An Efficient Coupled Modal Quasi-static Approach for Characterizing Non-linear Modal Properties of Prestressed Structures

Author(s):  
Nidish Narayanaa Balaji ◽  
Matthew R. W. Brake
Author(s):  
Liang Xu ◽  
Yi Hui ◽  
Ke Li

This study proposes an approach to set up a continuum full bridge model with spatially inclined cables based on the Hamilton principle. The dynamic governing functions, considering the geometric non-linearities of cables and deck, represent simultaneously the vertical motion of deck and vertical–horizontal motion of cable. With the comparison of the modal properties obtained from the model to those from the accurate model, results show that the proposed model is capable of accurately simulating the modal properties. The primary resonance responses and corresponding frequency-response curves are obtained through the multiple-scale-method. A finite element (FE) model is established, and the corresponding non-linear dynamic analysis in time domain is conducted. Comparing the results from two models, it can be checked that the proposed model is reliable. According to the results of the proposed model, it is found that the second-order shape functions (SOSFs) play a significant role in the system response. Once the non-linear vibration of the bridge becomes significant only considering the excited mode with using the classical Galerkin decomposition cannot correctly predict the structure response. The SOSFs can be classified into stationary and vibrating components. The vibrating component can deviate the time-series of response from the harmonic wave, and the stationary component directly determines the mean value of the time-series.


Author(s):  
Pietro Croce ◽  
Maria Luisa Beconcini ◽  
Paolo Formichi ◽  
Filippo Landi ◽  
Benedetta Puccini ◽  
...  

<p>Masonry structures represent a large part of existing buildings. As confirmed by the damage caused by recent seismic events, the assessment of seismic performance of existing masonry building is then a critical issue in Countries exposed to seismic risk. Moreover, common methods of analysis based on non-linear static approach are significantly influenced by the assumptions about the shear behavior of masonry walls and may lead to inconsistent or contradictory results.</p><p>Due to the relevance of the problem ad hoc studies have been performed to clarify how the most relevant parameters affect the theoretical structural behavior and to setup a proper method to define these parameters.</p><p>In the paper, the main sources of uncertainties regarding the definition of material parameters are investigated and a methodology for the identification of masonry classes is illustrated discussing the propagation of uncertainties related to masonry parameters in non-linear static analysis of masonry buildings. The analysis are carried out through a simplified non-linear pushover type algorithm developed by the authors and the outcomes are illustrated and critically discussed for a relevant case study.</p><p>The results show the capability of the proposed procedure for the identification of masonry classes and the evaluation of masonry mechanical parameters to provide a more refined probabilistic assessment of the seismic risk index.</p>


Author(s):  
W M To ◽  
D J Ewins

This paper presents a new procedure for determining the revised modal properties (eigenvalues and mass-normalized eigenvectors) in a structural modification analysis. The procedure is based on expressing the eigenvectors of the modified structure as a linear combination of the eigenvectors of the original structure and employs the stationary property of the Rayleigh quotient to determine the modified structure's eigenvalues. It has the same theoretical basis as first- and second-order sensitivity analysis, but here the non-linear effects contributed by all high-order terms [generally assumed to be small relative to the effect contributed by first- and second-order terms (1–6)] are preserved in full. Hence, the usual shortcoming of sensitivity analysis—that it is limited to small modifications—is overcome. A special feature of this procedure is that the exact modal properties of the modified structure are determined without solving the generalized eigenvalue problem for the modified structure. Thus, this procedure can greatly reduce the computation cost and increase the efficiency of structural modification analysis (or reanalysis) during a structural optimization process. Numerical examples demonstrate the superconvergence characteristic of the technique. The limitations caused by modal and coordinate incompleteness, and the sensitivity of this technique with respect to simulated measurement errors, are investigated by using a finite element model of a steel frame structure and a ten-degrees-of-freedom mass-spring model.


Author(s):  
Shashishekar Shivaswamy ◽  
Jianmin Li ◽  
Hamid M. Lankarani

Abstract Impact calculations suffer from several practical limitations which limit their application to establishing the approximate magnitude of the various phenomena involved. The transient force deformation response of a body subjected to impact can be explained accurately using stress wave propagation theory. As this approach is very complicated, a simpler quasi-static approach with non-linear force deformation Hertz relations can be employed for impact analysis. However, these relations can not explain the energy absorption and permanent deformations encountered during the impact. This necessitates independent non-linear force-deformation relations for compression and restitution phases of impact. In the present paper, impact tests conducted on Aluminum and Steel plates have been reported. The impact response of the system was compared with the various theoretical quasi-static force models. Considering the assumptions made in the quasi-static force models, the experimental results matched very well with the theoretical results. Non-linear force-deformation model with independent relations for compression and restitution phases was found to be the best approach to analyze impact problems. The value of the index in the non-linear force-deformation relations was found to be approximately 1.71 and 1.78 for Aluminum and Steel respectively. The values of impact parameters for a given material were found to depend on impact velocity.


2021 ◽  
Vol 906 (1) ◽  
pp. 012093
Author(s):  
Alberto Bolla ◽  
Paolo Paronuzzi

Abstract In the present work, a seismic analysis was performed in advance on a limestone rock slope (height = 150 m) outcropping along the Tagliamento River valley, in the Friuli Venezia Giulia Region, north-eastern Italy. The analysed slope is characterised by strong rock mass damage, thus resulting in a critical stability condition (unstable volume = 110,000–200,000 m3). The seismic analysis was performed adopting the 2D finite difference method (FDM) and employing both a pseudo-static approach and a non-linear dynamic approach. Model outcomes demonstrate that the seismic motion induces internal, localised ruptures within the rock mass. Some important differences in the mechanical behaviour of the rock slope were highlighted, depending on the specific modelling approach assumed. When adopting a pseudo-static approach, the slope failure occurs for PGA values ranging between 0.056 g and 0.124 g, depending on the different initial static stability condition assumed for the slope (Strength Reduction Factor SRF = 1.00–1.15). According to the non-linear dynamic approach, the slope failure is achieved for PGA values varying between 0.056 g and 0.213 g. Pre-collapse slope displacements calculated with the pseudo-static approach (12–15 cm) are much more greater than those obtained through the non-linear dynamic approach (0.5–3 mm). The modelling results obtained through the non-linear dynamic analysis also testify that the seismic topographic amplification is 1.5 times the target acceleration at the slope face and 2.5 times the target acceleration at the slope toe.


2007 ◽  
Vol 42 (3) ◽  
pp. 542-554 ◽  
Author(s):  
Walter Lacarbonara ◽  
Achille Paolone ◽  
Fabrizio Vestroni
Keyword(s):  

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

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