Optimal configuration of shakers for phase resonance testing using modal parameters

Author(s):  
Wei Chen ◽  
Mengshi Jin ◽  
Hanwen Song

The phase resonance testing is widely used in the ground vibration test for aircraft due to the advantages of distinguishing closely spaced modes and directly comparing normal mode shapes with those from finite element model. However, the process to configure the shakers is time-consuming. A method to configure the shakers, which calculates the appropriate force vector and estimates the optimal combination of excitation locations for phase resonance testing, is proposed in this paper. Compared with other configuration methods, where the frequency response function matrix is known a priori, the proposed method only requires a priori information of rough modal parameters. Therefore, less information is used in this method, which leads to the advantage of calculating the optimal configuration more efficiently. In this method, the modal force amplitude ratio of the target mode to all the modes, called the modal ratio indicator, is set up as the criterion to select the optimal configuration. Simulations of a discrete plate are performed to show the process of the method. An experiment of a steel beam is conducted to validate the effectiveness and reliability of this method.

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Chan-gi Pak

A simple and efficient approach for tuning finite element models to match computed frequencies, mode shapes, and mass properties to the experimental data is introduced in this study. The model tuning procedure proposed in this study is based on a series of optimizations. This approach has been successfully applied to create an equivalent beam finite element model for the X-37 drogue chute test fixture with the X-planes pylon. The goal was a simple model capable of being analyzed in a captive carry configuration with the B-52H mother ship. This study has shown that natural frequencies, corresponding mode shapes, and mass properties from the updated finite element model achieved at the final optimization iteration have excellent agreement with corresponding measured data.


Author(s):  
M. Richmond ◽  
S. Siedler ◽  
M. Häckell ◽  
U. Smolka ◽  
A. Kolios

Abstract The modal parameters extracted from a structure by accelerometers can be used for damage assessment as well as model updating. To extract modal parameters from a structure, it is important to place accelerometers at locations with high modal displacements. Sensor placement can be restricted by practical considerations, and installation might be conducted more based on engineering judgement rather than analysis. This leads to the question of how important the optimal sensor placement is, and if fewer sensors suffice to extract the modal parameters. In this work, an offshore wind substation (OSS) from the Wikinger offshore wind farm (owned by Iberdrola) is instrumented with 12, 3-axis accelerometers. This sensor setup consists of 6 sensors in a permanent campaign where sensors were placed based purely on engineering judgement, as well as 6 sensors in a temporary campaign, placed based on a placement analysis. An optimal sensor placement study was conducted using a finite element model of the structure in the software package FEMtools, resulting in optimal layouts. The temporary campaign sensors were placed such that they, in combination with the permanent campaign, can be used to complete the proposed layouts. Samples for each setup are processed using the software ARTeMIS modal to extract the mode shapes and natural frequencies through the Stochastic Subspace Identification (SSI) technique. The frequencies found by this approach are then clustered together using a k-means algorithm for a comparison within clusters. The modal assurance criterion (MAC) values are calculated for each result and compared to the finite element model from which the optimal sensor placement study was conducted. This is to match mode shapes between the two and thus determine the importance of off diagonal MAC elements in the sensor optimization process. MAC values are also calculated relative to a cluster-averaged set of eigenvectors to determine how they vary over the 1.5 months. The results show that for all sensor layouts, the three lower frequency modes are consistently identified. The most optimized sensor layout, consisting of only 3 sensors, was able to distinguish an additional, higher frequency mode which was never identified in the 6-sensor permanent layout. However, the reduced sensor layout shows slightly more scatter in the results than the 6-sensor layout. There is a higher signal to noise ratio in the temporary campaign which results in scatter. We conclude that with an optimized placement of accelerometers, more modes can be identified and distinguished. However, off diagonal elements in the original MAC matrix, as well as loss of sensor degrees of freedom, can result in additional scatter in the measurements. Some of these findings can be extended to other offshore jacket structures, such as those of wind turbines, in that it gives a better understanding of the consequence of an optimal sensor placement study.


Author(s):  
Loukas Papadopoulos ◽  
Ephrahim Garcia

Abstract A method is proposed for probabilistically model updating an initial deterministic finite element model using measured statistical changes in natural frequencies and mode shapes (i.e., modal parameters). The approach accounts for variations in the modal properties of a structure (due to experimental errors in the test procedure). A perturbation of the eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix. This stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix. Monte Carlo simulations, in conjunction with the variations of the structural modal parameters, are used to determine the variations of the stiffness reduction factors. These values will subsequently be used to estimate statistics for the corrected stiffness parameters. The effectiveness of the proposed technique is illustrated using simulated data on an aluminum cantilever Euler-Bernoulli beam.


2006 ◽  
Vol 129 (1) ◽  
pp. 121-127
Author(s):  
Daniel C. Kammer ◽  
Joseph Cessna ◽  
Andrew Kostuch

One of the most important tasks in pretest analysis and modal survey planning is the selection of target modes. The target modes are those mode shapes that are determined to be dynamically important using some definition. While there are many measures of dynamic importance, one of the measures that has been of greatest interest to structural dynamicists, is the contribution of each mode to the dynamic loads at an interface. Dynamically important modes contribute significantly to the interface loads and must be retained in any reduced analytical representation. These modes must be identified during a ground vibration test to validate the corresponding finite element model. Structural dynamicists have used interface load based effective mass measures to efficiently identify target modes for constrained structures. The advantage of these measures of dynamic importance is that they are absolute, in contrast to other measures that only indicate the importance of one mode shape relative to another. However, in many situations, especially in aerospace applications, structures must be tested in a free–free configuration. In the case of free–free elastic modes, the effective mass values are zero, making them useless measures of dynamic importance. This paper presents a new effective mass like measure of absolute dynamic importance that can be applied to free–free structures. The new method is derived based upon the free–free modal equations of motion. The approach is shown to be directly related to ranking mode shapes based on approximate balanced singular values. But, unlike the approximate balanced singular value approach, it is an absolute measure of importance. A numerical example of a general spacecraft system is presented to illustrate the application of the new technique. Dynamically important mode shapes were easily identified for modal acceleration, velocity, and displacement output. The new method provides an efficient technique for selecting target modes for a modal vibration test, or the reduction of a modal based analytical model to the dynamically important mode shapes.


Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5791
Author(s):  
Mark Richmond ◽  
Ursula Smolka ◽  
Athanasios Kolios

The modal response of a four-legged jacket structure to damages are explored and resulting considerations for damage detection are discussed. A finite element model of the Wikinger (Iberdrola) jacket structure is used to investigate damage detection. Damages, such as cracks, scour, corrosion and more, are modelled in a simulation environment. The resulting modal parameters are calculated, these parameters are compared to those from an unaltered structure and metrics are calculated including frequency change, modal assurance criterion and modal flexibility. A highly detailed design-model is used to conduct a sensitivity study on modal parameters for a range of changes. By conducting this on the same structure, this acts as a useful reference for those interested in the dynamic response of offshore wind jacket structures. Additionally, this paper addresses the issue of changes in mode parameters resulting from turbine yaw. This paper also considers the challenge of mode-swapping in semi-symmetric structures and proposes several approaches for addressing this. Damage typically results in a reduction of frequency and change in mode shapes, but in ways which can be distinguished from other structural changes, given the extent of this model. These findings are important considerations for modal-based damage detection of offshore wind support structures.


2005 ◽  
Vol 293-294 ◽  
pp. 599-606 ◽  
Author(s):  
R.A. Votsis ◽  
M.M. Abdel Wahab ◽  
M.K. Chryssanthopoulos

Simulations of damage scenarios were carried out using a finite element model of a newly constructed FRP composite footbridge, the Wilcott footbridge. This footbridge represents a new generation of suspension footbridges that have lightweight decks made of pultruded glass fibre reinforced polymer (GFRP) composite elements. It offers several advantages over conventional steel or concrete footbridges, e.g. speed of installation, high resistance to corrosion and saving in weight and foundations. On the other hand, its lightness and slenderness make it more sensitive to dynamic effects, both at serviceability and ultimate limit states. A finite element model using 3-D beam elements was constructed and damage scenarios were simulated and introduced in the model. The natural frequencies, mode shapes as well as time responses due to pedestrian loading were predicted. Different size of delamination in the composite deck was simulated at various locations along the bridge. The sensitivity of natural frequencies and mode shapes due to delamination were assessed by comparing the results of the damaged deck to those of the reference intact deck. The effect of changes in the cables’ initial strains on the modal parameters was also examined, and the sensitivity of modal parameters to cable degradation was assessed.


Author(s):  
Daniel P. Rohe ◽  
Matthew S. Allen

Experimental-to-Analytical Substructuring has been investigated as a way to avoid potentially costly tests and analysis on large systems by performing smaller, subcomponent-level tests. However, this has proven more difficult to implement than expected because the substructuring calculations can be sensitive to modal truncation and experimental noise and require the measurement of rotational motions at the interface. These issues seem to have led to decreased confidence in substructuring calculations, causing it to remain underutilized in industry. In recent work, the authors have proposed performing a small, inexpensive validation test to give confidence or reveal flaws in an experimentally-derived model. This work explores whether such an approach might be used to characterize the uncertainty in a substructure model due to measurement errors. Substructuring is simulated on a finite element model of a beam structure whose modal parameters have been contaminated with noise to simulate measurement errors and cross axis sensitivity. The beam is then coupled to a validation fixture, and the modal parameters of the validation experiment are investigated in a Monte-Carlo experiment to determine the correlation of a validation test to the actual application for different levels and types of errors in the measured mode shapes.


2012 ◽  
Vol 166-169 ◽  
pp. 1583-1586 ◽  
Author(s):  
Ting Hua Yi ◽  
Xiang Wang ◽  
Hong Nan Li

Modal kinetic energy (MKE) method gives a measure of the dynamic contribution of each finite element model physical degree of freedom to each of the target mode shapes, and provides a rough idea where the maximum responses could be measured. It could help to select those sensor positions with possible large amplitudes, and to increase the signal to noise ratio, which is critical in harsh and noisy circumstances. Kammar proposed a new optimal placement method of triaxial accelerometers based up on the effective independence algorithm (EfI3), which places triaxial accelerometers as single units in an optimal fashion. On the basis of EfI3, this paper fully considers the mutual influence of three directions and makes some improvements for the traditional MKE method. A novel optimal placement method of triaxial accelerometers called MKE3 is proposed which is proved rational and effective by analysis the relationship between the EfI algorithm and MKE method.


2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).


Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 311
Author(s):  
Chan-Jung Kim

Previous studies have demonstrated the sensitivity of the dynamic behavior of carbon-fiber-reinforced plastic (CFRP) material over the carbon fiber direction by performing uniaxial excitation tests on a simple specimen. However, the variations in modal parameters (damping coefficient and resonance frequency) over the direction of carbon fiber have been partially explained in previous studies because all modal parameters have only been calculated using the representative summed frequency response function without modal analysis. In this study, the dynamic behavior of CFRP specimens was identified from experimental modal analysis and compared five CFRP specimens (carbon fiber direction: 0°, 30°, 45°, 60°, and 90°) and an isotropic SCS13A specimen using the modal assurance criterion. The first four modes were derived from the SCS13A specimen; they were used as reference modes after verifying with the analysis results from a finite element model. Most of the four mode shapes were found in all CFRP specimens, and the similarity increased when the carbon fiber direction was more than 45°. The anisotropic nature was dominant in three cases of carbon fiber, from 0° to 45°, and the most sensitive case was found in Specimen #3.


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