scholarly journals Linear and Nonlinear Analyses of Skewed Plates

1967 ◽  
Vol 34 (2) ◽  
pp. 271-277 ◽  
Author(s):  
J. B. Kennedy ◽  
Simon Ng
Keyword(s):  
Aspect Ratio ◽  
Large Deflection ◽  
Successive Approximations ◽  
Rectangular Plates ◽  
Aspect Ratios ◽  
Linear And Nonlinear ◽  
Center Deflection ◽  
Skewed Plates ◽  
Skew Angles ◽  
Resultant Stress

The perturbation method is used to analyze small and large-deflection problems of clamped skewed plates under uniform pressure. The results are improved by successive approximations to the three displacement components of a point on the middle plane of the plate. Numerical and graphical results are presented. Comparisons are made with existing results for skewed plates with small deflections as well as with results for rectangular plates with small and large-deflection behavior; good agreement is shown. The effects of skew and aspect ratio on plates with large deflections are investigated. The ratios of maximum center deflection to thickness of plate at which linear and nonlinear theories start deviating significantly from each other are obtained for different aspect ratios and skew angles. It is shown that the center deflection decreases with increase in skew and aspect ratio, and that the maximum resultant stress occurs along the longer edges of the plates and is displaced toward the obtuse corners.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates

1981 ◽  
Vol 16 (2) ◽  
pp. 97-106 ◽  
Author(s):  
S Sreenivasamurthy ◽  
V Ramamurti
Keyword(s):  
Aspect Ratio ◽  
Degrees Of Freedom ◽  
Mode Frequency ◽  
Coriolis Effect ◽  
Skew Angle ◽  
Noticeable Effect ◽  
Torsional Mode ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Skew Angles

The Coriolis effect on the first bending and first torsional frequencies of flat rotating low aspect ratio cantilever plates has been investigated using finite element method. The cantilever plate has been modelled using plane triangular shell elements with three nodes and eighteen degrees of freedom. Three typical skew angles (0, 45, and 90 degrees) and two aspect ratios (1 and 2) are considered in the analysis. In addition to the Coriolis effect other effects, namely the geometric stiffness and the supplementary stiffness, have been considered. The mass and stiffness matrices have been derived using area coordinates. It has been found that the effect of including Coriolis effect is to lower the first two frequencies. This effect is negligible when the skew angle is 90 degrees. In the other two cases, skew of 0 and 45 degrees, there is a noticeable effect on the first torsional mode frequency when the aspect ratio is unity and on the first bending mode frequency when the aspect ratio is 2. An increase in the Coriolis effect is observed when the aspect ratio is increased from 1 to 2, with the skew angles of 0 and 45 degrees and a decrease when the skew angle is 90 degrees. The difference between the two frequencies (with and without Coriolis effect) becomes more and more noticeable as the rotational speed increases.

scholarly journals LINEAR AND NONLINEAR FREE VIBRATION ANALYSIS OF RECTANGULAR PLATE

2021 ◽  
Vol 12 (1) ◽  
pp. 15-25
Author(s):  
Edward Adah ◽  
David Onwuka ◽  
Owus Ibearugbulem ◽  
Chinenye Okere
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Middle Surface ◽  
Rectangular Plates ◽  
Nonlinear Free Vibration ◽  
Surface Displacements ◽  
Linear And Nonlinear

The major assumption of the analysis of plates with large deflection is that the middle surface displacements are not zeros. The determination of the middle surface displacements, u0 and v0 along x- and y- axes respectively is the major challenge encountered in large deflection analysis of plate. Getting a closed-form solution to the long standing von Karman large deflection equations derived in 1910 have proven difficult over the years. The present work is aimed at deriving a new general linear and nonlinear free vibration equation for the analysis of thin rectangular plates. An elastic analysis approach is used. The new nonlinear strain displacement equations were substituted into the total potential energy functional equation of free vibration. This equation is minimized to obtain a new general equation for analyzing linear and nonlinear resonating frequencies of rectangular plates. This approach eliminates the use of Airy’s stress functions and the difficulties of solving von Karman's large deflection equations. A case study of a plate simply supported all-round (SSSS) is used to demonstrate the applicability of this equation. Both trigonometric and polynomial displacement shape functions were used to obtained specific equations for the SSSS plate. The numerical results for the coefficient of linear and nonlinear resonating frequencies obtained for these boundary conditions were 19.739 and 19.748 for trigonometric and polynomial displacement functions respectively. These values indicated a maximum percentage difference of 0.051% with those in the literature. It is observed that the resonating frequency increases as the ratio of out–of–plane displacement to the thickness of plate (w/t) increases. The conclusion is that this new approach is simple and the derived equation is adequate for predicting the linear and nonlinear resonating frequencies of a thin rectangular plate for various boundary conditions.

Approximate Analysis of the Large Deflection Elastic Behaviour of Clamped, Uniformly Loaded, Rectangular Plates

1969 ◽  
Vol 11 (3) ◽  
pp. 256-268 ◽  
Author(s):  
R. Hooke
Keyword(s):  
Aspect Ratio ◽  
Perturbation Method ◽  
Large Deflection ◽  
Elastic Behaviour ◽  
Rectangular Plates ◽  
Approximate Analysis

An approximate analysis of the large deflection elastic behaviour of clamped, uniformly loaded, rectangular plates is carried out using a perturbation method. The solutions obtained are presented in a general form which allows the behaviour of a plate having any particular value of aspect ratio to be predicted. The predictions of the present solutions are compared with those of existing solutions where these are available.

Influence of the Aspect Ratio on the Dynamic Stability and Nonlinear Response of Rectangular Plates

1982 ◽  
Vol 104 (2) ◽  
pp. 417-425 ◽  
Author(s):  
G. L. Ostiguy ◽  
R. M. Evan-Iwanowski
Keyword(s):  
Aspect Ratio ◽  
Dynamic Stability ◽  
Nonlinear Response ◽  
Lateral Displacement ◽  
Parametric Instability ◽  
Mode Shapes ◽  
Additional Parameter ◽  
Rectangular Plates ◽  
Lower Mode ◽  
Aspect Ratios

The dynamic stability and nonlinear response of simply-supported rectangular plates subjected to parametric excitation are investigated. The large-deflection plate theory used in the analysis is derived in terms of the stress function F and lateral displacement w and is applied to rectangular plates with stress-free supported edges and uniformly stressed loaded edges. General rectangular plates are considered, the aspect ratio of the plate being regarded as an additional parameter of the system. Calculations are carried out for rectangular plates of various aspect ratios, and the relative importance of the principal regions of parametric instability associated with the lower mode shapes is clarified. The stationary response of the system within a principal region of instability is also evaluated. The results obtained indicate that the aspect ratio plays a crucial role in determining the stability of rectangular plates; elongated plates are more susceptible to various parametric resonances than square plates.

scholarly journals Effects of Steel Fiber Percentage and Aspect Ratios on Fresh and Harden Properties of Ultra-High Performance Fiber

2021 ◽  
Vol 2 (3) ◽  
pp. 501-515
Author(s):  
Rajib Kumar Biswas ◽  
Farabi Bin Ahmed ◽  
Md. Ehsanul Haque ◽  
Afra Anam Provasha ◽  
Zahid Hasan ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Aspect Ratio ◽  
High Performance ◽  
Steel Fiber ◽  
Setting Time ◽  
Fiber Reinforced Concrete ◽  
Future Research ◽  
Manufacturing Cost ◽  
Aspect Ratios ◽  
High Performance Fiber

Steel fibers and their aspect ratios are important parameters that have significant influence on the mechanical properties of ultrahigh-performance fiber-reinforced concrete (UHPFRC). Steel fiber dosage also significantly contributes to the initial manufacturing cost of UHPFRC. This study presents a comprehensive literature review of the effects of steel fiber percentages and aspect ratios on the setting time, workability, and mechanical properties of UHPFRC. It was evident that (1) an increase in steel fiber dosage and aspect ratio negatively impacted workability, owing to the interlocking between fibers; (2) compressive strength was positively influenced by the steel fiber dosage and aspect ratio; and (3) a faster loading rate significantly improved the mechanical properties. There were also some shortcomings in the measurement method for setting time. Lastly, this research highlights current issues for future research. The findings of the study are useful for practicing engineers to understand the distinctive characteristics of UHPFRC.

scholarly journals Surface Texturing of Si with Periodically Arrayed Oblique Nanopillars to Achieve Antireflection

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 380
Author(s):  
Jun-Hyun Kim ◽  
Sanghyun You ◽  
Chang-Koo Kim
Keyword(s):  
Aspect Ratio ◽  
Plasma Etching ◽  
Surface Texturing ◽  
Light Reflection ◽  
Si Substrate ◽  
Weighted Mean ◽  
Optical Reflectance ◽  
Si Substrates ◽  
Aspect Ratios ◽  
Shadowing Effect

Si surfaces were texturized with periodically arrayed oblique nanopillars using slanted plasma etching, and their optical reflectance was measured. The weighted mean reflectance (Rw) of the nanopillar-arrayed Si substrate decreased monotonically with increasing angles of the nanopillars. This may have resulted from the increase in the aspect ratio of the trenches between the nanopillars at oblique angles due to the shadowing effect. When the aspect ratios of the trenches between the nanopillars at 0° (vertical) and 40° (oblique) were equal, the Rw of the Si substrates arrayed with nanopillars at 40° was lower than that at 0°. This study suggests that surface texturing of Si with oblique nanopillars reduces light reflection compared to using a conventional array of vertical nanopillars.

scholarly journals Strength Analysis of Alternative Airframe Layouts of Regional Aircraft on the Basis of Automated Parametrical Models

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 80
Author(s):  
Dmitry V. Vedernikov ◽  
Alexander N. Shanygin ◽  
Yury S. Mirgorodsky ◽  
Mikhail D. Levchenkov
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
High Performance ◽  
Strength Analysis ◽  
Labor Input ◽  
Aerodynamic Loading ◽  
Aspect Ratios ◽  
Wide Range ◽  
Parametrical Design

This publication presents the results of complex parametrical strength investigations of typical wings for regional aircrafts obtained by means of the new version of the four-level algorithm (FLA) with the modified module responsible for the analysis of aerodynamic loading. This version of FLA, as well as a base one, is focused on significant decreasing time and labor input of a complex strength analysis of airframes by using simultaneously different principles of decomposition. The base version includes four-level decomposition of airframe and decomposition of strength tasks. The new one realizes additional decomposition of alternative variants of load cases during the process of determination of critical load cases. Such an algorithm is very suitable for strength analysis and designing airframes of regional aircrafts having a wide range of aerodynamic concepts. Results of validation of the new version of FLA for a high-aspect-ratio wing obtained in this work confirmed high performance of the algorithm in decreasing time and labor input of strength analysis of airframes at the preliminary stages of designing. During parametrical design investigation, some interesting results for strut-braced wings having high aspect ratios were obtained.

Influence of nozzle exit geometrical parameters on supersonic jet decay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Prasanta Kumar Mohanta ◽  
B. T. N. Sridhar ◽  
R. K. Mishra
Keyword(s):  
Aspect Ratio ◽  
Nozzle Exit ◽  
Ambient Air ◽  
Schlieren Image ◽  
Geometrical Parameters ◽  
Image Study ◽  
Aspect Ratios ◽  
Core Length ◽  
Supersonic Core Length ◽  
The Impact

Abstract Experiments and simulations were carried on C-D nozzles with four different exit geometry aspect ratios to investigate the impact of supersonic decay characteristics. Rectangular and elliptical exit geometries were considered for the study with various aspect ratios. Numerical simulations and Schlieren image study were studied and found the agreeable logical physics of decay and spread characteristics. The supersonic core decay was found to be of different length for different exit geometry aspect ratio, though the throat to exit area ratio was kept constant to maintain the same exit Mach number. The impact of nozzle exit aspect ratio geometry was responsible to enhance the mixing of primary flow with ambient air, without requiring a secondary method to increase the mixing characteristics. The higher aspect ratio resulted in better mixing when compared to lower aspect ratio exit geometry, which led to reduction in supersonic core length. The behavior of core length reduction gives the identical signature for both under-expanded and over-expanded cases. The results revealed that higher aspect ratio of the exit geometry produced smaller supersonic core length. The aspect ratio of cross section in divergent section of the nozzle was maintained constant from throat to exit to reduce flow losses.

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