A Time Domain Identification Technique: The Oversized Eigenmatrix (OEM) Method

1985 ◽  
Vol 107 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Yongxin Yang
Keyword(s):  
Cantilever Beam ◽  
Time Domain ◽  
High Efficiency ◽  
Natural Frequencies ◽  
Math Model ◽  
Noise Effect ◽  
Domain Identification ◽  
Free Decay ◽  
Identification Technique ◽  
Noisy Conditions

A method of identifying natural frequencies and associated damping ratios of a structure from its free decay response is presented. The method is based on the Prony’s algorithm with which the idea of using an oversized math model as in ITD to reduce the noise effect is incorporated. Two approaches are proposed for use in distinguishing the true poles from the extraneous poles introduced by oversizing the eigenmatrix. The simulated experiments on a cantilever beam show high efficiency of the method in reducing the noise effect on the identification results under extremely noisy conditions.

A Frequency Domain Versus a Time Domain Identification Technique for Nonlinear Parameters Applied to Wire Rope Isolators

2000 ◽  
Vol 123 (4) ◽  
pp. 645-650 ◽  
Author(s):  
Gaetan Kerschen ◽  
Vincent Lenaerts ◽  
Stefano Marchesiello ◽  
Alessandro Fasana
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Nonlinear Dynamical Systems ◽  
Wire Rope ◽  
Restoring Force ◽  
Nonlinear Parameters ◽  
Nonlinear Dynamical ◽  
Domain Identification ◽  
Identification Technique ◽  
Reverse Path Method

The present paper aims to compare two techniques for identification of nonlinear dynamical systems. The Conditioned Reverse Path method, which is a frequency domain technique, is considered together with the Restoring Force Surface method, a time domain technique. Both methods are applied for experimental identification of wire rope isolators and the results are compared. Finally, drawbacks and advantages of each technique are underlined.

New time-domain identification technique

1987 ◽  
Vol 10 (3) ◽  
pp. 313-316 ◽  
Author(s):  
Fang-Bo Yeh ◽  
Ciann-Dong Yang
Keyword(s):  
Time Domain ◽  
Domain Identification ◽  
Identification Technique ◽  
New Time

Modal participation in multiple input Ibrahim time domain identification

2017 ◽  
Vol 24 (1) ◽  
pp. 168-180 ◽  
Author(s):  
Rune Brincker ◽  
Peter Olsen ◽  
Sandro Amador ◽  
Martin Juul ◽  
Abdollah Malekjafarian ◽  
...  
Keyword(s):  
Simulation Study ◽  
Time Domain ◽  
Toeplitz Matrices ◽  
Full Rank ◽  
Impulse Response Functions ◽  
System Matrix ◽  
Estimation Errors ◽  
Domain Identification ◽  
Multiple Input ◽  
Identification Technique

The Ibrahim time domain (ITD) identification technique was one of the first techniques formulated for multiple output modal analysis based on impulse response functions or general free decays. However, the technique has not been used much in recent decades due to the fact that the technique was originally formulated for single input systems that suffer from well-known problems in case of closely spaced modes. In this paper, a known, but more modern formulation of the ITD technique is discussed. In this formulation the technique becomes multiple input by adding some Toeplitz matrices over a set of free decays. It is shown that a special participation matrix can be defined that cancels out whenever the system matrix is estimated. The participation matrix becomes rank deficient if a mode is missing in the responses, but if any mode is present in one of the considered free decays, the participation matrix has full rank. This secures that all modes will be contained in the estimated system matrix. Finally, it is discussed how correlation functions estimated from the operational responses of structures can be used as free decays for the multiple-input ITD formulation, and the estimation errors of the identification technique are investigated in a simulation study with closely spaced modes. The simulation study shows that the multiple-input formulation provides estimates with significantly smaller errors on both mode shape and natural frequency estimates.

Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement

2007 ◽  
Vol 353-358 ◽  
pp. 2285-2288
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
Crack Size ◽  
Force Sensors ◽  
Rotational Spring ◽  
Cantilever Deflection ◽  
Crack Location ◽  
Small Force ◽  
Point Of Intersection

Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.

Experimental Identification Technique of Nonlinear Beams in Time Domain

1997 ◽  
Author(s):  
Kimihio Yasuda ◽  
Keisuke Kamiya
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Least Square Method ◽  
Least Square ◽  
Governing Equations ◽  
Experimental Identification ◽  
Initial Values ◽  
Nonlinear Beams ◽  
Identification Technique ◽  
The Time Domain

Abstract In previous papers the authors proposed a new experimental identification technique applicable to elastic structures. The proposed technique is based on the principle of harmonic balance, and can be classified as the frequency domain technique. The technique requires the excitation force to be periodic. This is in some cases a restriction. So another technique free from this restriction is of use. In this paper, as a first step for developing such techniques, a technique applicable to beams is proposed. The proposed technique can be classified as the time domain one. Two variations of the technique are proposed, depending on what methods are used for estimating the parameters of the governing equations. The first method is based on the usual least square method. The second is based on solving a minimization problem with constraints. The latter usually yields better results. But in this method, an iteration procedure is used, which requires initial values for the parameters. To determine the initial values, the first method can be used. So both methods are useful. Finally the applicability of the proposed technique is confirmed by numerical simulation and experiments.

Vibration of Triangular Cantilever Plates by the Ritz Method

1954 ◽  
Vol 21 (4) ◽  
pp. 365-370
Author(s):  
B. W. Andersen
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Plan View ◽  
Modes Of Vibration ◽  
Accuracy Of Results ◽  
Isosceles Triangles

Abstract Using the method published by Ritz in 1909, natural frequencies and corresponding node lines have been determined for two symmetric and two antisymmetric modes of vibration of isosceles triangular plates clamped at the base and having length-to-base ratios of 1, 2, 4, and 7 and for the two lowest modes of right triangular plates clamped along one leg and having ratios of the length of the free leg to that of the clamped one of 2, 4, and 7. A nonorthogonal co-ordinate system was used which gave constant limits of integration over the area of the triangle. The co-ordinate transformation made it necessary to modify the functions used by Ritz in approximating deflections and to consider cross products in the integration. The integration was done numerically, using tables compiled by Young and Felgar in 1949. To check the accuracy of results, a solution was obtained to the problem of a vibrating cantilever beam of uniform depth and triangular plan view. The results obtained were found to be consistent with those obtained for the plates by using an eight-term series to approximate the deflections of the symmetric plates (isosceles triangles) and a six-term series to approximate the deflections of the unsymmetric plates (right triangles).

The Modelling of the Opening and Closure of a Crack

1995 ◽  
Vol 117 (3A) ◽  
pp. 370-377 ◽  
Author(s):  
O. N. L. Abraham ◽  
J. A. Brandon
Keyword(s):  
Fourier Series ◽  
Cantilever Beam ◽  
Time Domain ◽  
Dry Friction ◽  
Transverse Crack ◽  
Normal Modes ◽  
Time Varying ◽  
Interaction Forces ◽  
Vibration Properties ◽  
Connection Matrices

The paper presents a method which utilizes substructure normal modes to predict the vibration properties of a cantilever beam with a breathing transverse crack. The two segments of the cantilever beam, separated by the crack, are related to one another by time varying connection matrices representing the interaction forces. The connection matrices are expanded in a Fourier series leading to a classical eigenvalue problem. Subsequently, the initial formulation is extended to avoid interference of the crack interfaces with a time domain formulation. The Lagrange multipliers, used to enforce the exact continuity constraints when the crack is closed, produce the interfaces forces needed for the modelling of interface dry friction.

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