In-plane vibration of circular arc beam, cross sections of which suddenly vary stepwise. Case of small slenderness ratio.

How do we assess the capability of a compliant mechanism of given topology and shape? The kinetoelastostatic maps proposed in this paper help answer this question. These maps are drawn in 2D using two non-dimensional quantities, one capturing the nonlinear static response and the other the geometry, material, and applied forces. Geometrically nonlinear finite element analysis is used to create the maps for compliant mechanisms consisting of slender beams. In addition to the topology and shape, the overall proportions and the proportions of the cross-sections of the beam segments are kept fixed for a map. The finite region of the map is parameterized using a non-dimensional quantity defined as the slenderness ratio. The shape and size of the map and the parameterized curves inside it indicate the complete kinetoelastostatic capability of the corresponding compliant mechanism of given topology, shape, and fixed proportions. Static responses considered in this paper include input/output displacement, geometric amplification, mechanical advantage, maximum stress, etc. The maps can be used to compare mechanisms, to choose a suitable mechanism for an application, or re-design as may be needed. The usefulness of the non-dimensional maps is presented with multiple applications of different variety. Non-dimensional portrayal of snap-through mechanisms is one such example. The effect of the shape of the cross-section of the beam segments and the role of different segments in the mechanism as well as extension to 3D compliant mechanisms, the cases of multiple inputs and outputs, and moment loads are also explained. The effects of disproportionate changes on the maps are also analyzed.

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In-plane vibration analysis of cantilevered circular arc beams undergoing rotational motion

Journal of Mechanical Science and Technology ◽

10.1007/s12206-007-1013-x ◽

2008 ◽

Vol 22 (1) ◽

pp. 113-119 ◽

Cited By ~ 5

Author(s):

Guang Hui Zhang ◽

Zhan Sheng Liu ◽

Hong Hee Yoo

Keyword(s):

Rotational Motion ◽

Vibration Analysis ◽

Circular Arc ◽

Plane Vibration

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EXACT SOLUTION OF FREE IN-PLANE VIBRATION OF SHALLOW CIRCULAR ARCHES

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455401000226 ◽

2001 ◽

Vol 01 (03) ◽

pp. 409-428 ◽

Cited By ~ 15

Author(s):

EKREM TÜFEKÇİ

Keyword(s):

Exact Solution ◽

Boundary Conditions ◽

Shear Deformation ◽

Slenderness Ratio ◽

Mode Shapes ◽

Rotatory Inertia ◽

Shallow Arch ◽

Inertia Effects ◽

Plane Vibration ◽

Axial Extension

The free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects. The exact solution of the governing differential equations is obtained by the initial value method. By employing the same solution procedure, the solutions are also given for the other cases, in which each effect is considered alone, as well as no effect. The frequency coefficients are obtained for the lowest five vibration modes of arches with five combinations of classical boundary conditions, and various slenderness ratios and opening angles. The results show that the shear deformation and rotatory inertia effects are also very important as well as the axial extension effect, even if a slender shallow arch is considered. The discrepancies among the results of the five cases decrease, when opening angle increases for a constant radius and slenderness ratio. The effects of the boundary conditions and the slenderness ratio of the arch are investigated. The discrepancies among the results of the cases become much more important in higher modes. The mode shapes of a shallow arch are obtained for each case.

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Buckling Behaviour of Stainless Steel Square Hollow Sections

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.853.301 ◽

2016 ◽

Vol 853 ◽

pp. 301-305

Author(s):

Shameem Ahmed ◽

Mahmud Ashraf ◽

Mohammad Anwar-Us-Saadat

Keyword(s):

Stainless Steel ◽

Strain Hardening ◽

Cross Sections ◽

Design Method ◽

Numerical Models ◽

Slenderness Ratio ◽

Design Guidelines ◽

Material Nonlinearity ◽

Cross Sectional ◽

Steel Design

Structural stainless steel design guidelines should appropriately recognise its characteristic beneficial properties such as material nonlinearity and significant strain hardening. The Continuous Strength Method (CSM) exploits those through a strain based approach for both stocky and slender cross-sections. In this paper, a new design method is proposed that combines the CSM with Perry type buckling curves. Numerical models were developed to investigate effects of various parameters on column strength and to develop full column curves. It was observed that material nonlinearity significantly influence column strengths, and hence, different column curves were developed for a total of 20 material property combinations by calibrating imperfection factor and limiting slenderness ratio for each set. Proposed method includes the strain hardening benefits for stocky section, and abolished the necessity of calculating effective cross-sectional properties for slender sections. Performance of the proposed technique is compared against those obtained by the Eurocode EN1993-1-4.

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Modeling of Strain and Stress States for Straight Rods with Particular Cross Sections Subjected to Torsion

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.837.699 ◽

2013 ◽

Vol 837 ◽

pp. 699-704

Author(s):

Marilena Glovnea ◽

Cornel Suciu

Keyword(s):

Cross Section ◽

Cross Sections ◽

Circular Cross Section ◽

Segment Length ◽

Circular Arc ◽

Tangential Stresses ◽

Applied Torque ◽

The Cross ◽

Stress States ◽

Model Strain

In the case of shaft-hub joints with cylindrical pins found in both macro and micro-devices, a longitudinal gutter with an almost half-circular cross section is practiced along the length of the shaft segment. The center of the circular arc is placed on the circular edge of the cross section. The present paper aims to model strain and stress states within such a shaft, when the material elastic properties are known along with shaft segment length and applied torque. Using the MathCad environment, 3D and constant stress level plots were obtained for the distribution of tangential stresses over the cross section. After application of torque, the transverse cross sections shift and become anti-symmetric as illustrated by the obtained 3D and constant strain plots.

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Dynamic Modelling and Free Vibration Characteristics Analysis of Rotating Beams

10.1115/gtindia2021-76426 ◽

2021 ◽

Author(s):

D. Sachin ◽

Mallikarjuna Reddy

Keyword(s):

Differential Equations ◽

Free Vibration ◽

Cantilever Beam ◽

Natural Frequencies ◽

Slenderness Ratio ◽

Turbine Blades ◽

Dynamic Modelling ◽

Free Vibration Analysis ◽

Beam Model ◽

Plane Vibration

Abstract Turbine blades are ideally modeled as cantilever beams on a disc rotating at a constant angular velocity. A study is made to understand the dynamic relationships between a rotating cantilever beam and various factors like hub radius, rotation speed, and slenderness ratio in in-plane vibration (Chordwise motion) and out-of-plane vibration (Flapwise motion). Hub is assumed to be rigid in the study. Using Hamilton’s principle, governing differential equations of movement for free vibration analysis of Euler-Bernoulli beam (EB) and Timoshenko (TB) beam under rotation are derived. The effects of the Gyroscopic couple are taken into account in the equations. The beam model is discretized using the Finite element approach. Derived differential equations are transformed into dimensionless quantities in which dimensionless parameters are identified. Under rotation, it is observed that the natural frequencies increase with the increase in rotational speed for both flapwise and chordwise motions of the beam. An interesting phenomenon is observed in the chordwise motion results, where Natural frequencies veer off at certain rotational speeds and certain modes. Slenderness ratios also influence this phenomenon, which shifts the veer-off region and the tuned angular frequency. Numerical results are obtained for different rotational speeds with various hub radius ratios, and it was observed that hub radius directly influences the natural frequencies of the rotating uniform cantilever beam. A thorough study on the influence of the slenderness ratio showed that, for lower slenderness ratio, frequency veering region occurs at the fundamental natural frequency, but for higher slenderness ratios’ there is a shift in frequency veering region for higher modes.

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The Centre of Shear for Sections Bounded by Two Circular Arcs

Journal of the Royal Aeronautical Society ◽

10.1017/s036839310009773x ◽

1954 ◽

Vol 58 (518) ◽

pp. 138-139

Author(s):

L. G. Whitehead ◽

L. A. McQuillin

Keyword(s):

Cross Section ◽

Cross Sections ◽

Present Note ◽

Structural Data ◽

Limited Range ◽

Data Sheet ◽

Relative Influence ◽

Circular Arc ◽

Torsion Function ◽

Circular Arcs

In two recent notes Jacobs and Duncan considered the St. Venant torsion and flexure problems for beams of aerofoil cross section and have given methods for determining the centre of shear once the torsion function for the section has been found. The purpose of the present note is to give results for the location of the centre of shear for a limited range of cross sections bounded by two circular arcs for which the torsion function has long been known. The calculations shed some light on the relative influence of camber and thickness on the location of the centre of shear and are compared with the well known results for thin circular arc sections illustrated in the Structural Data Sheet 00.06.04.

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Probabilistic strength assessment through analytical modelling of pillars found in ship structures

MATEC Web of Conferences ◽

10.1051/matecconf/202134903007 ◽

2021 ◽

Vol 349 ◽

pp. 03007

Author(s):

Angelos S. Vasileiou ◽

Konstantinos N. Anyfantis

Keyword(s):

Cross Sections ◽

Slenderness Ratio ◽

Statistical Nature ◽

Ship Structures ◽

Strength Assessment ◽

Sample Data ◽

Stratified Sample ◽

Regulatory Bodies ◽

Input Variables ◽

Probabilistic Nature

The compressive strength of pillars found in ship structures is studied under a reliability perspective. Monte Carlo Simulations (MCS) are applied, aided by a stratified sample scheme (i.e. Latin Hypercube), to account for uncertainty within the problem’s input variables (yield stress, elastic modulus, initial bow imperfection). MCSs were applied for three slenderness ratio values (low, medium, high), for hollow-circular, hollow-square and “H” shape cross-sections, and multiple geometries per slenderness ratio, per cross-section. The pillar’s strength is calculated based on the Perry-Robertson formula. The probabilistic resistance per pillar was modelled by generating the probability density function that best describes the statistical nature of the sample data. In this paper we illustrate the probabilistic nature of the compression column resistance, and compare it to the deterministic resistance suggested by regulatory bodies.

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Lateral-torsional buckling of girders with class 4 web: Investigation of coupled instability in EC3-based design approach

Advances in Structural Engineering ◽

10.1177/1369433220915623 ◽

2020 ◽

Vol 23 (11) ◽

pp. 2442-2457

Author(s):

Noémi Seres ◽

Krisztina Fejes

Keyword(s):

Cross Sections ◽

Slenderness Ratio ◽

Limit State ◽

General Definition ◽

Ultimate Limit State ◽

Lateral Torsional Buckling ◽

Torsional Buckling ◽

Cross Sectional ◽

Plate Buckling ◽

Buckling Resistance

This article focuses on the lateral-torsional buckling resistance of girders with slender, class 4 cross-sections with a research aim to check the accuracy of the design resistance model of EN1993-1-1 and EN1993-1-5 on the coupled instability of lateral-torsional buckling and local plate buckling resistances. The current Eurocode-based design method considers in the effective cross-sectional resistance calculation that yield strength is reached in the extreme fibre of the cross-section, and the reduction factor [Formula: see text] related to local plate buckling is calculated based on this assumption. However, if lateral-torsional buckling occurs, maximum stress in the web can be significantly smaller at the ultimate limit state which is not considered in the effective cross-sectional resistance calculation. On the other side, EN1993-1-1 proposes to consider the effective bending moment resistance in the relative slenderness calculation of lateral-torsional buckling, which is in contradiction with the general definition of the relative slenderness ratio [Formula: see text], which should refer to the plastic resistance divided by the critical load of the structure. This article aims to check if the current Eurocode-based design rules need improvement and to check the effect of the above-mentioned specific issues on the calculated lateral-torsional buckling resistance. An extensive numerical research programme is executed to check and compare the lateral-torsional buckling resistance of class 3 (as reference) and class 4 cross-sections, and results are compared to Eurocode-based design models.

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