STABILITY OF DAMPED COLUMNS ON A WINKLER FOUNDATION UNDER SUB-TANGENTIAL FOLLOWER FORCES

2013 ◽  
Vol 13 (02) ◽  
pp. 1350020 ◽  
Author(s):  
MOON-YOUNG KIM ◽  
JUN-SEOK LEE ◽  
MARIO M. ATTARD
Keyword(s):  
Dynamic Stability ◽  
Evaluation Method ◽  
Mass Matrix ◽  
Time History ◽  
Winkler Foundation ◽  
Nonconservative System ◽  
Axial Forces ◽  
Stiffness Matrices ◽  
Follower Forces ◽  
Hermitian Interpolation

This study examines the dynamic stability regions of damped columns on a Winkler foundation that are subjected to sub-tangentially distributed follower forces. A nondimensionalized equation of motion for the column subjected to linearly distributed follower forces is firstly derived based on the extended Hamilton's principle. A finite element procedure, using Hermitian interpolation functions, is employed to develop the mass matrix, Rayleigh damping matrix, Winkler foundation matrix, elastic and geometric stiffness matrices due to distributed axial forces, and a load correction stiffness matrix to account for sub-tangential follower forces. Subsequently, a time history analysis using the Newmark-β method and an evaluation method for the flutter and divergence loads of the nonconservative system are presented. Finally, the dynamic stability characteristics of the nonconservative system that display the jumping phenomenon in the second flutter load are explored through a parametric study. In particular, how the stable and unstable regions of the undamped and damped Leipholz columns translate with changes in the Winkler foundation stiffness is demonstrated and discussed.

scholarly journals Study on Seismic Coefficient Calculation Method of Slope Seismic Stability Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pai Lifang ◽  
Wu Honggang ◽  
Yang Tao ◽  
Zhong Feifei
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Failure Mode ◽  
Evaluation Method ◽  
Time History ◽  
Seismic Action ◽  
Landslide Stability ◽  
Seismic Coefficient ◽  
Average Maximum ◽  
History Of

In this paper, a pseudostatic seismic coefficient evaluation method for slope dynamic stability analysis was explored with Yushu Airport Road 3# landslide as a typical engineering case, and the shaking table test and numerical calculation were performed during the exploration. The loading waveform was selected as Yushu wave, and the acceleration time-history of seismic waves was measured and analyzed, revealing the failure mode of slopes. Based on the rigid-body limit equilibrium theory, the instantaneous additional seismic forces of each block and the time-history landslide stability coefficient were calculated. According to the time-history of the landslide, dynamic stability coefficients were calculated. Subsequently, we proposed a pseudostatic seismic coefficient evaluation method and discussed the seismic coefficient slope dynamic stability analysis. The results showed that as the vibration frequency rose, the average acceleration and the residual displacement of the slope decreased, but the slope grew more dynamically stable. With the proposed method, we calculated the period of slope seismic action to be 0.126 s and the average maximum acceleration to be 0.156 g, which was close to the designed ground motion acceleration of 0.15 g. Besides, we calculated the safety factor of landslides under earthquake to be 0.93∼0.97, which was close to that obtained from the building code method and in accordance with the present seismic deformation and failure mode of landslides. Moreover, the results obtained from the method of nuclear power plant specification were relatively small compared to other specification methods. The research is significant because it provides a new idea for the evaluation of seismic landslide stability in practical engineering.

Controversy Associated With the So-Called “Follower Forces”: Critical Overview

2005 ◽  
Vol 58 (2) ◽  
pp. 117-142 ◽  
Author(s):  
Isaac Elishakoff
Keyword(s):  
Dynamic Stability ◽  
Elastic Stability ◽  
Winkler Foundation ◽  
Static And Dynamic Stability ◽  
New Information ◽  
Experimental Side ◽  
Pipes Conveying Fluid ◽  
Follower Forces ◽  
Stability Of Structures ◽  
Critical Overview

This paper is inspired by two articles on the title subject, namely by Koiter and by Sugiyama, Langthjem and Ryu. The former warned the engineering community to beware of the above forces. The latter maintained that these forces are realistic. It is hoped that this review sheds some additional light on an issue that seems to perplex many students of dynamic stability. The paper does not contain any new information unknown to researchers; it represents a critical review of pertinent papers dedicated to the topic of dynamic stability of structures under so called “follower” forces. The attempt here is to present an account of the literature in a manner that is both objective and humble. This paper reviews both the theoretical and experimental contributions to the theory of nonconservative problems with a single objective in mind, to attempt to answer a nagging question “Is the model of the statically applied follower forces useful?,” that arose due to the papers by Koiter and Sugiyama, Langthjem and Ryu. This article explores the static and dynamic stability criteria as pertaining to the nonconservative problems; the experimental side of the problem; the results pertaining to Beck’s column placed on homogenous or inhomogeneous elastic foundations; and criticisms expressed in the literature about the result on the immunity of the instability load to the Winkler foundation modulus: The paper then discusses Koiter’s ideas on nonconservative instability problems, and attempts to provide insights on the abovementioned question. Special emphasis is placed on pipes conveying fluid with or without an elastic foundation. It then summarizes the literature on the “follower forces.” Such a summary is inevitably incomplete because of the huge literature accumulated so far on the nonconservative problems in the theory of elastic stability. There are 202 references cited in this review article, and a supplementary bibliography is provided.

scholarly journals The Krylov problem in the case of a beam on Vlasov inertial foundation

2018 ◽  
Vol 19 (6) ◽  
pp. 728-736
Author(s):  
Wacław Szcześniak ◽  
Magdalena Ataman
Keyword(s):  
Closed Form ◽  
Compressive Force ◽  
Elastic Beam ◽  
Forced Vibrations ◽  
Critical Force ◽  
Winkler Foundation ◽  
Static Deflection ◽  
Numerical Examples ◽  
Moving Force ◽  
Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

Development of an Evaluation Method for Seismic Isolation Systems of Nuclear Power Facilities: Part 2 — Application of CCFS Method to the Multiply Supported Systems

2014 ◽  
Author(s):  
Koichi Tai ◽  
Keisuke Sasajima ◽  
Shunsuke Fukushima ◽  
Noriyuki Takamura ◽  
Shigenobu Onishi
Keyword(s):  
Power Plant ◽  
Nuclear Power ◽  
Seismic Isolation ◽  
Evaluation Method ◽  
Time History ◽  
Piping System ◽  
History Analysis ◽  
Piping Systems ◽  
Isolation Systems ◽  
Seismic Isolation Systems

This paper provides a part of series of “Development of an Evaluation Method for Seismic Isolation Systems of Nuclear Power Facilities”. Paper is focused on the seismic evaluation method of the multiply supported systems, as the one of the design methodology adopted in the equipment and piping system of the seismic isolated nuclear power plant in Japan. Many of the piping systems are multiply supported over different floor levels in the reactor building, and some of the piping systems are carried over to the adjacent building. Although Independent Support Motion (ISM) method has been widely applied in such a multiply supported seismic design of nuclear power plant, it is noted that the shortcoming of ignoring correlations between each excitations is frequently misleaded to the over-estimated design. Application of Cross-oscillator, Cross-Floor response Spectrum (CCFS) method, proposed by A. Asfura and A. D. Kiureghian[1] shall be considered to be the excellent solution to the problems as mentioned above. So, we have introduced the algorithm of CCFS method to the FEM program. The seismic responses of the benchmark model of multiply supported piping system are evaluated under various combination methods of ISM and CCFS, comparing to the exact solutions of Time History analysis method. As the result, it is demonstrated that the CCFS method shows excellent agreement to the responses of Time History analysis, and the CCFS method shall be one of the effective and practical design method of multiply supported systems.

A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Confirmation of Reduction Effect Due to Tank’s Rocking Behavior and Proposal for a Simplified Evaluation Method of Nonlinear Seismic Response

2003 ◽  
Author(s):  
Satoru Yamaguchi ◽  
Hideyuki Tazuke ◽  
Kazuo Ishida
Keyword(s):  
Nonlinear Analysis ◽  
Seismic Response ◽  
Evaluation Method ◽  
Time History ◽  
Bottom Plate ◽  
Response Factor ◽  
Mass System ◽  
Nonlinear Seismic Response ◽  
Reduction Effect ◽  
Rocking Behavior

Aboveground LNG storage tank consists of inner and outer cylindrical containers. LNG is stored in the inner container made by 9%Ni steel. Anchorages are attached to some tanks in order to prevent bottom plate from excessive uplifting by seismic overturning moment. However tanks without anchorages have some probability that the seismic response factor decreases since the resonance period of tank is lengthened by nonlinear behaviors, for example uplifting of bottom plate (rocking behavior). In this paper, the reduction effect of response factor due to rocking behavior was quantitatively confirmed by 3-dimensional FEM nonlinear analysis and time-history nonlinear analysis that was modeled with single-degree-of-freedom spring-mass system. And a simplified evaluation method that allows easily calculating the reduction effect was proposed. As the result of study, it was proved that this method gave valid and conservative results.

scholarly journals Study on the Applicability of Dynamic Stability Evaluation Criteria by Comparison of Trackside Measurement Results of Different Track Structures

2020 ◽  
Vol 10 (22) ◽  
pp. 8245
Author(s):  
Kyuhwan Oh ◽  
Jaeik Lee ◽  
Junhyeok Choi ◽  
Yonggul Park
Keyword(s):  
Dynamic Stability ◽  
Evaluation Method ◽  
Evaluation Criteria ◽  
Railway Track ◽  
Stability Evaluation ◽  
Design Specification ◽  
Wheel Load ◽  
Field Instrumentation ◽  
Load Fluctuation ◽  
Concrete Type

Countries such as Korea adopt design codes, evaluation criteria and specifications from standards originating abroad; this leads to a lack of distinction of the separate applications of dynamic stability evaluation parameters between various track structures of different track moduli. This paper discusses the applicability of the dynamic stability evaluation method of railway track structures by assessing 10 different types of railway track sections of a newly constructed railway operation line (5 ballasted and 5 concrete type track structures) by field instrumentation testing. Parameters of track support stiffness (TSS), wheel load fluctuation, derailment coefficient, and rail displacement are measured. The respective results are first compared to the standard criteria (design specification) and comparisons between the different track types are presented as ratios. Findings show that while all of the tracks satisfy the design specification requirements, each track type measurement result varies by a noticeable degree, particularly when comparing between concrete and ballast type track structures. Results of the study demonstrate that using the same dynamic stability evaluation criteria can lead to an incorrect assessment of the track performance evaluation of track structure, and a separate evaluation parameter for ballasted and concrete track structures is required.

Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid?

2000 ◽  
Vol 68 (2) ◽  
pp. 206-212 ◽  
Author(s):  
I. Elishakoff ◽  
N. Impollonia
Keyword(s):  
Critical Velocity ◽  
Entire Length ◽  
Velocity Versus ◽  
Winkler Foundation ◽  
Strengthening Effect ◽  
Pipe Conveying Fluid ◽  
Follower Forces ◽  
The Stability ◽  
Realistic Structure ◽  
Conveying Fluid

The effect of the elastic Winkler and rotatory foundations on the stability of a pipe conveying fluid is investigated in this paper. Both elastic foundations are partially attached to the pipe. It turns out that the single foundation, either translational or rotatory, which is attached to the pipe along its entire length, increases the critical velocity. Such an intuitively anticipated strengthening effect is surprisingly missing for the elastic column on Winkler foundation subjected to the so-called statically applied follower forces. Yet, partial foundation for the pipe conveying fluid is associated with a nonmonotonous dependence of the critical velocity versus the attachment ratio defined as the length of the partial foundation over the entire length of the pipe. It is concluded that such a paradoxical nonmonotonicity is shared by both the realistic structure (pipe conveying fluid) and in the “imagined system,” to use the terminology of Herrmann pertaining to the column under to follower forces.

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