Output-Only Modal Identification of a Nonuniform Beam by Using Decomposition Methods

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Rickey A. Caldwell ◽  
Brian F. Feeny
Keyword(s):  
Decomposition Methods ◽  
Analytical Approximation ◽  
Orthogonal Decomposition ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Accelerometer Data ◽  
Pass Filter ◽  
Modal Damping ◽  
Output Only

Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.

Output Only Modal Analysis of a Nonuniform Beam Experiment by Using Decomposition Methods

2011 ◽  
Author(s):  
Rickey A. Caldwell ◽  
Brian F. Feeny
Keyword(s):  
Natural Frequencies ◽  
Normal Modes ◽  
Decomposition Methods ◽  
Analytical Approximation ◽  
Orthogonal Decomposition ◽  
Modal Assurance Criterion ◽  
Beam Experiment ◽  
Saw Blade ◽  
Output Only ◽  
Nonuniform Beam

This work explores the application of reduced-order mass-weighted proper orthogonal decomposition (RMPOD), state variable modal decomposition (SVMD), and smooth orthogonal decomposition (SOD) for extracting approximations of linear normal modes (LNMs) of a free vibrating thin lightly damped nonuniform beam experiment. The application of these decomposition methods involves organizing sensed outputs into ensemble matrices. The ensemble matrices are utilized to create correlation matrices, which are used in solving an eigenvalue problem. This is realized experimentally by sensing a thin nonuniform cantilevered beam, a saw blade, with eleven equally spaced accelerometers, during free vibration. The first mode was filtered out since its frequency was below the threshold of reliable accelerometers performance. RMPOD was able to extract the second, third, and fourth mode as implied by modal assurance criterion (MAC) in a comparison with an analytical approximation of the nonuniform Euler-Bernoulli beam modes. SVMD was able to extract an approximation to the LNMs and natural frequencies for the second, third, and fourth modes. SOD was able to extract the second, third, and fourth modes and natural frequencies successfully.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

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-).

scholarly journals Output-Only Modal Analysis Based on Improved Empirical Mode Decomposition Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Shiqiang Qin ◽  
Qiuping Wang ◽  
Juntao Kang
Keyword(s):  
Modal Analysis ◽  
Empirical Mode Decomposition ◽  
Modal Parameters ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Random Decrement Technique ◽  
Mode Decomposition ◽  
Frequency Components ◽  
Output Only ◽  
Emd Method

The output-only modal analysis for bridge structures based on improved empirical mode decomposition (EMD) is investigated in this study. First, a bandwidth restricted EMD is proposed for decomposing nonstationary output measurements with close frequency components. The advantage of bandwidth restricted EMD to standard EMD is illustrated by a numerical simulation. Next, the modal parameters are extracted from intrinsic mode function obtained from the improved EMD by both random decrement technique and stochastic subspace identification. Finally, output-only modal analysis of a railway bridge is presented. The study demonstrates the mode mixing issues of standard EMD can be restrained by introducing bandwidth restricted signal. Further, with the improved EMD method, band-pass filter is no longer needed for separating the closely spaced frequency components. The modal parameters extracted based on the improved EMD method show good agreement with those extracted by conventional modal identification algorithms.

scholarly journals Vibration-Based Damage Assessment in Gravity-Based Wind Turbine Tower under Various Waves

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Cong-Uy Nguyen ◽  
So-Young Lee ◽  
Heon-Tae Kim ◽  
Jeong-Tae Kim
Keyword(s):  
Wind Turbine ◽  
Damage Assessment ◽  
Natural Frequencies ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Damage Scenarios ◽  
Wind Turbine Tower ◽  
Induced Variation ◽  
Wave Induced

In this study, the feasibility of vibration-based damage assessment in a wind turbine tower (WTT) with gravity-based foundation (GBF) under various waves is numerically investigated. Firstly, a finite element model is constructed for the GBF WTT which consists of a tower, caisson, and foundation bed. Eigenvalue analysis is performed to identify a few vibration modes of interest, which represent complex behaviors of a flexible tower, rigid caisson, and deformable foundation. Secondly, wave-induced dynamic pressures are analyzed for a few selected wave conditions and damage scenarios are also designed to simulate the main components of the target GBF WTT. Thirdly, forced vibration responses of the GBF WTT are analyzed for the wave-induced excitation. Then modal parameters (i.e., natural frequencies and mode shapes) are extracted by using a combined use of time-domain and frequency-domain modal identification methods. Finally, the variation of modal parameters is estimated by measuring relative changes in natural frequencies and mode shapes in order to quantify the damage-induced effects. Also, the wave-induced variation of modal parameters is estimated to relatively assess the effect of various wave actions on the damage-induced variation of modal parameters.

Vibratory Parameters of Blades From Coordinate Measurement Machine (CMM) Data

2005 ◽  
Author(s):  
Alok Sinha ◽  
Benjamin Hall ◽  
Brice Cassenti ◽  
Gary Hilbert
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Natural Frequencies ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of a procedure to model geometric variations of blades. Specifically, vibratory parameters of blades are extracted from CMM data on an integrally bladed rotor (IBR). The method is based on proper orthogonal decomposition (POD) of CMM data, solid modeling and finite element techniques. In addition to obtaining natural frequencies and mode shapes of each blade on an IBR, statistics of these modal parameters are also computed and characterized. Numerical results are validated by comparison with experimental results.

Extending Blind Modal Identification to the Underdetermined Case for Ambient Vibration

2012 ◽  
Author(s):  
Scot McNeill
Keyword(s):  
Natural Frequencies ◽  
Second Order ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Frequency Domain Method ◽  
Blind Identification ◽  
Vibration Data ◽  
Modal Damping ◽  
Six Dof

The modal identification framework known as Blind Modal Identification (BMID) has recently been developed, drawing on techniques from Blind Source Separation (BSS). Therein, a BSS algorithm known as Second Order Blind Identification (SOBI) was adapted to solve the Modal IDentification (MID) problem. One of the drawbacks of the technique is that the number of modes identified must be less than the number of sensors used to measure the vibration of the equipment or structure. In this paper, an extension of the BMID method is presented for the underdetermined case, where the number of sensors is less than the number of modes to be identified. The analytic signal formed from measured vibration data is formed and the Second Order Blind Identification of Underdetermined Mixtures (SOBIUM) algorithm is applied to estimate the complex-valued modes and modal response autocorrelation functions. The natural frequencies and modal damping ratios are then estimated from the corresponding modal auto spectral density functions using a simple Single Degree Of Freedom (SDOF), frequency-domain method. Theoretical limitations on the number of modes identified given the number of sensors are provided. The method is demonstrated using a simulated six DOF mass-spring-dashpot system excited by white noise, where displacement at four of the six DOF is measured. All six modes are successfully identified using data from only four sensors. The method is also applied to a more realistic simulation of ambient building vibration. Seven modes in the bandwidth of interest are successfully identified using acceleration data from only five DOF. In both examples, the identified modal parameters (natural frequencies, mode shapes, modal damping ratios) are compared to the analytical parameters and are demonstrated to be of good quality.

scholarly journals DETERMINATION OF THE EFFECT OF TiO2 ON THE DYNAMIC BEHAVIOR OF SCALED CONCRETE CHIMNEY BY OMA

2021 ◽  
Vol 55 (3) ◽  
Author(s):  
Sertaç Tuhta ◽  
Furkan Günday
Keyword(s):  
Titanium Dioxide ◽  
Outer Surface ◽  
Ground Level ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Dynamic Parameters ◽  
Vibration Data ◽  
Output Only ◽  
Frequency Domain Decomposition

In this article, the dynamic parameters (frequencies, mode shapes, damping ratios) of a scaled concrete chimney and the dynamic parameters (frequencies, mode shapes, damping ratios) of the entire outer surface of the 80-micron-thick titanium dioxide are compared using the operational modal analysis method. Ambient excitation was provided from micro tremor ambient vibration data at ground level. Enhanced Frequency Domain Decomposition (EFDD) is used for the output-only modal identification. From this study, very best correlation is found between the mode shapes. Titanium dioxide applied to the entire outer surface of the scaled concrete chimney has an average of 16.34 % difference in frequency values and 9.81 % in damping ratios, proving that nanomaterials can be used to increase the rigidity in chimneys, in other words, for reinforcement. Another important result determined in the study is that it has been observed that the adherence of titanium dioxide and similar nanomaterials mentioned in the introduction to concrete chimney surfaces is at the highest level.

Dynamics of Multibody Tracked Vehicles Using Experimentally Identified Modal Parameters

1996 ◽  
Vol 118 (3) ◽  
pp. 499-507 ◽  
Author(s):  
Toshikazu Nakanishi ◽  
Xuegang Yin ◽  
A. A. Shabana
Keyword(s):  
Equations Of Motion ◽  
Kinematic Chain ◽  
General Purpose ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Modal Damping ◽  
Modal Mass ◽  
The Individual

The mode shapes, frequencies, and modal mass and stiffness coefficients of multibody systems such as tracked vehicles can be determined using experimental identification techniques. In multibody simulations, however, knowledge of the modal parameters of the individual components is required, and consequently, a procedure for extracting the component modes from the mode shapes of the assembled system must be used if experimental modal analysis techniques are to be used with general purpose multibody computer codes. In this investigation, modal parameters (modal mass, modal stiffness, modal damping, and mode shapes), which are determined experimentally, are employed to simulate the nonlinear dynamic behavior of a multibody tracked vehicle which consists of interconnected rigid and flexible components. The equations of motion of the vehicle are formulated in terms of a set of modal and reference generalized coordinates, and the theoretical basis for extracting the component modal parameters of the chassis from the modal parameters of the assembled vehicle is described. In this investigation, the track of the vehicle is modeled as a closed kinematic chain that consists of rigid links connected by revolute joints, and the effect of the chassis flexibility on the motion singularities of the track is examined numerically. These singularities which are encountered as the result of the change in the track configuration are avoided by using a deformable secondary joint instead of using the loop-closure equations.

scholarly journals Autonomous Modal Identification of the Space Shuttle Tail Rudder

1997 ◽  
Author(s):  
Richard S. Pappa ◽  
George H. James ◽  
David C. Zimmerman
Keyword(s):  
Natural Vibration ◽  
Space Shuttle ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Detection Techniques ◽  
Cpu Time ◽  
Free Decay ◽  
Periodic Monitoring ◽  
Analysis Engine

Abstract Autonomous modal identification automates the calculation of natural vibration frequencies, damping, and mode shapes of a structure from experimental data. This technology complements damage detection techniques that use continuous or periodic monitoring of vibration characteristics. The approach shown in the paper incorporates the Eigensystem Realization Algorithm (ERA) as a data analysis engine and an autonomous supervisor to condense multiple estimates of modal parameters using ERA’s Consistent-Mode Indicator and correlation of mode shapes. The procedure was applied to free-decay responses of a Space Shuttle tail rudder and successfully identified the seven modes of the structure below 250 Hz. The final modal parameters are a condensed set of results for 87 individual ERA cases requiring approximately five minutes of CPU time on a DEC Alpha computer.

scholarly journals Modal identification of Bridge 44 of the Carajás Railroad and numerical modeling using the finite element method

2020 ◽  
Vol 13 (1) ◽  
pp. 39-68
Author(s):  
M. S. SILVA ◽  
F. A. NEVES
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Dynamic Characteristics ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
The Finite Element Method ◽  
Vibration Tests ◽  
Element Method

Abstract Regular use and the effects of time can affect the behavior of a structure. Over time, problems such as the occurrence of small fissures, oxidation of steel elements, and excessive displacements at some points may arise in a structure. In this context, the monitoring of structures through experimental tests has gained more importance, because it allows for the identification of the dynamic characteristics (natural frequencies, mode shapes, and damping rate) of structures. The dynamic characteristics can be obtained through forced vibration tests, which are based on measuring the response of a structure subjected to an excitation of known magnitude, or through tests in which only the structural response is measured, such as free vibration and ambient vibration tests. The present study aims to identify the modal parameters of bridge 44 of the Carajás Railroad, using experimental data obtained on site by monitoring the vibration caused by a group of people jumping, and it compares them with the results obtained through numerical modeling performed using the finite element method, developed in CSiBridge. The modal parameters were obtained using the commercial software ARTeMIS Modal, and stochastic subspace identification was used for modal identification.

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