Transverse Vibration of a Viscoelastic Column With Initial Curvature Under Periodic Axial Load

1969 ◽  
Vol 36 (4) ◽  
pp. 814-818 ◽  
Author(s):  
K. K. Stevens
Keyword(s):  
Polymethyl Methacrylate ◽  
Transverse Vibration ◽  
Axial Load ◽  
Dynamic Instability ◽  
Complex Modulus ◽  
Lateral Vibrations ◽  
Lateral Response ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
Frequency Curves

The lateral response of a slightly curved viscoelastic column subjected to a periodic axial load P0 + P1 cos ωt is investigated. The analysis makes use of the complex modulus representation for linear viscoelastic materials. It is shown that the lateral vibrations stemming from imperfections can be of significant amplitude. Experimentally determined amplitude-frequency curves for a polymethyl methacrylate (Plexiglas) column are presented, and are found to be in excellent agreement with the theory. It is shown that there is an analogy between the dynamic instability and the static buckling of imperfect columns.

Dynamic stability of viscoelastic columns loaded by a follower force

2004 ◽  
Vol 218 (10) ◽  
pp. 1091-1101 ◽  
Author(s):  
T T Darabseh ◽  
J Genin
Keyword(s):  
Boundary Value Problems ◽  
Dynamic Instability ◽  
Element Model ◽  
Follower Load ◽  
Dynamic Approach ◽  
Stability Analyses ◽  
Damping Coefficients ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
The Stability

This paper analyses the motion of a linear viscoelastic column using the dynamic approach. The viscoelastic material is mathematically represented by the four-element model. Using this model as a recursion equation, the elastic, one-, two-, three- and four-element models are solved and their results compared. The stability analyses of these systems are investigated by studying the eigenvalues of the characteristic equations for the solution to the boundary value problems. The stability analyses determined the smallest value of the follower load beyond which the system, under a suitable disturbance, will perform oscillations with increasing amplitudes. The dynamic instability is found to occur in the form of flutter. The effect of damping on the critical follower load is also examined. Three damping parameters are considered that affect the results. They are the damping coefficients related to a Maxwell unit, to a Kelvin unit and one appropriate to a combination of the two. The destabilization effects of viscosity are discussed.

Analysis of Shear-critical reinforced concrete columns under variable axial load

2022 ◽  
pp. 1-24
Author(s):  
Dimitrios K. Zimos ◽  
Panagiotis E. Mergos ◽  
Vassilis K. Papanikolaou ◽  
Andreas J. Kappos
Keyword(s):  
Reinforced Concrete ◽  
Axial Load ◽  
Shear Failure ◽  
Progressive Collapse ◽  
Full Range ◽  
Element Model ◽  
Independent Verification ◽  
Lateral Response ◽  
Proposed Model ◽  
Compressive Axial Load

Older existing reinforced concrete (R/C) frame structures often contain shear-dominated vertical structural elements, which can experience loss of axial load-bearing capacity after a shear failure, hence initiating progressive collapse. An experimental investigation previously reported by the authors focused on the effect of increasing compressive axial load on the non-linear post-peak lateral response of shear, and flexure-shear, critical R/C columns. These results and findings are used here to verify key assumptions of a finite element model previously proposed by the authors, which is able to capture the full-range response of shear-dominated R/C columns up to the onset of axial failure. Additionally, numerically predicted responses using the proposed model are compared with the experimental ones of the tested column specimens under increasing axial load. Not only global, but also local response quantities are examined, which are difficult to capture in a phenomenological beam-column model. These comparisons also provide an opportunity for an independent verification of the predictive capabilities of the model, because these specimens were not part of the initial database that was used to develop it.

Prediction of axial hysteresis in locked coil ropes

1996 ◽  
Vol 31 (5) ◽  
pp. 341-351 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Theoretical Model ◽  
Cross Section ◽  
Axial Load ◽  
Dynamic Instability ◽  
Contact Forces ◽  
Damping Capacity ◽  
Outermost Layer ◽  
Parametric Studies ◽  
Load Perturbations ◽  
Practical Implications

In published literature, the strand constructions dealt with have almost invariably involved only wires which are circular in cross-section. There are, however, instances when shaped wires are used in, for example, half-lock and full-lock coil constructions. The paper reports details of a theoretical model which enables an insight to be gained into various characteristics of axially loaded lock coil ropes. The model is based on an extension of a previously reported orthotropic sheet concept and provides a fairly simple means of estimating wire kinematics, interwire/interlayer contact forces, effective axial stiffnesses and axial hysteresis in axially preloaded locked coil ropes experiencing uniform cyclic axial load perturbations. The theory takes interwire contact deformations and friction into account. Final numerical results based on theoretical parametric studies on some substantial cables highlight the substantial role that the outermost layer(s) with shaped wires play as regards the overall axial damping capacity of fully bedded-in (old) locked coil ropes, and it is found that (for the same lay angles and outer diameters) axial hysteresis in locked coil ropes is generally higher than spiral strands which are composed of only round wires. This finding may have significant practical implications in terms of the design against dynamic instability of structures supported by such cables.

scholarly journals Vortex excitation of tower-like structures of circular cross-sections.

2007 ◽  
Vol 1 (1) ◽  
pp. 119-143
Author(s):  
Tomasz Lipecki
Keyword(s):  
Mathematical Model ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Theoretical Background ◽  
Lateral Vibrations ◽  
Lateral Response ◽  
Analysis Of Results ◽  
Lateral Displacements ◽  
Corrosion Of Steel

The paper deals with the description of vortex excitation phenomenon in cases of structures of circular cross-sections. Other sources of across-wind load (fluctuations of wind direction or aerodynamic interference) are neglected in this paper. The main aim of this paper is presentation of a theoretical background of a new mathematical model of critical vortex excitation of slender structures of circular cross-sections. All calculations have been performed using own computer programme according to numerical implementation of mathematical model. That programme allows to simulate across-wind action caused by vortices as well as a lateral response of the analysed structure. Simulations of vortex excitation are performed in real time on the basis of lateral displacements. Sensitivity analysis of results has been carried out for the purpose of determination of the importance of particular parameters describing mathematical model for lateral displacement of analysed structures. Final results concerning maximum lateral top displacements of the structures obtained according to the new model have been compared with available full-scale data for steel and concrete chimneys. Maximum lateral top displacements have been also compared with results obtained according to procedures included in codes and standards. Moreover, additional aspects of vortex excitation are presented: the influence of corrosion of steel chimneys and the influence of feedbacks between vortex shedding and lateral vibrations on lateral response of analysed structures.

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