Moderately Large Amplitude Plate Vibration Modes

1980 ◽  
Vol 102 (2) ◽  
pp. 405-411
Author(s):  
J. C. Kennedy
Keyword(s):  
Amplitude Ratio ◽  
Analog Computer ◽  
System Response ◽  
Vibration Modes ◽  
Simply Supported ◽  
Plate Equations ◽  
Simplifying Assumptions ◽  
Versus Amplitude ◽  
Ratio Versus ◽  
Made In

The influence of moderately large amplitudes on the frequency of vibration for the fundamental mode and some higher modes of the simply supported rectangular plate is established. Plate equations that are valid for the moderately large motions are programmed for solution on the analog computer. The effect of eliminating in-plane motions and accelerations on the system response is quantitatively established. It is shown that frequency ratio versus amplitude ratio is aspect ratio dependent and the study shows how simplifying assumptions made in some previous studies affect this dependence.

scholarly journals Drop Shapes and Axis Ratio Distributions: Comparison between 2D Video Disdrometer and Wind-Tunnel Measurements

2009 ◽  
Vol 26 (7) ◽  
pp. 1427-1432 ◽  
Author(s):  
M. Thurai ◽  
V. N. Bringi ◽  
M. Szakáll ◽  
S. K. Mitra ◽  
K. V. Beard ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Close Agreement ◽  
Drop Diameter ◽  
Wind Tunnel Experiments ◽  
Axis Ratio ◽  
Wind Tunnel Measurements ◽  
Mean Shape ◽  
The Mean ◽  
Ratio Versus ◽  
Made In

Abstract Comparisons of drop shapes between measurements made using 2D video disdrometer (2DVD) and wind-tunnel experiments are presented. Comparisons are made in terms of the mean drop shapes and the axis ratio distributions. Very close agreement of the mean shapes is seen between the two sets of measurements; the same applies to the mean axis ratio versus drop diameter. Also, in both sets of measurements, an increase in the oscillation amplitudes with increasing drop diameter is observed. In the case of the 2DVD, a small increase in the skewness was also detected. Given that the two sets of measurements were conducted in very different conditions, the agreement between the two sets of data implies a certain “robustness” in the mean shape of oscillating drops that may be extended to natural raindrop oscillations, at least in steady rainfall and above the surface layer.

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Erasmo Carrera ◽  
Fiorenzo Adolfo Fazzolari ◽  
Luciano Demasi
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Virtual Displacement ◽  
Simply Supported ◽  
Order Expansion ◽  
Thickness Layer ◽  
Made In

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carrera’s unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

Penetration of a Rate Sensitive Geological Target by the Compaction Ring Theory

2002 ◽  
Author(s):  
Martin R. Gilmore ◽  
S. E. Jones ◽  
Joseph C. Foster
Keyword(s):  
Model Development ◽  
Target Material ◽  
Rate Sensitivity ◽  
Target Strength ◽  
Strain Rates ◽  
Linear Rate ◽  
Cat Scan ◽  
Strain And Strain Rate ◽  
Simplifying Assumptions ◽  
Made In

In an earlier paper, the authors presented a theory for the penetration of geologically based semi-infinite targets [5]. This theory was suitable for application to targets in which compaction due to the crushing of voids is the primary deformation mechanism. This phenomenon has been observed in concrete targets with a ring of dense material around the tunnel region, see figure 1 for a cat scan of a concrete target after penetration. This was the motivation for the model development. A number of simplifying assumptions were made in the application of the theory to data from concrete penetration experiments. One of the assumptions was that the target strength was constant, or independent of strain and strain rate. This assumption leads to generally consistent results for the same ogive nose geometry. However, it was noted that there was a discrepancy between the strength predictions when two different ogive nose geometries were used. This paper investigates the discrepancy by assuming that the target material is rate sensitive. The results indicate that the strain rates in the target are indeed affected by the nose geometry. A detailed analysis for a target material with linear rate sensitivity is provided in the paper and the results provide a favorable comparison with available experimental evidence.

ELIMINATION OF SEISMIC GHOST REFLECTIONS BY MEANS OF A LINEAR FILTER

Geophysics ◽  
1960 ◽  
Vol 25 (1) ◽  
pp. 130-140 ◽  
Author(s):  
J. P. Lindsey
Keyword(s):  
Autocorrelation Function ◽  
Measurement Technique ◽  
Amplitude Ratio ◽  
Linear Filter ◽  
Record Time ◽  
Principal Assumption ◽  
Made In

A technique is described for elimination of ghost reflections on magnetically recorded seismograph records by means of a linear filter. The application of this filter does not alter the character of primary reflections although eliminating the ghost reflections. The principal assumption made in the development of the technique is that the effect of AGC in altering the amplitude ratio of primary and ghost reflections is uniform for all record time. A realization of the required filter is given and a measurement technique is outlined for detecting the existence of ghost reflections based on the autocorrelation function of the seismograph trace.

Purposive vagueness: an evaluative dimension of vague quantifying expressions

1985 ◽  
Vol 21 (1) ◽  
pp. 31-50 ◽  
Author(s):  
Mava Jo Powell
Keyword(s):  
Model Theory ◽  
Noun Phrases ◽  
Evaluative Dimension ◽  
Precise Meaning ◽  
Simplifying Assumptions ◽  
The One ◽  
Made In

Extending Montague's (1974) framework, Barwise and Cooper (1981) argue that some generalized expressions (which I shall call vague quantifying expressions), such as most, many ana few, correspond not to quantifiers, but to determiners within noun phrases. They argue that we need not determine the meanings of these expressions by logic; rather, we may draw upon an idea similar to the one we employ when interpreting the meaning of the quantifier Qxø(x), that is, we may appeal to an underlying topology for their interpretation (1981: 161). Similarly, they invoke one of the ‘simplifying assumptions often made in model theory’; namely, … that one has a fixed context which determines the meaning of the basic expressions. We can think of this context as providing an interpretation for non-logical determiners… We shall assume… that there is a rich context held fixed that determines the PRECISE MEANING [my emphasis here] for the basic expressions, even those like ‘most’, ‘many’ and ‘few’. We refer to this as the fixed context assumption…The fixed context assumption is our way of finessing the vagueness of non-logical determiners. We think that a theory of vagueness like that given by Kamp (1975) for other kinds of basic expressions could be superimposed on our theory (1981: 163).

scholarly journals The evolutionary interplay of intergroup conflict and altruism in humans: a review of parochial altruism theory and prospects for its extension

2014 ◽  
Vol 281 (1794) ◽  
pp. 20141539 ◽  
Author(s):  
Hannes Rusch
Keyword(s):  
Empirical Evidence ◽  
Explanatory Power ◽  
Intergroup Conflict ◽  
Substantial Role ◽  
Direct Benefits ◽  
Central Notion ◽  
Simplifying Assumptions ◽  
Group Members ◽  
Cultural Traits ◽  
Made In

Drawing on an idea proposed by Darwin, it has recently been hypothesized that violent intergroup conflict might have played a substantial role in the evolution of human cooperativeness and altruism. The central notion of this argument, dubbed ‘parochial altruism’, is that the two genetic or cultural traits, aggressiveness against the out-groups and cooperativeness towards the in-group, including self-sacrificial altruistic behaviour, might have coevolved in humans. This review assesses the explanatory power of current theories of ‘parochial altruism’. After a brief synopsis of the existing literature, two pitfalls in the interpretation of the most widely used models are discussed: potential direct benefits and high relatedness between group members implicitly induced by assumptions about conflict structure and frequency. Then, a number of simplifying assumptions made in the construction of these models are pointed out which currently limit their explanatory power. Next, relevant empirical evidence from several disciplines which could guide future theoretical extensions is reviewed. Finally, selected alternative accounts of evolutionary links between intergroup conflict and intragroup cooperation are briefly discussed which could be integrated with parochial altruism in the future.

Nonlinear Vibrations of Rectangular Plates With Different Boundary Conditions: Theory and Experiments

2005 ◽  
Author(s):  
M. Amabili ◽  
C. Augenti
Keyword(s):  
Boundary Condition ◽  
Good Accuracy ◽  
Continuation Method ◽  
Laser System ◽  
Normal Displacement ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Actual Geometry

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Ka´rma´n nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges, and (iii) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.

scholarly journals First natural frequency of multi-segment floor joists with variable cross section

2019 ◽  
Vol 28 (4) ◽  
pp. 526-538
Author(s):  
Marek Chalecki ◽  
Jacek Jaworski ◽  
Olga Szlachetka
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Constant Width ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Uniform Load ◽  
Simply Supported ◽  
Made In

The Rayleigh’s method can be used to determine the first natural frequency of beams with variable cross-section. The authors analyse multi-segment simply supported beams, symmetrical with respect to their midpoint, having a constant width and variable height. The beams consist generally of five segments. It has been assumed that the neutral bar axis deflected during vibrations has a shape of a beam deflected by a static uniform load. The calculations were made in Mathematica environment and their results are very close to those obtained with FEM.

scholarly journals Time development of electric fields and currents in space plasmas

2006 ◽  
Vol 24 (3) ◽  
pp. 1137-1143
Author(s):  
A. T. Y. Lui
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Electric Fields ◽  
Time Development ◽  
Space Plasmas ◽  
Simplifying Assumptions ◽  
Electric Fields And Currents ◽  
Definition Of ◽  
The Magnetic Field ◽  
Made In

Abstract. Two different approaches, referred to as Bu and Ej, can be used to examine the time development of electric fields and currents in space plasmas based on the fundamental laws of physics. From the Bu approach, the required equation involves the generalized Ohm's law with some simplifying assumptions. From the Ej approach, the required equation can be derived from the equation of particle motion, coupled self-consistently with Maxwell's equation, and the definition of electric current density. Recently, some strong statements against the Ej approach have been made. In this paper, we evaluate these statements by discussing (1) some limitations of the Bu approach in solving the time development of electric fields and currents, (2) the procedure in calculating self-consistently the time development of the electric current in space plasmas without taking the curl of the magnetic field in some cases, and (3) the dependency of the time development of magnetic field on electric current. It is concluded that the Ej approach can be useful to understand some magnetospheric problems. In particular, statements about the change of electric current are valid theoretical explanations of change in magnetic field during substorms.

Single whole rock K—Ar isochrons

1976 ◽  
Vol 113 (1) ◽  
pp. 1-10 ◽  
Author(s):  
F. J. Fitch ◽  
J. A. Miller ◽  
P. J. Hooker
Keyword(s):  
Isotopic Composition ◽  
Isotope Ratio ◽  
Fusion Method ◽  
Special Circumstance ◽  
General Applicability ◽  
Step Heating ◽  
Simplifying Assumptions ◽  
Total Fusion ◽  
Age Determinations ◽  
Made In

SummaryConventional K—Ar age determinations are frequently discrepant. A major factor is the failure of rocks to conform to the basic simplifying assumptions made in the total fusion method. Many rocks incorporate initial argon with an isotopic composition different from the present atmosphere and others have not remained closed systems.By careful sampling and the application of isochron geochronometry more reliable and geologically acceptable K-Ar ages can be obtained. K-Ar step heating isochrons from Kenyan Miocene volcanic sanidines are used to illustrate the accumulating evidence for the presence in ancient rocks of initial argon with an isotope ratio unlike that of the modern atmosphere. Single whole rock total fusion K-Ar isochrons from the Olduvai basalt, Tanzania and the Upper basalts of Antrim are presented to illustrate a new version of the K-Ar isochron technique. Special circumstance multiple rock K-Ar isochrons from the Belfast section of the Antrim basalts and from an ignimbrite-ash flow unit in Bed I, Olduvai Gorge, are used in a further discussion of the general applicability and usefulness of K-Ar isochrons.

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