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.

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.

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.)

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

ESTIMATION OF GROWTH – TIME TEMPERATURE CHARACTERISTICS FOR ISOLATES OF FOMES PINI, A HEART ROT FUNGUS

1964 ◽  
Vol 42 (12) ◽  
pp. 1635-1652 ◽  
Author(s):  
Lee A. Paine ◽  
Gideon Schwarzbart ◽  
William G. O'Regan
Keyword(s):  
Regression Analysis ◽  
Cross Section ◽  
Growth Pattern ◽  
Storage Temperature ◽  
Three Dimensional ◽  
Douglas Fir ◽  
Growth Time ◽  
Optimum Temperature ◽  
Analysis Techniques ◽  
White Fir

Regression analysis techniques were applied to an estimation of three-dimensional surfaces representing the growth of Fomes pini as a function of time and temperature. These methods were judged to be valuable in their economy of data and in their provision of readily available plotting points for any desired cross section of the surface.The growth pattern of F. pini taken from Douglas fir was distinct from that of the form of F. pini found on nearby white fir. Growth of isolates from Douglas fir was more than twice that of white fir isolates after 18 days at near-optimum temperatures on malt agar. Estimates of growth trends and optimum temperatures were examined both for individual isolates of F. pini and for averages of isolates from the two host species, Douglas fir and white fir. Results suggest that chronological changes in the optimum temperature may be affected by the relation between the storage temperature preceding initial measurements and the terminal optimum temperature.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1995 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

Abstract Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.

scholarly journals A three-dimensional theory of wind pumping

1991 ◽  
Vol 37 (125) ◽  
pp. 89-96 ◽  
Author(s):  
Garry K. C. Clarke ◽  
Edwin D. Waddington
Keyword(s):  
Heat Source ◽  
Surface Pressure ◽  
Air Flow ◽  
Pressure Fluctuations ◽  
Normal Component ◽  
Three Dimensional ◽  
Lower Atmosphere ◽  
Dimensional Theory ◽  
Theoretical Formulation ◽  
Near Surface

AbstractQuantitative understanding of the processes that couple the lower atmosphere to the upper surface of ice sheets is necessary for interpreting ice-core records. Of special interest are those processes that involve the exchange of energy or atmospheric constituents. One such process, wind pumping, entails both possibilities and provides a possible mechanism for converting atmospheric kinetic energy into a near-surface heat source within the firn layer. The essential idea is that temporal and spatial variations in surface air pressure, resulting from air motion, can diffuse into permeable firn by conventional Darcy flow. Viscous friction between moving air and the solid firn matrix leads to energy dissipation in the firn that is equivalent to a volumetric heat source.Initial theoretical work on wind pumping was aimed at explaining anomalous near-surface temperatures measured at sites on Agassiz Ice Cap, Arctic Canada. A conclusion of this preliminary work was that, under highly favourable conditions, anomalous warming of as much as 2°C was possible. Subsequent efforts to confirm wind-pumping predictions suggest that our initial estimates of the penetration depth for pressure fluctuations were optimistic. These observations point to a deficiency of the initial theoretical formulation — the surface-pressure forcing was assumed to vary temporally, but not spatially. Thus, within the firn there was only a surface-normal component of air flow. The purpose of the present contribution is to advance a three-dimensional theory of wind pumping in which air flow is driven by both spatial and temporal fluctuations in surface pressure. Conclusions of the three-dimensional analysis are that the penetration of pressure fluctuations, and hence the thickness of the zone of frictional interaction between air and permeable firn, is related to both the frequency of the pressure fluctuations and to the spatial coherence length of turbulence cells near the firn surface.

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