scholarly journals Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

scholarly journals Sensitivity Analysis of Buckling Loads of Bisymmetric I-Section Columns with Bracing Elements / Analiza Wrazliwosci Siły Krytycznej Słupa Cienkosciennego Ze Stezeniami

2010 ◽  
Vol 56 (1) ◽  
pp. 69-88 ◽  
Author(s):  
P. Iwicki
Keyword(s):  
Sensitivity Analysis ◽  
Critical Load ◽  
Cross Section ◽  
Exact Relation ◽  
Buckling Loads ◽  
Numerical Examples ◽  
First Order ◽  
Order Variation ◽  
Thin Walled ◽  
Open Cross Section

Abstract The first order variation of critical loads of thin-walled columns with bisymmetric open cross-section due to some variations of the stiffness and location of bracing elements is derived. The considerations are based on the classical linear theory of thin-walled beams with non-deformable cross-section introduced by Vlasov [1]. Both lateral braces and braces that restraint warping and torsion of the cross-section have been taken into account. In the numerical examples dealing with I-column, the functions describing the influence of location of the braces with unit stiffness on the critical load of torsional and flexural buckling are derived. The linear approximation of the exact relation of the critical load due to the variation of the stiffness and location of braces is determined.

scholarly journals Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

Constrained-Layer Damping of Torsional Vibration of Thin-Walled Tubes

2001 ◽  
Author(s):  
Samir A. Nayfeh
Keyword(s):  
Closed Form ◽  
Torsional Vibration ◽  
Unit Length ◽  
Constrained Layer Damping ◽  
Cross Sectional ◽  
Thin Walled ◽  
Viscoelastic Layers

Abstract In this paper, we take up the problem of damping torsional vibration of thin-walled tubes with closed sections. Assuming that the deformation obeys the Saint-Venant hypotheses, we develop a model suitable for predicting the complex stiffness per unit length in tubes with constrained viscoelastic layers over part or all of their perimeter. For some basic cross-sectional shapes, we solve the warping problem and thence obtain closed-form expressions for the complex stiffness per unit length. Finally, we provide some guidelines for the design of tubes with high damping in torsion.

scholarly journals An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170080 ◽  
Author(s):  
Duncan Joyce ◽  
William J. Parnell ◽  
Raphaël C. Assier ◽  
I. David Abrahams
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Effective Properties ◽  
Circular Cross Section ◽  
Rational Functions ◽  
High Volume ◽  
Cross Sectional ◽  
Antiplane Elasticity ◽  
Unidirectional Fibre ◽  
Explicit Expressions

In Parnell & Abrahams (2008 Proc. R. Soc. A 464 , 1461–1482. ( doi:10.1098/rspa.2007.0254 )), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.

Collapse of Thin-Walled Elliptical Tubes for High Values of Major-to-Minor Axis Ratio

1993 ◽  
Vol 115 (4A) ◽  
pp. 432-440 ◽  
Author(s):  
C. Ribreau ◽  
S. Naili ◽  
M. Bonis ◽  
A. Langlet
Keyword(s):  
Contact Pressure ◽  
Cross Section ◽  
External Pressure ◽  
Straight Line Segment ◽  
Minor Axis ◽  
Cross Sectional ◽  
Axis Ratio ◽  
Straight Line ◽  
Thin Walled ◽  
The Cross

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse’s ellipticity ko, defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure p1. For p<p1, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and p1 are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).

scholarly journals ADJOINT APPROACH SENSITIVITY ANALYSIS OF THIN‐WALLED BEAMS AND FRAMES

2005 ◽  
Vol 11 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ireneusz Kreja ◽  
Tomasz Mikulski ◽  
Czeslaw Szymczak
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Fem Model ◽  
Static Loads ◽  
Shell Elements ◽  
Beam Elements ◽  
Thin Walled ◽  
The One ◽  
Adjoint Approach ◽  
Open Cross Section

Sensitivity analysis of beams and frames assembled of thin‐walled members is presented within the adjoint approach. Static loads and structures composed of thin‐walled members with the bisymmetrical open cross‐section are considered. The analysed structure is represented by the one‐dimensional model consisting of thin‐walled beam elements based on the classical assumptions of the theory of thin‐walled beams of non‐deformable cross‐section together with superelements applied in place of location of structure nodes, restraints and stiffeners. The results of sensitivity analysis, obtained for the structure model described above, are compared with the results of the detailed FEM model, where the whole structure is discretised with the use of QUAD4 shell elements of the system MSC/NASTRAN.

Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section

1965 ◽  
Vol 7 (3) ◽  
pp. 292-299 ◽  
Author(s):  
S. A. Hasan ◽  
A. D. S. Barr
Keyword(s):  
Cross Section ◽  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Characteristic Functions ◽  
Curved Beam ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Circular Arc ◽  
Beam Geometry ◽  
Thin Walled

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.

Sign in / Sign up

Export Citation Format

Share Document