoshenko Beams With General Boundary Conditions

1998 ◽  
Vol 65 (3) ◽  
pp. 770-772 ◽  
Author(s):  
J. W. Zu ◽  
J. Melanson
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Normal Modes ◽  
General Boundary ◽  
Mode Shapes ◽  
General Boundary Conditions ◽  
Timoshenko Beams ◽  
Classical Boundary

Vibration analysis of externally damped spinning Timoshenko beams with general boundary conditions is performed analytically. Exact solutions for natural frequencies and normal modes for the six classical boundary conditions are derived for the first time. In the numerical simulations, the trend between the complex frequencies and the damping coefficient is investigated, and complex mode shapes are presented in three-dimensional space.

scholarly journals Oscillation Modes of Weld Pool in Stationary GTA Welding Using Structure Laser Method

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Xingpei Wu ◽  
Jiankang Huang ◽  
Jing He ◽  
Shien Liu ◽  
Guangyin Liu ◽  
...  
Keyword(s):  
Weld Pool ◽  
Optical Measurement ◽  
Capital Expenditure ◽  
Three Dimensional ◽  
Oscillation Mode ◽  
Gta Welding ◽  
Simulation Software ◽  
Laser Method ◽  
Oscillation Modes ◽  
Structure Laser

AbstractResearchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method. However, the deficiency of simulation software will result in significant capital expenditure. Both simulations and experiments are performed in this study, and the Bessel equation is used to analyze the oscillation mode of a weld pool. The laser dot matrix images of (0, 1), (1, 1), (2, 1), and (0, 2) oscillation modes at different times are obtained via structured laser optical measurement simulation. The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment. Results show that the simulated laser dot matrix images are consistent with the experiment results. The oscillation mode of the weld pool can be recognized based on the laser dot matrix image. This study not only provides conditions for assessing the penetrating state of a weld pool, but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.

The Effect of Roughness Features on Mos Surface Electric Field and Fowler-Nordheim Tunneling Behavior

1997 ◽  
Vol 473 ◽  
Author(s):  
Heng-Chih Lin ◽  
Edwin C. Kan ◽  
Toshiaki Yamanaka ◽  
Simon J. Fang ◽  
Kwame N. Eason ◽  
...  
Keyword(s):  
Electric Field ◽  
Three Dimensional ◽  
Tunneling Current ◽  
Gate Oxide ◽  
Oxide Thickness ◽  
Interface Roughness ◽  
Normal Electric Field ◽  
Surface Electric Field ◽  
Tunneling Behavior ◽  
Nordheim Tunneling

ABSTRACTFor future CMOS GSI technology, Si/SiO2 interface micro-roughness becomes a non-negligible problem. Interface roughness causes fluctuations of the surface normal electric field, which, in turn, change the gate oxide Fowler-Nordheim tunneling behavior. In this research, we used a simple two-spheres model and a three-dimensional Laplace solver to simulate the electric field and the tunneling current in the oxide region. Our results show that both quantities are strong functions of roughness spatial wavelength, associated amplitude, and oxide thickness. We found that RMS roughness itself cannot fully characterize surface roughness and that roughness has a larger effect for thicker oxide in terms of surface electric field and tunneling behavior.

Application of partial eigenvalue assignment techniques to dampen electromechanical oscillations in multi-machine power systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Erick Baleeiro da Silva ◽  
José Mário Araújo
Keyword(s):  
Power Systems ◽  
The Other ◽  
Mode Shapes ◽  
Eigenstructure Assignment ◽  
Power System Stabilizers ◽  
Control Effort ◽  
Electromechanical Oscillations ◽  
Oscillation Modes ◽  
Partial Controllability

AbstractIn this study, a methodology for partial eigenstructure assignment (PEVA) is applied to dampen electromechanical oscillations in electrical multi-machine power systems. The approach is anchored in allocating a small number of undesirable eigenvalues, for example, which are poorly damped, preserving the other eigenvalues in the system - the so-called no-spillover spectrum. The new position of the selected eigenvalues is carried out based on the partial controllability analysis of the system, in order to minimize the control effort. Simulation examples using a system with 68 buses, 16 generators and five areas showed that the presented methodology is efficient in dampening the local and inter-area oscillation modes when compared to the classic power system stabilizers (PSS). The quality of the solution is illustrated through computer simulations, eigenvalues tables and mode-shapes.

scholarly journals Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven

Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana
Keyword(s):  
Temperature Distribution ◽  
Electric Field ◽  
Three Dimensional ◽  
Development Stage ◽  
Microwave Oven ◽  
Computational Time ◽  
Plastic Package ◽  
Heating Uniformity ◽  
The Cost ◽  
Good Agreement

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

scholarly journals Identification of Mode Shapes of a Composite Cylinder Using Convolutional Neural Networks

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2801
Author(s):  
Bartosz Miller ◽  
Leonard Ziemiański
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Composite Structures ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Identification Algorithm ◽  
Material Degradation ◽  
Local Material ◽  
Noisy Input ◽  
Shape Vector

The aim of the following paper is to discuss a newly developed approach for the identification of vibration mode shapes of multilayer composite structures. To overcome the limitations of the approaches based on image analysis (two-dimensional structures, high spatial resolution of mode shapes description), convolutional neural networks (CNNs) are applied to create a three-dimensional mode shapes identification algorithm with a significantly reduced number of mode shape vector coordinates. The CNN-based procedure is accurate, effective, and robust to noisy input data. The appearance of local damage is not an obstacle. The change of the material and the occurrence of local material degradation do not affect the accuracy of the method. Moreover, the application of the proposed identification method allows identifying the material degradation occurrence.

Sign in / Sign up

Export Citation Format

Share Document