Nonlinear Stresses and Deflections of Beams Subjected to Random Time Dependent Uniform Pressure

1976 ◽  
Vol 98 (3) ◽  
pp. 1014-1020 ◽  
Author(s):  
P. Seide
Keyword(s):  
Accurate Determination ◽  
Equivalent Linearization ◽  
Uniform Pressure ◽  
Mean Square ◽  
Maximum Displacement ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
White Noise Excitation ◽  
End Conditions

The nonlinear mean-square multimode response of beams subjected to uniform pressure uncorrelated in time is investigated. The method of equivalent linearization is used to obtain mean-square stresses and displacements in beams with arbitrary end conditions. Calculations are carried out for beams with both ends either simply-supported or clamped, for the case of white noise excitation. Although the maximum displacement can be obtained with the use of only a single-degree-of-freedom model, it is necessary to consider as many as 100 modal functions for accurate determination of the stresses. The maximum mean-square deflection of the clamped beam is found to be somewhat less than the simply-supported beam, whereas the maximum mean-square stresses are as much as twice as large.

On Equivalent Linearization Using Wavelet Transform

1999 ◽  
Vol 121 (4) ◽  
pp. 429-432 ◽  
Author(s):  
B. Basu ◽  
V. K. Gupta
Keyword(s):  
Wavelet Transform ◽  
Duffing Oscillator ◽  
Time Dependent ◽  
Equivalent Linearization ◽  
Equivalent System ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Mean ◽  
The Given

This paper proposes a wavelet-based formulation for linearizing a base-excited single-degree-of-freedom nonlinear system to a time-variant linear (TVL) system. The given system is assumed to be nonlinear in stiffness, and the time-dependent natural frequency of the equivalent system is proposed to he estimated through instantaneous minimization of the mean-square error. A duffing oscillator has been considered to illustrate the performance of the proposed TVL system.

Dynamic Axisymmetric Buckling of Shallow Conical Shells Subjected to Impulsive Loads

1965 ◽  
Vol 32 (1) ◽  
pp. 129-134 ◽  
Author(s):  
R. E. Fulton
Keyword(s):  
Conical Shell ◽  
Strain Energy ◽  
Maximum Displacement ◽  
Spherical Cap ◽  
Single Degree Of Freedom ◽  
Conical Shells ◽  
Simply Supported ◽  
Single Degree ◽  
Impulsive Loads ◽  
Axisymmetric Buckling

A theoretical investigation is made of the axisymmetric snap-through buckling of a shallow conical shell subjected to an idealized impulse applied uniformly over the surface of the shell. The shell is assumed to behave as a single-degree-of-freedom system, and a study is made of the strain energy at maximum displacement: i.e., zero velocity. Under certain conditions this equilibrium position becomes unstable and the shell can snap through (or buckle). Nonlinear strain displacement equations are used and solutions are obtained for clamped and simply supported boundaries at the edge of the shell. Results for the cone are compared with similar results for a shallow spherical cap having the same rise as the cone. This comparison indicates that the spherical shell can resist a larger impulse than the conical shell before buckling.

Simplified Determination of Stability Bounds in Nonlinear Vibration Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 319-325 ◽  
Author(s):  
K. Peleg ◽  
S. Hinga
Keyword(s):  
Coulomb Friction ◽  
Accurate Determination ◽  
Steady State Solution ◽  
Single Degree Of Freedom ◽  
Frequency Bands ◽  
Vibration Problems ◽  
Duffing Model ◽  
Instability Frequency ◽  
Vibrating Systems

Even slight nonlinearities in vibrating systems introduce instability frequency bands and unstable amplitudes. In many vibration problems it is desirable to know precisely the bounds of the instability frequencies and the associated amplitude ranges. Using a general nonlinear single degree of freedom system, based on a Coulomb friction augmented Duffing model, simplified graphical/analytical modus operandi was developed for computing singular amplitudes in the frequency domain. The method may be used in lieu of the usual phase plane approach wherein the physical meaning of the different vibration modes is obscured. In previous publications approximate estimation of instability frequency bands of the Duffing system was achieved by assuming variations about the steady state solution. The new method presented herein allows accurate determination of instability frequency ranges in a more general class of vibration systems, while quantifying “Horizontal Tangents Amplitudes,” in addition to the usual “Resonance Amplitudes” and “Vertical Tangents Amplitudes.”

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

Computer-Assisted High-Re Solution TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 162-163
Author(s):  
F.A. Ponce ◽  
H. Hikashi
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Computer Software ◽  
Video Camera ◽  
Image Contrast ◽  
Objective Lens ◽  
Computer Assisted ◽  
Optical Parameters ◽  
Astigmatism Correction

The determination of the atomic positions from HRTEM micrographs is only possible if the optical parameters are known to a certain accuracy, and reliable through-focus series are available to match the experimental images with calculated images of possible atomic models. The main limitation in interpreting images at the atomic level is the knowledge of the optical parameters such as beam alignment, astigmatism correction and defocus value. Under ordinary conditions, the uncertainty in these values is sufficiently large to prevent the accurate determination of the atomic positions. Therefore, in order to achieve the resolution power of the microscope (under 0.2nm) it is necessary to take extraordinary measures. The use of on line computers has been proposed [e.g.: 2-5] and used with certain amount of success.We have built a system that can perform operations in the range of one frame stored and analyzed per second. A schematic diagram of the system is shown in figure 1. A JEOL 4000EX microscope equipped with an external computer interface is directly linked to a SUN-3 computer. All electrical parameters in the microscope can be changed via this interface by the use of a set of commands. The image is received from a video camera. A commercial image processor improves the signal-to-noise ratio by recursively averaging with a time constant, usually set at 0.25 sec. The computer software is based on a multi-window system and is entirely mouse-driven. All operations can be performed by clicking the mouse on the appropiate windows and buttons. This capability leads to extreme friendliness, ease of operation, and high operator speeds. Image analysis can be done in various ways. Here, we have measured the image contrast and used it to optimize certain parameters. The system is designed to have instant access to: (a) x- and y- alignment coils, (b) x- and y- astigmatism correction coils, and (c) objective lens current. The algorithm is shown in figure 2. Figure 3 shows an example taken from a thin CdTe crystal. The image contrast is displayed for changing objective lens current (defocus value). The display is calibrated in angstroms. Images are stored on the disk and are accessible by clicking the data points in the graph. Some of the frame-store images are displayed in Fig. 4.

A novel method for the determination of linting propensity of paper

TAPPI Journal ◽  
2012 ◽  
Vol 11 (10) ◽  
pp. 9-17
Author(s):  
ALESSANDRA GERLI ◽  
LEENDERT C. EIGENBROOD
Keyword(s):  
Ash Content ◽  
The Novel ◽  
Offset Printing ◽  
Excellent Correlation ◽  
End Conditions ◽  
Bottom Side ◽  
Novel Method ◽  
Total Fraction

A novel method was developed for the determination of linting propensity of paper based on printing with an IGT printability tester and image analysis of the printed strips. On average, the total fraction of the surface removed as lint during printing is 0.01%-0.1%. This value is lower than those reported in most laboratory printing tests, and more representative of commercial offset printing applications. Newsprint paper produced on a roll/blade former machine was evaluated for linting propensity using the novel method and also printed on a commercial coldset offset press. Laboratory and commercial printing results matched well, showing that linting was higher for the bottom side of paper than for the top side, and that linting could be reduced on both sides by application of a dry-strength additive. In a second case study, varying wet-end conditions were used on a hybrid former machine to produce four paper reels, with the goal of matching the low linting propensity of the paper produced on a machine with gap former configuration. We found that the retention program, by improving fiber fines retention, substantially reduced the linting propensity of the paper produced on the hybrid former machine. The papers were also printed on a commercial coldset offset press. An excellent correlation was found between the total lint area removed from the bottom side of the paper samples during laboratory printing and lint collected on halftone areas of the first upper printing unit after 45000 copies. Finally, the method was applied to determine the linting propensity of highly filled supercalendered paper produced on a hybrid former machine. In this case, the linting propensity of the bottom side of paper correlated with its ash content.

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