A Method to Simulate Structural Intensity Fields in Plates and General Structures Induced by Spatially and Temporally Random Excitation Fields

2007 ◽  
Author(s):  
Michael J. Daley ◽  
Stephen A. Hambric
Keyword(s):  
Finite Difference ◽  
Pressure Fluctuations ◽  
Practical Interest ◽  
Random Excitation ◽  
New Method ◽  
Thin Plates ◽  
Finite Differencing ◽  
Structural Intensity ◽  
Bending Waves ◽  
Pressure Fields

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. Most studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations. Additionally, such studies typically employ finite differencing techniques to estimate the shear, bending and twisting components of intensity, and are therefore only applicable to simple homogenous uniform structures such as thin plates and beams. Often, however, finite differencing techniques are not applicable to practical structures of interest. The present study introduces a new method to compute the structural intensity induced by spatially random pressure fields in general structures which does not require the use of finite differencing techniques. The results of this method are validated using those obtained using finite-difference based techniques in a thin plate. The simulated fields from the new analytic technique are shown to be similar to those estimated via finite difference-based techniques, thus validating this new method. Both methods show intensity patterns different from those caused by deterministic point drives. The new general method may be applied in the future to complex non-homogenous structures which include discontinuities and curvature.

A Method to Simulate Structural Intensity Fields in Plates and General Structures Induced by Spatially and Temporally Random Excitation Fields

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Michael J. Daley ◽  
Stephen A. Hambric
Keyword(s):  
Multiple Input Multiple Output ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Practical Interest ◽  
Random Excitation ◽  
Thin Plates ◽  
Analysis Techniques ◽  
Finite Differencing ◽  
Structural Intensity ◽  
Pressure Fields

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. Most studies to date, however, have considered only the structural intensity induced by deterministic localized drives. Many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations. Additionally, such studies typically employ finite differencing techniques to estimate the shear, bending, and twisting components of intensity, and are therefore only applicable to simple homogenous uniform structures such as thin plates and beams. Often, however, finite differencing techniques are not applicable to practical structures of interest. The present study introduces a new analytic method to compute the structural intensity induced by spatially random pressure fields in general structures, which does not require the use of finite differencing techniques. This method uses multiple-input multiple-output random analysis techniques, combining frequency response function matrices generated from analytic or finite element (FE) models with cross-spectral density matrices of spatially random pressure fields to compute intensities in structures. The results of this method are validated using those obtained using finite-difference-based techniques in a flat plate. Both methods show intensity patterns different from those caused by deterministic point drives. The new general method, combined with FE analysis techniques, may be applied in the future to complex nonhomogenous structures, which include discontinuities, curvature, anisotropic materials, and general three-dimensional features.

Simulating and Measuring Structural Intensity Fields in Plates Induced by Spatially and Temporally Random Excitation

2004 ◽  
Author(s):  
Michael J. Daley ◽  
Stephen A. Hambric
Keyword(s):  
Pressure Fluctuations ◽  
Laser Doppler Vibrometer ◽  
Practical Interest ◽  
Analytical Techniques ◽  
Random Excitation ◽  
Plate Structures ◽  
Scanning Laser Doppler Vibrometer ◽  
Structural Intensity ◽  
Bending Waves ◽  
Pressure Fields

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in plates excited by such fields are presented here. The structural intensity at various frequencies in a simply-supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives.

Simulating and Measuring Structural Intensity Fields in Plates Induced by Spatially and Temporally Random Excitation

2005 ◽  
Vol 127 (5) ◽  
pp. 451-457 ◽  
Author(s):  
Michael J. Daley ◽  
Stephen A. Hambric
Keyword(s):  
Pressure Fluctuations ◽  
Laser Doppler Vibrometer ◽  
Practical Interest ◽  
Analytical Techniques ◽  
Random Excitation ◽  
Flat Plates ◽  
Plate Structures ◽  
Scanning Laser Doppler Vibrometer ◽  
Structural Intensity ◽  
Bending Waves

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in flat plates excited by such fields are presented here. The structural intensity at various frequencies in a simply supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives. Specifically, no clear source regions are apparent in the randomly driven intensity fields, although the energy flow patterns do clearly converge toward a point damper attached to the plate.

scholarly journals The elastic stability of an annular plate

1924 ◽  
Vol 106 (737) ◽  
pp. 268-284 ◽  
Keyword(s):  
Annular Plate ◽  
Practical Interest ◽  
Middle Surface ◽  
Elastic Stability ◽  
Thin Plates ◽  
Thin Shells ◽  
Stability Equation ◽  
Inner Radius ◽  
Plane Plate ◽  
The Stability

1. Introduction and Summary. —This paper deals with the elastic stability of a circular annular plate under uniform shearing forces applied at its edges. Investigations of the stability of plane plates are altogether simpler than those necessary in the case of curved plates or shells. In the first place, as shown by Mr. R. V. Southwell, two of the three equations of stability relate to a mode of instability that is not of practical interest, and are entirely independent of the third equation which gives the ordinary mode of instability resulting in the familiar bending of the middle surface of the plate. Consequently with a plane plate there is only one equation of stability to be solved, as contrasted with the case of a shell where the three equations are dependent, and must all be solved. In the second place the theory of thin shells can be used with confidence in a plane plate problem, though a more laborious procedure is necessary to deal adequately with a shell. The only stability equation required for the annular plate is therefore deduced without trouble from the theory of thin shells, and its solution presents no difficulty in the case of uniform shearing forces. A numerical discussion is given of the stability of the plate under such forces, the “favourite type of distortion” and the stess that will produce it being obtained for plates with clamped edges in wich the ratio of the outer to the inner radius exceeds 3·2. To some extent to results have been checked by experiment, in which part of the work the viter is indebted to Prof. G. I. Taylor for his valuable help and advice. Distrtion of the type predicted by the theory took place in the two thin plates of rober different ratio of radii, which were used. The disposition of the loci of points which undergo maximum normal displace nt gives some idea of the appearance of the plate after distortion has taken pce. The points have been calculated for a plate in which the ratio of radii 4·18, and the loci are shown on a diagram, which may be compared with a potograph of a distorted plate in which this ratio is 4·3. The ratio of normal dplacements of points of the plate can be seen from contours drawn on the ne diagram. (See pp. 280, 281.)

An explicit method to calculate implicit spatial finite differences

Geophysics ◽  
2021 ◽  
pp. 1-71
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Computational Cost ◽  
New Method ◽  
Seismic Exploration ◽  
Explicit Method ◽  
Lu Decomposition ◽  
Implicit Methods ◽  
Band Matrices ◽  
Explicit Finite Difference

The finite-difference solution of the second-order acoustic wave equation is a fundamental algorithm in seismic exploration for seismic forward modeling, imaging, and inversion. Unlike the standard explicit finite difference (EFD) methods that usually suffer from the so-called "saturation effect", the implicit FD methods can obtain much higher accuracy with relatively short operator length. Unfortunately, these implicit methods are not widely used because band matrices need to be solved implicitly, which is not suitable for most high-performance computer architectures. We introduce an explicit method to overcome this limitation by applying explicit causal and anti-causal integrations. We can prove that the explicit solution is equivalent to the traditional implicit LU decomposition method in analytical and numerical ways. In addition, we also compare the accuracy of the new methods with the traditional EFD methods up to 32nd order, and numerical results indicate that the new method is more accurate. In terms of the computational cost, the newly proposed method is standard 8th order EFD plus two causal and anti-causal integrations, which can be applied recursively, and no extra memory is needed. In summary, compared to the standard EFD methods, the new method has a spectral-like accuracy; compared to the traditional LU-decomposition implicit methods, the new method is explicit. It is more suitable for high-performance computing without losing any accuracy.

scholarly journals Fictitious Domain Technique for the Calculation of Time-Periodic Solutions of Scattering Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Ling Rao ◽  
Hongquan Chen
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Scattering Problem ◽  
Finite Element Approximation ◽  
New Method ◽  
Fictitious Domain ◽  
Finite Difference Schemes ◽  
Element Approximation ◽  
Dirac Delta ◽  
Time Periodic

The fictitious domain technique is coupled to the improved time-explicit asymptotic method for calculating time-periodic solution of wave equation. Conventionally, the practical implementation of fictitious domain method relies on finite difference time discretizations schemes and finite element approximation. Our new method applies finite difference approximations in space instead of conventional finite element approximation. We use the Dirac delta function to transport the variational forms of the wave equations to the differential form and then solve it by finite difference schemes. Our method is relatively easier to code and requires fewer computational operations than conventional finite element method. The numerical experiments show that the new method performs as well as the method using conventional finite element approximation.

An Introduction to Finite Differencing

1998 ◽  
Author(s):  
T. N. Krishnamurti ◽  
H. S. Bedi ◽  
V. M. Hardiker
Keyword(s):  
Finite Difference ◽  
Finite Differences ◽  
Single Point ◽  
Finite Differencing ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Student Reading ◽  
Higher Derivatives ◽  
Derivatives Of

This chapter on finite differencing appears oddly placed in the early part of a text on spectral modeling. Finite differences are still traditionally used for vertical differencing and for time differencing. Therefore, we feel that an introduction to finite-differencing methods is quite useful. Furthermore, the student reading this chapter has the opportunity to compare these methods with the spectral method which will be developed in later chapters. One may use Taylor’s expansion of a given function about a single point to approximate the derivative(s) at that point. Derivatives in the equation involving a function are replaced by finite difference approximations. The values of the function are known at discrete points in both space and time. The resulting equation is then solved algebraically with appropriate restrictions. Suppose u is a function of x possessing derivatives of all orders in the interval (x — n∆x, x + n∆x). Then we can obtain the values of u at points x ± n∆ x, where n is any integer, in terms of the value of the function and its derivatives at point x, that is, u(x) and its higher derivatives.

scholarly journals Numerical Analysis and Characterization of Surface Pressure Fluctuations of High-Speed Trains Using Wavenumber–Frequency Analysis

2019 ◽  
Vol 9 (22) ◽  
pp. 4924
Author(s):  
Lee ◽  
Cheong ◽  
Kim ◽  
Kim
Keyword(s):  
Flow Field ◽  
Open Field ◽  
Frequency Analysis ◽  
Surface Pressure ◽  
High Speed ◽  
Pressure Fluctuations ◽  
Interior Noise ◽  
High Speed Train ◽  
Pressure Fields ◽  
Time Space

The high-speed train interior noise induced by the exterior flow field is one of the critical issues for product developers to consider during design. The reliable numerical prediction of noise in a passenger cabin due to exterior flow requires the decomposition of surface pressure fluctuations into the hydrodynamic (incompressible) and the acoustic (compressible) components, as well as the accurate computation of the near aeroacoustic field, since the transmission characteristics of incompressible and compressible pressure waves through the wall panel of the cabin are quite different from each other. In this paper, a systematic numerical methodology is presented to obtain separate incompressible and compressible surface pressure fields in the wavenumber–frequency and space–time domains. First, large eddy simulation techniques were employed to predict the exterior flow field, including a highly-resolved acoustic near-field, around a high-speed train running at the speed of 300 km/h in an open field. Pressure fluctuations on the train surface were then decomposed into incompressible and compressible fluctuations using the wavenumber–frequency analysis. Finally, the separated incompressible and compressible surface pressure fields were obtained from the inverse Fourier transform of the wavenumber–frequency spectrum. The current method was illustratively applied to the high-speed train HEMU-430X running at a speed of 300 km/h in an open field. The results showed that the separate incompressible and compressible surface pressure fields in the time–space domain could be obtained together with the associated aerodynamic source mechanism. The power levels due to each pressure field were also estimated, and these can be directly used for interior noise prediction.

Sign in / Sign up

Export Citation Format

Share Document