Effect of an Acoustic Medium on the Dynamic Buckling of Plates

1956 ◽  
Vol 23 (2) ◽  
pp. 201-206
Author(s):  
F. L. DiMaggio
Keyword(s):  
Elastic Plate ◽  
Infinite Plate ◽  
Approximate Solutions ◽  
Dynamic Buckling ◽  
Steel Plates ◽  
Acoustic Medium ◽  
Middle Plane ◽  
Numerical Example ◽  
Compressive Stresses ◽  
Surrounding Fluid

Abstract The effect of a surrounding fluid on the dynamic buckling of an elastic plate under suddenly applied compressive stresses in its middle plane is studied. Assuming an infinite plate supported at regular intervals and a semi-infinite acoustic medium, exact and approximate solutions are obtained. By a numerical example, it is shown that for steel plates in water, with dimensions usually encountered in ship structures, the compressibility of water can be neglected.

BENDING OF A SUBTLE-FINISHED PLATE ON ELASTIC BASE WITH SPECIAL CONDITIONS OF ITS WORK

2019 ◽  
pp. 424-430
Author(s):  
A. T. Marufiy ◽  
A. S. Kalykov
Keyword(s):  
Analytical Solution ◽  
Working Conditions ◽  
Fourier Transforms ◽  
Infinite Plate ◽  
Elastic Base ◽  
Generalized Solutions ◽  
Middle Plane ◽  
Actual Working

In this article, an analytical solution is obtained for the problem of bending a semi-infinite plate on an elastic Winkler base, taking into account incomplete contact with the base and the influence of longitudinal forces applied in the middle plane of the plate. The analytical solution is obtained by the method of generalized solutions using integral Fourier transforms. Any analytical solution is the result, approaching the actual working conditions of the designed structures.

Evaluation of Residual Stresses in PVD Coatings by Means of Strip Substrate Length Variation and Curvature Method of Plate Substrate

2017 ◽  
Vol 267 ◽  
pp. 212-218 ◽  
Author(s):  
Harri Lille ◽  
Alexander Ryabchikov ◽  
Jakub Kõo ◽  
Eron Adoberg ◽  
Liina Lind ◽  
...  
Keyword(s):  
Residual Stresses ◽  
Length Change ◽  
Steel Plates ◽  
Length Variation ◽  
Pvd Coatings ◽  
Compressive Stresses ◽  
Steel Strips ◽  
Middle Cross Section ◽  
Method Strip

The aim of the study was to determine macroscopic residual stresses in Physical Vapor Deposits (PVD) coatings through measurement of the length variation of the strip substrates coated on both sides. The length change of the strip was reduced to the deflection of the middle cross-section of the elastic element and was recorded by four strain gauges. For validating the obtained results, the conventional curvature method was used. As an application, residual stresses in hard AlCrN PVD coatings were investigated. The coatings were nanolayered to achieve better coating toughness for blanking and punching applications. The steel strips and steel plates with two thicknesses were used as the substrate. The values of the compressive residual stresses, determined by both methods for the investigated coatings, were very high (3.3 -3.6 GPa) independent of coating thickness and practically equal within the measurement uncertainty of the method. Good agreement between the experimental results obtained with both methods suggests that the presented method, strip length variation, is applicable for determination of residual stresses in coatings. Compressive stresses in coatings are desirable as they strengthen the coating.

The General theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads

1949 ◽  
Vol 53 (461) ◽  
pp. 461-483 ◽  
Author(s):  
J. Hadji-Argyris ◽  
P. C. Dunne
Keyword(s):  
General Theory ◽  
Cross Sections ◽  
Approximate Solutions ◽  
Torsional Stiffness ◽  
Numerical Example ◽  
Bending Loads ◽  
Present Part

SummaryParts 1 to 5 of this paper (February, September and November 1947 issues of the JOURNAL) investigated the stresses and deformations of closed tubes in which the thicknesses were governed by the ts* and t* laws. In the present part, the analysis is extended to multi-cell tubes with openings, open tubes with or without St. Venant torsional stiffness, and to tubes formed by joining elements of different cross-sections. To illustrate the theory a numerical example of the stressing of a four-boom wing consisting of seven joined elements is fully worked out. Finally, an appendix gives practical methods of dealing with tubes which do not conform to the ts* and t* laws, and of finding approximate solutions for four-boom tubes with direct stress carrying covers.

The Response of a Plate on an Elastic Foundation

1968 ◽  
Vol 35 (1) ◽  
pp. 186-187 ◽  
Author(s):  
J. P. Jones
Keyword(s):  
Elastic Foundation ◽  
Elastic Plate ◽  
Pressure Pulse ◽  
Specific Problem ◽  
Underground Structure ◽  
Approximate Equation ◽  
Step Function ◽  
Simple Expression ◽  
Acoustic Medium ◽  
Recent Interest

There has been much recent interest in the possibility of hardening an underground structure by means of an elastic plate placed on the ground above the structure. To obtain a simple expression for the interaction pressure between the ground and the plate, the present analysis treats the problem of a plate on top of an acoustic medium subjected to a uniformly moving pressure pulse. It is found that an approximate equation suggested by S. B. Baldorf is quite valid in the superseismic range of load speed. The specific problem of a step function loading traveling with uniform velocity, superseismic to the foundation, is treated. The extension of this problem to an actual elastic foundation is straightforward and is not treated.

scholarly journals Almost complete convergence for the sequence of approximate solutions in linear calibration problem with α-mixing random data

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3251-3264
Author(s):  
Samia Khalfoune ◽  
Halima Zerouati
Keyword(s):  
Exact Solution ◽  
Complete Convergence ◽  
Approximate Solutions ◽  
Stochastic Method ◽  
Linear Calibration ◽  
Random Data ◽  
Exponential Inequalities ◽  
Numerical Example ◽  
Calibration Problem ◽  
Confidence Domain

In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with ?-mixing random data. We establish exponential inequalities of Fuk Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

scholarly journals Elastic Modes of an Anisotropic Ridge Waveguide

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ameya Galinde ◽  
Masoud Koochakzadeh ◽  
Abbas Abbaspour-Tamijani
Keyword(s):  
Infinite Plate ◽  
Single Crystal Silicon ◽  
Approximate Solutions ◽  
Free Edge ◽  
Critical Issue ◽  
Crystal Silicon ◽  
Ridge Waveguides ◽  
Edge Surface ◽  
Elastic Modes ◽  
Antisymmetric Solutions

A semi-analytical method for finding the elastic modes propagating along the edge of an anisotropic semi-infinite plate is presented. Solutions are constructed as linear combinations of a finite number of the corresponding infinite plate modes with the constraint that they decay in the direction perpendicular to the edge and collectively satisfy the free boundary condition over the edge surface. Such modes that are confined to the edge can be used to approximate solutions of acoustic ridge waveguides whose supporting structures are sufficiently far away from the free edge. The semi-infinite plate or ridge is allowed to be oriented arbitrarily in the anisotropic crystal. Modifications to the theory to find symmetric and antisymmetric solutions for special crystal orientations are also presented. Accuracy of the solutions can be improved by including more plate modes in the series. Numerical techniques to find modal dispersion relations and orientation dependent modal behavior, are discussed. Results for ridges etched in single crystal Silicon are found to be in good agreement with Finite Element simulations. It is found that variations in modal phase velocity with respect to crystal orientation are not significant, suggesting that anisotropy may not be a critical issue while designing ridge waveguides in Silicon.

EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENT

2007 ◽  
Vol 04 (02) ◽  
pp. 265-281
Author(s):  
LALITHA CHATTOPADHYAY ◽  
S. SRIDHARA MURTHY ◽  
S. VISWANATH
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Plate ◽  
Integral Transform ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Single Line ◽  
Bending Stress ◽  
Single Crack ◽  
Classical Plate Theory

The problem of estimating the bending stress distribution in the vicinity of cracks located on a single line in an elastic plate subjected to concentrated moment is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in detail for the case in which there is a single crack in an infinite plate, and the bending stress intensity factor is determined in a closed form. Two examples are considered to illustrate the present approach.

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