Identification of Pressure-Dependent Modal Properties of Non-Linear Brake Pads by Using Scalable Dirac Impulse

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.

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Non-Linear Sensitivity Analysis of Mechanical Structures Using Modal Data

Proceedings of the Institution of Mechanical Engineers Part C Mechanical Engineering Science ◽

10.1243/pime_proc_1991_205_092_02 ◽

1991 ◽

Vol 205 (1) ◽

pp. 67-75 ◽

Cited By ~ 7

Author(s):

W M To ◽

D J Ewins

Keyword(s):

Sensitivity Analysis ◽

Measurement Errors ◽

Structural Modification ◽

Element Model ◽

Rayleigh Quotient ◽

Second Order ◽

Frame Structure ◽

Original Structure ◽

Modal Properties ◽

Non Linear

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.

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

Nonlinear Structures & Systems, Volume 1 - Conference Proceedings of the Society for Experimental Mechanics Series ◽

10.1007/978-3-030-47626-7_41 ◽

2020 ◽

pp. 287-290

Author(s):

Nidish Narayanaa Balaji ◽

Matthew R. W. Brake

Keyword(s):

Modal Properties ◽

Non Linear ◽

Static Approach ◽

Prestressed Structures

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Non-linear modal properties of non-shallow cables

International Journal of Non-Linear Mechanics ◽

10.1016/j.ijnonlinmec.2007.02.013 ◽

2007 ◽

Vol 42 (3) ◽

pp. 542-554 ◽

Cited By ~ 35

Author(s):

Walter Lacarbonara ◽

Achille Paolone ◽

Fabrizio Vestroni

Keyword(s):

Modal Properties ◽

Non Linear

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(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.)

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