An Approximate Analysis of Circular Plates With Variable Thickness

1982 ◽  
Vol 104 (3) ◽  
pp. 533-535
Author(s):  
A. K. Naghdi
Keyword(s):  
Variable Thickness ◽  
Simple Technique ◽  
Bending Moment ◽  
The Other ◽  
Uniform Pressure ◽  
Approximate Analysis ◽  
Circular Plates ◽  
Numerical Examples ◽  
Classic Theory ◽  
Rotationally Symmetric

Based on classic theory of beams and certain modifications, a simple technique is derived in order to obtain an approximate value of the maximum bending moment in a rotationally symmetric circular plate with a variable thickness. It is assumed that one of the two concentric boundaries of the plate is clamped, and the other is free. Numerical examples for both cases of constant and variable thickness plates subject to uniform pressure or rim line loading are presented.

A Simple Spline Integral Equation Method for Circular Plates with Variable Thickness

2007 ◽  
Vol 353-358 ◽  
pp. 2687-2690
Author(s):  
Xin Zhu Zhou ◽  
Jian Jun Zheng
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Analytical Solution ◽  
Variable Thickness ◽  
Order Differential Equation ◽  
Spline Interpolation ◽  
Bending Moment ◽  
Integral Equation Method ◽  
Equation Method ◽  
Circular Plates

A simple spline integral equation method is presented in this paper for the axisymmetrical bending of circular plates with variable thickness. Firstly, the fundamental solution of a second-order differential equation is derived. With the slope of the deflection surface taken as an unknown function, an integral equation is then established for circular plates with variable thickness. The integral equation is solved numerically by cubic spline interpolation and the deflection and bending moment at any point within the circular plate are obtained. Finally, the validity of the proposed method is verified with the analytical solution obtained from the literature.

Bending and Vibration of Plates of Variable Thickness

1976 ◽  
Vol 98 (1) ◽  
pp. 166-170 ◽  
Author(s):  
S. S. H. Chen
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
The Other ◽  
Polar Coordinates ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Plates Of Variable Thickness

The problem of bending and vibration of plates of variable thickness and arbitrary shapes and with mixed boundary conditions was solved by a modified energy method of the Rayleigh-Ritz type. General trial functions of deflection were obtained, one in Cartesian coordinates for rectangular plates and the other in polar coordinates for other shapes. The forced boundary conditions were satisfied approximately by introducing fixity factors which depended upon the prescribed conditions. Central deflections for circular plates subjected to static bending were within 0.2 percent of published results while they were within 1 percent for rectangular plates. The differences of natural frequencies of various rectangular plates were from 0.05 percent for simple, 2.9 percent for clamp, and up to 4.3 percent for free-free plates based on the published values.

Practical Correction of Three Fold Astigmatism in the Philips CM TEM

1996 ◽  
Vol 54 ◽  
pp. 418-419
Author(s):  
Arno J. Bleeker ◽  
Mark H.F. Overwijk ◽  
Max T. Otten
Keyword(s):  
Optical Properties ◽  
Phase Contrast ◽  
The Other ◽  
Objective Lens ◽  
Symmetric Part ◽  
A Posteriori ◽  
Contrast Transfer Function ◽  
High Brightness ◽  
Rotationally Symmetric ◽  
Brightness Field

With the improvement of the optical properties of the modern TEM objective lenses the point resolution is pushed beyond 0.2 nm. The objective lens of the CM300 UltraTwin combines a Cs of 0. 65 mm with a Cc of 1.4 mm. At 300 kV this results in a point resolution of 0.17 nm. Together with a high-brightness field-emission gun with an energy spread of 0.8 eV the information limit is pushed down to 0.1 nm. The rotationally symmetric part of the phase contrast transfer function (pctf), whose first zero at Scherzer focus determines the point resolution, is mainly determined by the Cs and defocus. Apart from the rotationally symmetric part there is also the non-rotationally symmetric part of the pctf. Here the main contributors are not only two-fold astigmatism and beam tilt but also three-fold astigmatism. The two-fold astigmatism together with the beam tilt can be corrected in a straight-forward way using the coma-free alignment and the objective stigmator. However, this only works well when the coefficient of three-fold astigmatism is negligible compared to the other aberration coefficients. Unfortunately this is not generally the case with the modern high-resolution objective lenses. Measurements done at a CM300 SuperTwin FEG showed a three fold-astigmatism of 1100 nm which is consistent with measurements done by others. A three-fold astigmatism of 1000 nm already sinificantly influences the image at a spatial frequency corresponding to 0.2 nm which is even above the point resolution of the objective lens. In principle it is possible to correct for the three-fold astigmatism a posteriori when through-focus series are taken or when off-axis holography is employed. This is, however not possible for single images. The only possibility is then to correct for the three-fold astigmatism in the microscope by the addition of a hexapole corrector near the objective lens.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

The Mechanical Performance Evaluation of a Mechanism with Curved Edge Driving Component

2013 ◽  
Vol 834-836 ◽  
pp. 1290-1294
Author(s):  
Xin Qin Liu
Keyword(s):  
Performance Evaluation ◽  
Fast Moving ◽  
Mechanical Performance ◽  
Gain Coefficient ◽  
The Other ◽  
Force Transmission ◽  
Transmission Performance ◽  
Connecting Rod ◽  
Numerical Examples ◽  
Straight Line

Mechanicalmethods were employed to study the motion and force transmission performance ofa kind of connecting rod slider mechanism with a curved edge driving component.The deduction methods and the computation formulae of the slider displacement,velocity, acceleration and the executive force gain coefficient were given.Considering two cases of the driving components with straight line edge andexponential function edge, the numerical examples was computed respectively,the results show that the former one is suitable for the force transmission andcan be used in the grip design and the other one is suitable for the motiontransmission which can be used in the fast moving mechanism

The Circular Cylinder With a Band of Uniform Pressure on a Finite Length of the Surface

1941 ◽  
Vol 8 (3) ◽  
pp. A97-A104 ◽  
Author(s):  
M. V. Barton
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Infinite Series ◽  
Fundamental Problem ◽  
The Other ◽  
Complete Picture ◽  
Uniform Pressure ◽  
Uniform Tension ◽  
Special Cases ◽  
Stress And Deformation

Abstract The solution to the fundamental problem of a cylinder with a uniform pressure over one half its length and a uniform tension on the other half is found by using the Papcovitch-Neuber solution to the general equations. In this paper, the results, given analytically in terms of infinite-series expressions, are exhibited as curves giving a complete picture of the stress and deformation. The case of a cylinder with a band of uniform pressure of any length, with the exception of very small ones, is then solved by the method of superposition. The stresses and displacements are evaluated for the special cases of a cylinder with a uniform pressure load of 1 diam and 1/2 diam in length. The problem of a cylinder heated over one half its length is solved by the same means.

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