Prediction of Structure-Borne Sound in Orthotropic Plates for Far-Field Conditions

2002 ◽  
Vol 8 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Nirmal Kumar Mandal ◽  
M. Salman Leong ◽  
R. Abd. Rahman
Keyword(s):  
Power Flow ◽  
Power Transmission ◽  
Field Conditions ◽  
Finite Difference Approximation ◽  
Wave Number ◽  
Total Power ◽  
Difference Approximation ◽  
Far Field ◽  
Orthotropic Plates ◽  
Structural Intensity

Structural intensity method is used to formulate vibration power flow model in naturally orthotropic plates in the frequency domain for far-field conditions considering bending waves. Dimensionless parameters are used in classical orthotropic plate equations to get this power. Techniques of Fourier transform and finite difference approximation are used in the formulation. Shear force components of vibration power transmission in x-direction and y-direction are obtained separately. Total power is obtained from the idea of far-field conditions. Cross-spectral density functions of field signal are used to facilitate the estimation of power transmission. Structural intensity is formulated, which is similar to that of the conventional two-transducer method. A transducer array of two points is required to get an intensity vector in one direction of a point in the plates. A new bending wave number and a modified Laplace operator are also proposed.

scholarly journals Far-Field Power Transmissions in Orthotropic Plates: A New Approach

2008 ◽  
Vol 15 (1) ◽  
pp. 71-78
Author(s):  
Nirmal K. Mandal
Keyword(s):  
Plate Theory ◽  
Field Conditions ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Far Field ◽  
Orthotropic Plates ◽  
Structural Intensity ◽  
Dual Channel ◽  
Plate Equations ◽  
Force Components

The structural intensity (SI) technique is an essential tool for locating and ranking vibration sources and sinks on structures. It can quantify vibration fields by plotting a vector map of energy transmission on the structures. In this paper, a different strategy, changing coordinate systems of plate equations, is used to develop an intensity equation from shear force components in both x and y directions. The formulation is carried out in the frequency domain considering flexural waves. Orthotropic plate theory, far-field conditions, Fourier transform, and finite difference approximation are considered. The same intensity definition is obtained using this different strategy. A dual-channel FFT analyser is essential for data acquisition to get an intensity vector in a particular direction for far-field conditions.

Structure-Borne Power Transmission in Thin Naturally Orthotropic Plates: General Case

2003 ◽  
Vol 9 (10) ◽  
pp. 1189-1199 ◽  
Author(s):  
Nirmal Kumar Mandal ◽  
Roslan Abd. Rahman ◽  
M. Salman Leong
Keyword(s):  
Fourier Transform ◽  
Power Flow ◽  
Power Transmission ◽  
Far Field ◽  
Orthotropic Plates ◽  
Flow Estimation ◽  
Structural Intensity ◽  
Vibration Power Flow ◽  
Conventional Idea ◽  
Bending Wave

The structural intensity technique is usually used to estimate vibration power flow in structures. This method is used to determine vibration power flow in thin naturally orthotropic plates. The bending wave is considered to find general vibration power transmission in the frequency domain that is not approximated by far field conditions. This intensity formulation defines power flow per unit width of the plates (W m−1) similar to that of the conventional idea. Power flow estimation is formulated using cross-spectra of field signals, facilitating the use of a fast Fourier transform analyzer.

Determining the Power Flow in a Rectangular Plate Using a Generalized Two-Step Regressive Discrete Fourier Series

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Cedric Vuye ◽  
Patrick Guillaume ◽  
Steve Vanlanduit ◽  
Flavio Presezniak ◽  
Gunther Steenackers
Keyword(s):  
Power Flow ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Domain Model ◽  
Wave Number ◽  
Engineering Structures ◽  
Structural Power ◽  
Structural Intensity ◽  
Number Frequency ◽  
Nonlinear Least Squares Method

The evaluation of structural power flow (or structural intensity (SI)) in engineering structures is a field of increasing interest in connection with vibration analysis and noise control. In contrast to classical techniques such as modal analysis, the SI indicates the magnitude and direction of the vibratory energy traveling in the structures, which yields information about the positions of the sources/sinks, along with the energy transmission path. In this paper, a new algorithm is proposed to model operational deflection shapes (ODS). The model is a two-dimensional Fourier domain model that is estimated by using a weighted nonlinear least-squares method. From the wave number-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. The proposed method is less sensitive to measurement noise than traditional power flow estimation techniques. A numerical model of a simply supported plate excited by two shakers, phased to act as an energy source and sink, is used as a simulation case. Measurements are executed on a clamped plate excited by an electromagnetic shaker in combination with a damper.

Improving the efficiency of oilfield electric power distribution

2019 ◽  
pp. 79-87
Author(s):  
Yu. F. Yu. F. Romaniuk ◽  
О. V. Solomchak ◽  
М. V. Hlozhyk
Keyword(s):  
Power Distribution ◽  
Reactive Power ◽  
Power Transmission ◽  
Transmission Efficiency ◽  
Active Power ◽  
Oil Field ◽  
Total Power ◽  
Simultaneous Increase ◽  
Active Load ◽  
Step Down

The issues of increasing the efficiency of electricity transmission to consumers with different nature of their load are considered. The dependence of the efficiency of the electric network of the oil field, consisting of a power line and a step-down transformer, on the total load power at various ratios between the active and reactive components of the power is analyzed, and the conditions under which the maximum transmission efficiency can be ensured are determined. It is shown by examples that the power transmission efficiency depends not only on the active load, but also largely on its reactive load. In the presence of a constant reactive load and an increase in active load, the total power increases and the power transmission efficiency decreases. In the low-load mode, the schedule for changing the power transmission efficiency approaches a parabolic form, since the influence of the active load on the amount of active power loss decreases, and their value will mainly depend on reactive load, which remains unchanged. The efficiency reaches its maximum value provided that the active and reactive components of the power are equal. In the case of a different ratio between them, the efficiency decreases. With a simultaneous increase in active and reactive loads and a constant value of the power factor, the power transmission efficiency is significantly reduced due to an increase in losses. With a constant active load and an increase in reactive load, efficiency of power transmission decreases, since with an increase in reactive load, losses of active power increase, while the active power remains unchanged. The second condition, under which the line efficiency will be maximum, is full compensation of reactive power.  Therefore, in order to increase the efficiency of power transmission, it is necessary to compensate for the reactive load, which can reduce the loss of electricity and the cost of its payment and improve the quality of electricity. Other methods are also proposed to increase the efficiency of power transmission by regulating the voltage level in the power center, reducing the equivalent resistance of the line wires, optimizing the loading of the transformers of the step-down substations and ensuring the economic modes of their operation.

Improving Power Flow of Power Transmission System Using UPFC

2014 ◽  
Vol 9 (9th) ◽  
pp. 1-16
Author(s):  
Heba Allah Ahmed ◽  
T. Abdel Salam ◽  
M. Mostafa ◽  
M. Badr
Keyword(s):  
Power Flow ◽  
Power Transmission ◽  
Transmission System ◽  
Power Transmission System

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

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