A New Methodology for the Accurate and Consistent Identification of Modal Parameters Using Multi-FRF Analysis

1995 ◽  
Author(s):  
R. M. Lin ◽  
S.-F. Ling
Keyword(s):  
Eigenvalue Problem ◽  
Loss Factor ◽  
Frequency Response Function ◽  
Natural Frequencies ◽  
Identification Problem ◽  
Modal Parameters ◽  
Frequency Range ◽  
Case Examples ◽  
Measured Frequency Response ◽  
Damping Loss Factor

Abstract A new method for the estimation of modal parameters is presented in this paper. Unlike the majority of the existing methods which involve complicated curve fitting and interpolative procedures, the proposed method calculates the modal parameters by solving eigenvalue problem of an equivalent eigensystem derived from measured frequency response function (FRF) data. It is developed based on the practical assumption that only one incomplete column of the FRF matrix of the test structure has been measured in a frequency range of interest. All the measured FRFs are used simultaneously to construct the equivalent eigensystem matrices from which natural frequencies, damping loss factor and modeshape vectors of interest can be directly solved. Since the identification problem is reduced to an eigenvalue problem of an equivalent system, natural frequencies and damping loss factors identified are consistent. Further procedures for normalizing the identified eigenvectors so that they become mass-normalized are developed. Numerical case examples are given to demonstrate the practicality of the proposed method and results obtained are indeed very promising. It is believed that with the availability of such identification method, modal analysts’ dream of intelligent and full automatic modal analysis will become a reality.

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

scholarly journals A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1996 ◽  
Author(s):  
Ming-Ta Yang ◽  
Jerry H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

scholarly journals Damping Determination by Half-Power Bandwidth Method for a Slightly Damped Rectangular Steel Plate in the Mid-Frequency Range

2020 ◽  
Vol 13 (3) ◽  
pp. 177-196
Author(s):  
Marcell Ferenc Treszkai ◽  
David Sipos ◽  
Daniel Feszty
Keyword(s):  
Loss Factor ◽  
Steel Plate ◽  
Sampling Frequency ◽  
Test Case ◽  
Response Functions ◽  
Frequency Range ◽  
Damping Loss Factor ◽  
Simulation Results ◽  
Db Difference ◽  
Half Power

This paper presents a novel methodology for measuring the Damping Loss Factor (DLF) of a slightly damped plate in the mid-frequency range (400-1000 Hz) by the Half Power Bandwidth Method (HPBM). A steel flat plate of 650 x 550 x 2 mm was considered as the test case, which was excited by both a shaker and an impact hammer to quantify the effect of the excitation type for slightly damped plate. Since the HPBM is based on extracting the damping data from the modal resonance peaks, working with the correct Frequency Response Functions (FRF) was found to be a crucial factor. Therefore, the effects of coherence and resolution of the sampling frequency were examined in detail in the measurements. The obtained DLF results were statistically analysed and then applied in SEA simulations. Comparison of the simulation and experimental results showed that the method of extracting the DLF data from the measurements can have as much as 10 dB influence on the simulation results. The best results, with only 2 dB difference between measurement and simulation, were obtained when the statistical expected value of the data was used as the input in the SEA simulations.

Damping Loss Factor Estimation for Test-Based Vehicle SEA Modeling

2001 ◽  
Author(s):  
Jae-Hak Woo ◽  
Xiandi Zeng
Keyword(s):  
Loss Factor ◽  
Bias Error ◽  
Reverberation Time ◽  
Frequency Range ◽  
Air Cavity ◽  
Damping Loss Factor ◽  
Factor Estimation

Abstract In the test-based SEA models, the major parameters are measured or estimated from measured quantities. One of the parameters is Damping Loss Factor (DLF) of the air (passenger) cavity of a vehicle. In the SEA model, the air cavity is divided into several sub-cavities. The required DLF for each sub-cavity can be calculated from the reverberation time (T60) measured in that sub-cavity in the vehicle. However, if nothing is done to separate one sub-cavity from other sub-cavities in the T60 measurement in the vehicle, the measured T60 for that sub-cavity is the T60 of the whole air cavity. When the resulted DLF is used in SEA model of that sub-cavity, it is the DLF of the whole air cavity that is used for a sub-cavity, which will result in an over/under-damped. Thus, the prediction from such a SEA model will have bias error especially in the higher frequency range. This has been seen in the results of a vehicle SEA model. In this paper, a method is proposed to estimate the DLF of each sub-cavity based on the T60 of the whole air cavity. When these estimated DLF’s are used in the SEA model for each sub-cavity, the correlation in SEA model was improved by 2.5∼3 dB above 1kHz.

scholarly journals Aspects of Strength Testing of Tank Containers in Compliance with the Requirements of the UN Navigation Rules and Regulations

2021 ◽  
Vol 9 (3) ◽  
pp. 349
Author(s):  
Andrii Sulym ◽  
Pavlo Khozia ◽  
Eduard Tretiak ◽  
Václav Píštěk ◽  
Oleksij Fomin ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Response Spectrum ◽  
Experimental Curve ◽  
Bulk Liquid ◽  
Frequency Range ◽  
Test Configuration ◽  
Shock Response ◽  
Shock Response Spectrum ◽  
Spectrum Curve ◽  
The Impact

This article deals with the method of computer-aided studies of the results of tank container impact tests to confirm the ability of portable tanks and multi-element gas containers to withstand the impact in the longitudinal direction on a specially equipped test rig or using a railway flat car by impacting a flat car with a striking car, in compliance with the requirements of the UN Navigation Rules and Regulations. It is shown that the main assessed characteristic of the UN requirements is the spectrum of the shock response (accelerations) for the interval natural frequencies of the shock pulse. The calculation of the points of the shock response spectrum curve based on the test results is reproduced in four stages. A test configuration of the impact testing of the railway flat car with a tank container is presented, and the impact is performed in such a way that, under a single impact, the shock spectrum curve obtained during the tests for both fittings subjected to impact repeats or exceeds the minimum shock spectrum curve for all frequencies in the range of 2 Hz to 100 Hz. Formulas for determining the relative displacements and accelerations for the interval natural frequencies of the shock wave are given. The research results are presented in graphical form, indicating that the experimental values of the shock response spectrum exceed the minimum permissible values; the equation of the experimental curve of the shock response spectrum in the frequency range 0–100 Hz is described by power-law dependence. The coefficients of the equation were determined by the statistical method of maximum likelihood with the determination factor being 0.897, which is a satisfactory value; a comparative analysis showed that the experimental curve of the impact response spectrum in the frequency range 0–100 Hz exceeds the normalized curve, which confirms compliance with regulatory requirements. A new test configuration is proposed using a tank car with a bulk liquid, the processes in which upon impact differ significantly from other freight wagons under longitudinal impact loads of the tank container. The hydraulic impact resulting from the impact on the tank container and the platform creates an overturning moment that causes the rear fittings to be unloaded.

scholarly journals Detection and localization of multiple small damages in beam

2021 ◽  
Vol 13 (1) ◽  
pp. 168781402098732
Author(s):  
Ayisha Nayyar ◽  
Ummul Baneen ◽  
Syed Abbas Zilqurnain Naqvi ◽  
Muhammad Ahsan
Keyword(s):  
Frequency Response ◽  
Natural Frequencies ◽  
Signal To Noise Ratio ◽  
Moving Average ◽  
A Priori ◽  
Damage Index ◽  
High Signal ◽  
Frequency Range ◽  
Spatial Locality ◽  
System Frequency

Localizing small damages often requires sensors be mounted in the proximity of damage to obtain high Signal-to-Noise Ratio in system frequency response to input excitation. The proximity requirement limits the applicability of existing schemes for low-severity damage detection as an estimate of damage location may not be known  a priori. In this work it is shown that spatial locality is not a fundamental impediment; multiple small damages can still be detected with high accuracy provided that the frequency range beyond the first five natural frequencies is utilized in the Frequency response functions (FRF) curvature method. The proposed method presented in this paper applies sensitivity analysis to systematically unearth frequency ranges capable of elevating damage index peak at correct damage locations. It is a baseline-free method that employs a smoothing polynomial to emulate reference curvatures for the undamaged structure. Numerical simulation of steel-beam shows that small multiple damages of severity as low as 5% can be reliably detected by including frequency range covering 5–10th natural frequencies. The efficacy of the scheme is also experimentally validated for the same beam. It is also found that a simple noise filtration scheme such as a Gaussian moving average filter can adequately remove false peaks from the damage index profile.

SIMP for Complex Structures

2016 ◽  
Vol 846 ◽  
pp. 535-540
Author(s):  
David J. Munk ◽  
David W. Boyd ◽  
Gareth A. Vio
Keyword(s):  
Natural Frequencies ◽  
Dynamic Loads ◽  
Topology Optimisation ◽  
Complex Structures ◽  
Structural Failure ◽  
Frequency Range ◽  
Aerodynamic Loading ◽  
Frequency Excitation ◽  
Wing Structure ◽  
Lifting Surfaces

Designing structures with frequency constraints is an important task in aerospace engineering. Aerodynamic loading, gust loading, and engine vibrations all impart dynamic loads upon an airframe. To avoid structural resonance and excessive vibration, the natural frequencies of the structure must be shifted away from the frequency range of any dynamic loads. Care must also be taken to ensure that the modal frequencies of a structure do not coalesce, which can lead to dramatic structural failure. So far in industry, no aircraft lifting surfaces are designed from the ground up with frequency optimisation as the primary goal. This paper will explore computational methods for achieving this task.This paper will present a topology optimisation algorithm employing the Solid Isotropic Microstructure with Penalisation (SIMP) method for the design of an optimal aircraft wing structure for rejection of frequency excitation.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

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