• Wind and Structures
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• v.16 no.2
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• pp.157-178
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• 2013

Output-only modal parameter identification is based on the assumption that external forces on a linear structure are white noise. However, harmonic excitations are also often present in real structural vibrations. In particular, it has been realized that the use of forced acceleration responses without knowledge of external forces can pose a problem in the modal parameter identification, because an external force is imparted to its impulse acceleration response function. This paper provides a three-stage identification procedure as a solution to the problem of harmonic and white noise excitations in the acceleration responses of a linear dynamic system. This procedure combines the uses of the mode indicator function, the complex mode indication function, the enhanced frequency response function, an iterative rational fraction polynomial method and mode shape inspection for the correlation-related functions of the force-embedded acceleration responses. The procedure is verified via numerical simulation of a five-floor shear building and a two-dimensional frame and also applied to ambient vibration data of a large-span roof structure. Results show that the modal parameters of these dynamic systems can be satisfactorily identified under the requirement of wide separation between vibration modes and harmonic excitations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.5
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• pp.833-839
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• 2003

The effects of stiffeners on the modal characteristics of rectangular plates are investigated. A modeling method for the modal analysis of rectangular plates with stiffeners is presented. A mass density Dirac's delta function is used to idealize the stiffeners mathematically. The equations of motion for the plates are derived and transformed into a dimensionless form. To confirm the accuracy of the method presented in this study, numerical result are obtained and compared to those of a commercial program. The mode shape variations due to some parameter variations are also exhibited.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.601-606
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• 1993

The natural frequency measurement of passenger car tire under the load and rotation are studied. In order to obtain theoretical natural frequency and mode shape, the plane vibration of a tire is modeled to that of circular beam. By using the Tickling method based on Hamilton's principle, theoretical results are determined by considering tension force due to tire inflation pressure, rotational velocity and tangential, radial stiffness. Modal parameters varying the inflation pressure, load, rotational velocity are determined experimentally by using frequency response function method. The results show that experimental conditions are parameter for shifting of natural frequency.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.1-13
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• 1996

The measurement of radial directional natural frequency ina passenger car tire rotating under the load is studied. In order to obtain theoretical matural frequency and mode shape, the ploane vibration of a tire is modeled to that of circular beam. By esing the Tieking method based on Hamiltons's principle, theoretical results are determined by considering tension horce due to tire inflation pressure, retational velocity and tangential, radial stiffness. Radial directional modal parameters varying with the inflation pressure, load, rotational velocity are experimentally determined by using frequency response function method. The results show that experimental conditions canbe considered as the parameters which shift the natural frequency.

• Journal of KSNVE
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• v.7 no.6
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• pp.1049-1058
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• 1997

To verify the Finite Element Method(FEM) model of an Exhaust System, Frequency Response Function(FRF) is utilized. Up to now, generally, comparisons of natural frequencies and mode shapes of the Exhaust System between numerical analysis and experimental results are adopted to prove completion of the FEM model. However, the comparisons of natural frequencies and mode shapes are not sufficient to have the perfect FEM model of the Exhaust system. Instead of these comparisons. FRF method is introduced for the more accurate FEM model.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.29 no.1
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• pp.39-55
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• 1993

Modal Analysis is the process of characterizing the dynamic properties of an elastic structure by identifying its modes of vibration. A mode of vibration is a global property of an elastic structure. That is, a mode has a specific natural frequency and damping factor which can be identified from response data at practically any point on a structure, and it has a characteristic mode shape which identifies the mode spatially over the entire structure. Modal testing is able to be performed on structural and mechanical structure in an effort to learn more about their elastic behavior. Once the dynamic properties of a structure are known its behavior can be predicted and therefore controlled or corrected. Resonant frequencies, damping factors and mode shape data can be used directly by a mechanical designer to pin point weak spots in a structure design, or this data can also be used to confirm or synthesize equations of motion for the elastic structure. These differential equations can be used to simulate structural response to know input forces and to examine the effects of pertubations in the distributed mass, stiffness and damping properties of the structure in more detail. In this paper the measurement of transfer functions in digital form, and the application of digital parameter identification techniques to identify modal parameters from the measured transfer function data are discussed. It is first shown that the transfer matrix, which is a complete dynamic model of an elastic plate structure can be written in terms of the structural modes of vibration. This special mathematical form allows one to identify the complete dynamics of the structure from a much reduced set of test data, and is the essence of the modal approach to identifying the dynamics of a structure. Finally, the application of transfer function models and identification techniques for obtaining modal parameters from the transfer function data are discussed. Characteristics on vibration response of elastic plate structure obtained from the dynamic analysis by Finite Element Method are compared with results of modal analysis.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.3
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• pp.450-466
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• 2017

This paper defines the modified effective membrane stiffness, bending stiffness considering the directionally dependent mechanical properties and mode shape function of a composite lattice rectangular plate, which is assumed to be a Kirchhoff-Love plate. It subsequently presents an approximate method of conducting a buckling analysis of the composite lattice rectangular plate with various boundary conditions under uniform compression using the Ritz method. This method considers the coupled buckling mode as well as the global and local buckling modes. The validity of the present method is verified by comparing the results of the finite element analysis. In addition, this paper performs a parametric analysis to investigate the effects of the design parameters on the critical load and buckling mode shape of the composite lattice rectangular plate based on the present method. The results allow a database to be obtained on the buckling characteristics of composite lattice rectangular plates. Consequently, it is concluded that the present method which facilitates the calculation of the critical load and buckling mode shape according to the design parameters as well as the parametric analysis are very useful not only because of their structural design but also because of the buckling analysis of composite lattice structures.

• Smart Structures and Systems
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• v.4 no.3
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• pp.343-365
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• 2008

In this study, the frequency domain method which utilizes the evaluation of changes in the structural mode shape is adopted to identify regions which contain localized damages. Frequency response function (FRF) values corresponding to the modal frequency, analogous to the mode shape coefficients, are used since change in natural frequency of the system is usually insignificant for localized damage. This method requires only few sensors to obtain the dynamic response of the structure at specific locations to determine the FRF via fast-Fourier transform (FFT). Numerical examples of an aluminum plate, which includes damages of varying severity, locations and combinations of multiple locations, are presented to demonstrate the feasibility of the method. An experimental verification of the method is also done using an aluminum plate with two different degrees of damage, namely a half-through notch and a through notch. The inconsistency in attaining the FRF values for practical applications due to varying impact load may be overcome via statistical averaging, although large variations in the loading in terms of the contact duration should still be avoided. Nonetheless, this method needs special attention when the damages induce notable changes in the modal frequency, such as when the damages are of high severity or cover more extensive area or near the boundary where the support condition is modified. This is largely due to the significant decrease in the frequency term compared to the increase in the vibration amplitude. For practical reasons such as the use of limited number of sensors and to facilitate automation, extending the resolution of this method of identification may not be efficient. Hence, methods based on wave propagation can be employed as a complement on the isolated region to provide an accurate localization as well as to trace the geometry of the damage.

• Smart Structures and Systems
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• v.31 no.5
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• pp.485-500
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• 2023

Machine learning-based structural health monitoring (ML-based SHM) methods are researched extensively in the recent decade due to the availability of advanced information and sensing technology. ML methods are well-known for their pattern recognition capability for complex problems. However, the main obstacle of ML-based SHM is that it often requires pre-collected historical data for model training. In most actual scenarios, damage presence can be detected using the unsupervised learning method through anomaly detection, but to further identify the damage types would require prior knowledge or historical events as references. This creates the cold-start problem, especially for new and unobserved structures. Modal-based methods identify damages based on the changes in the structural global properties but often require dense measurements for accurate results. Therefore, a two-stage hybrid modal-machine learning damage detection scheme is proposed. The first stage detects damage presence using Principal Component Analysis-Frequency Response Function (PCA-FRF) in an unsupervised manner, whereas the second stage further identifies the damage. To solve the cold-start problem, mode shape assessment using the first mode is initiated when no trained model is available yet in the second stage. The damage identified by the modal-based method would be stored for future training. This work highlights the performance of the scheme in alleviating the cold-start issue as it transitions through different phases, starting from zero damage sample available. Results showed that single and multiple damages can be identified at an acceptable accuracy level even when training samples are limited.

• Journal of KSNVE
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• v.10 no.2
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• pp.312-318
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• 2000

A modeling method for the vibration analysis of rotating cantilever plastes with stiffeners is presented. The equations of motion for the plates aer derived and trnasformed into a dimensionless form. A mass density Dirac's delta function is used to idealize the stiffener mathematically. The effects of stiffeners on the model characteristics of the plate are investigated, and mode shape variations due to some parameter variation are exhibited. It is found that veering phenomena occur between some loci and associated mode shapes change significantly during the veering phenomena.