scholarly journals Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kiran D. Mali ◽  
Pravin M. Singru
Keyword(s):  
Analytical Model ◽  
Perforated Plate ◽  
Rectangular Plates ◽  
Perforated Plates ◽  
Cosine Series ◽  
Circular Holes ◽  
Support Conditions ◽  
Mechanical Devices ◽  
The Galerkin Method

This paper is concerned with a vibration analysis of perforated rectangular plates with rectangular perforation pattern of circular holes. The study is particularly useful in the understanding of the vibration of sound absorbing screens, head plates, end covers, or supports for tube bundles typically including tube sheets and support plates used in the mechanical devices. An energy method is developed to obtain analytical frequencies of the perforated plates with clamped edge, support conditions. Perforated plate is considered as plate with uniformly distributed mass. Holes are considered as concentrated negative masses. The analytical procedure using the Galerkin method is adopted. The deflected surface of the plate is approximated by the cosine series which satisfies the boundary conditions. Finite element method (FEM) results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well for holes of small size.

Effective Bending Properties for Stress Analysis of Rectangular Tubesheets

1977 ◽  
Vol 99 (3) ◽  
pp. 365-370 ◽  
Author(s):  
A. I. Soler ◽  
W. S. Hill
Keyword(s):  
Stress Analysis ◽  
Research Effort ◽  
Perforated Plate ◽  
Bending Stiffness ◽  
Analytical Relationship ◽  
Simple Analytical Expression ◽  
Large Power ◽  
Perforated Plates ◽  
Tube Arrays

The analysis of perforated plates has immediate application to tubesheet design. However, successful tubesheet stress analysis requires knowledge of tubesheet elastic properties; considerable effort has therefore been directed toward their determination. The research effort to date has focused on triangular and square, fully packed tube arrays usually employed in circular tubesheets. In this paper, a simple analytical expression is proposed which is suitable for determination of the effective bending stiffness of a perforated plate having both fully packed and laned arrays. Using available data on triangular and square tube arrays, together with some additional test data on tube arrays in common use on large power plant condensers with rectangular tubesheets, it is shown that a simple analytical relationship for determination of required effective bending stiffness gives good agreement with available data.

scholarly journals A semi-analytical model on the critical buckling load of perforated plates with opposite free edges

2022 ◽  
pp. 095440622110568
Author(s):  
Weigang Fu ◽  
Bin Wang
Keyword(s):  
Analytical Model ◽  
Perforated Plate ◽  
Beam Theory ◽  
Buckling Load ◽  
Width Ratio ◽  
Geometrical Parameters ◽  
Engineering Structures ◽  
Perforated Plates ◽  
Critical Buckling Load ◽  
Free Edges

Perforated plates are widely used in thin-walled engineering structures, for example, for lightweight designs of structures and access for installation. For the purpose of analysis, such perforated plates with two opposite free edges might be considered as a series of successive Timoshenko beams. A new semi-analytical model was developed in this study using the Timoshenko shear beam theory for the critical buckling load of perforated plates, with the characteristic equations derived. Results of the proposed modelling were compared with those obtained by FEM and show good agreement. The influence of the dividing number of the successive beams on the accuracy of the critical buckling load was studied with respect to various boundary conditions. And the effect of geometrical parameters, such as the aspect ratio, the thickness-to-width ratio and the cutout-to-width ratio were also investigated. The study shows that the proposed semi-analytical model can be used for buckling analysis of a perforated plate with opposite free edges with the capacity to consider the shear effect in thick plates.

Evaluation of web reinforcements in prestressed concrete box girders through shear-transverse bending domains

2020 ◽  
pp. 136943322098170
Author(s):  
Michele Fabio Granata ◽  
Antonino Recupero
Keyword(s):  
Analytical Model ◽  
Prestressed Concrete ◽  
3D Analysis ◽  
Box Girders ◽  
Element Analysis ◽  
Cross Sectional ◽  
Interaction Domains ◽  
Global And Local ◽  
Resultant Forces

In concrete box girders, the amount and distribution of reinforcements in the webs have to be estimated considering the local effects due to eccentric external loads and cross-sectional distortion and not only the global effect due to the resultant forces of a longitudinal analysis: shear, torsion and bending. This work presents an analytical model that allows designers to take into account the interaction of all these effects, global and local, for the determination of the reinforcements. The model is based on the theory of stress fields and it has been compared to a 3D finite element analysis, in order to validate the interaction domains. The results show how the proposed analytical model allows an easy and reliable reinforcement evaluation, in agreement with a more refined 3D analysis but with a reduced computational burden.

Elastic Design Methods for Perforated Plates

1978 ◽  
Vol 100 (2) ◽  
pp. 356-362 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Finite Element ◽  
Thermal Loading ◽  
Solid Material ◽  
Perforated Plates ◽  
Finite Element Stress Analysis ◽  
Effective Elastic Constants ◽  
New Methods ◽  
Circular Holes ◽  
Elastic Design ◽  
Generalized Plane Strain

Methods for performing finite element stress analysis of perforated plates under pressure and complex thermal loading conditions are described. The concept of the equivalent solid material of anisotropic properties is employed to define the elasticity matrices to be used for axisymmetric analysis of plates containing triangular and square patterns of circular holes. Generalized plane strain effective elastic constants are used for better approximation of the overall plate behavior. New methods and curves for obtaining local ligament stresses from the nominal stresses in the equivalent solid material are given.

The Dynamics of a Cantilevered Pipe Aspirating Fluid Studied by Experimental, Numerical and Analytical Methods

2010 ◽  
Author(s):  
Dana Giacobbi ◽  
Stephanie Rinaldi ◽  
Christian Semler ◽  
Michael P. Pai¨doussis
Keyword(s):  
Analytical Model ◽  
Low Flow ◽  
Computational Fluid Dynamics Cfd ◽  
Computational Structural Mechanics ◽  
Cantilevered Pipe ◽  
The Galerkin Method ◽  
Csm Model ◽  
Ocean Mining ◽  
Flow Experiments ◽  
Flow Velocities

This paper investigates the dynamics of a slender, flexible, aspirating cantilevered pipe, ingesting fluid at its free end and conveying it towards its clamped end. The problem is interesting not only from a fundamental perspective, but also because applications exist, notably in ocean mining [1]. First, the need for the present work is demonstrated through a review of previous research into the topic — spanning many years and yielding often contradictory results — most recently concluding that the system loses stability by flutter at relatively low flow velocities [2]. In the current paper, that conclusion is refined and expanded upon by exploring the problem in three ways: experimentally, numerically and analytically. First, air-flow experiments, in which the flow velocity of the fluid was varied and the frequency and amplitude of oscillation of the pipe were measured, were conducted using different elastomer pipes and intake shapes. Second, a fully-coupled Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM) model was developed in ANSYS in order to simulate experiments and corroborate experimental results. Finally, using an analytical approach, the existing linear equation of motion describing the system was significantly improved upon, and then solved via the Galerkin method in order to determine its stability characteristics. Heavily influenced by a CFD analysis, the proposed analytical model is different from previous ones, most notably because of the inclusion of a two-part fluid depressurization at the intake. In general, both the actual and numerical experiments suggest a first-mode loss of stability by flutter at relatively low flow velocities, which agrees with the results from the new analytical model.

Reinforced Circular Holes in Bending With Shear

1953 ◽  
Vol 20 (2) ◽  
pp. 279-285
Author(s):  
S. R. Heller
Keyword(s):  
Stress Distribution ◽  
Arbitrary Shape ◽  
Theoretical Solution ◽  
Bead Type ◽  
Circular Holes ◽  
Radial Thickness ◽  
Bending With Shear ◽  
The Web

Abstract The object of this paper is the determination of the effect of the reinforcement of circular holes on the stress distribution in the webs of beams subjected to bending with shear. A theoretical solution for a bead-type reinforcement, i.e., small radial thickness, is developed. The stress distribution in the web for arbitrary shape reinforcement is based on the work of Reissner and Morduchow (1). The theory developed is valid provided the diameter of the hole does not exceed one fourth of the depth of the beam.

Some Unexpected Results in the Stress Calculation Around Multiple Holes in an Isotropic Plate Under In-Plane-Loads

2014 ◽  
Author(s):  
Ghazi H. Asmar ◽  
Elie A. Chakar ◽  
Toni G. Jabbour
Keyword(s):  
Finite Element ◽  
Isotropic Plate ◽  
Potential Method ◽  
The Finite Element Method ◽  
Close Proximity ◽  
Complex Fourier Series ◽  
Circular Holes ◽  
Complex Potential Method ◽  
Multiple Holes

The Schwarz alternating method, along with Muskhelishvili’s complex potential method, is used to calculate the stresses around non-intersecting circular holes in an infinite isotropic plate subjected to in-plane loads at infinity. The holes may have any size and may be disposed in any manner in the plate, and the loading may be in any direction. Complex Fourier series, whose coefficients are calculated using numerical integration, are incorporated within a Mathematica program for the determination of the tangential stress around any of the holes. The stress values obtained are then compared to published results in the literature and to results obtained using the finite element method. It is found that part of the results generated by the authors do not agree with some of the published ones, specifically, those pertaining to the locations and magnitudes of certain maximum stresses occurring around the contour of holes in a plate containing two holes at close proximity to each other. This is despite the fact that the results from the present authors’ procedure have been verified several times by finite element calculations. The object of this paper is to present and discuss the results calculated using the authors’ method and to underline the discrepancy mentioned above.

High Speed Flow through Perforated Plates

1960 ◽  
Vol 64 (590) ◽  
pp. 103-105
Author(s):  
P. G. Morgan
Keyword(s):  
Pressure Drop ◽  
High Speed ◽  
Perforated Plate ◽  
Wire Mesh ◽  
Flow Conditions ◽  
High Speed Flow ◽  
Perforated Plates ◽  
Speed Flow ◽  
Flow Through ◽  
Points Of View

The flow through porous screens has been widely studied from both the theoretical and experimental points of view. The most widely used types of screen are the wire mesh and the perforated plate, and the majority of the literature has been concerned with the former. Several attempts have been made to correlate the parameters governing the flow through such screens, i.e. the pressure drop, the flow conditions and the geometry of the mesh.

Determination of the Stress Distribution at the Interface Metal-Oxide: Numerical and Theoretical Considerations

2005 ◽  
Vol 237-240 ◽  
pp. 145-150 ◽  
Author(s):  
Sébastien Garruchet ◽  
A. Hasnaoui ◽  
Olivier Politano ◽  
Tony Montesin ◽  
J. Marcos Salazar ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Stress Distribution ◽  
Oxide Film ◽  
Metal Oxide ◽  
Reaction Kinetics ◽  
Analytical Model ◽  
Equilibrium Thermodynamics ◽  
Theoretical Considerations ◽  
Molecular Dynamics Results

In this paper we give a brief presentation of the approaches we have recently developed on the oxidation of metals. Firstly, we present an analytical model based on non-equilibrium thermodynamics to describe the reaction kinetics present during the oxidation of a metal. Secondly, we present the molecular dynamics results obtained with a code specially tailored to study the oxidation and growth of an oxide film of aluminium. Our simulations present an excellent agreement with experimental results.

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