Variation Of Modal Frequencies Research Articles

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

The Effect of Damages on Modal Frequencies of Flat Glass Fiber Reinforced Polyurethane Foam Sandwich Structures

Finite element model of a cable-stayed bridge updated with vibration measurements and its application to investigate the variation of modal frequencies in monitoring

Ambient vibration measurements of a cable-stayed bridge in Taiwan were first conducted to identify its dominant modal parameters with a reliable stochastic subspace identification algorithm recently developed. A finite element model is then constructed based on the identified frequencies and shape vectors of four vertically bending, one torsional, and one horizontally bending modes. This model is also updated by adjusting the girder-pier connection with the addition of a rotational spring to reflect the actual conditions and its accuracy is demonstrated with less than 1% of error for the first two vertically bending modes. As a solid application for probing the environmental effects in structural health monitoring, the vibration measurements of 24 hours were further conducted and combined with the well calibrated model to investigate the controlling factor for its variation in modal frequencies. It is found that the frequencies of the first two vertically bending modes are closely correlated to the root-mean-square velocity representing the traffic excitation intensity. Moreover, it is shown with the updated model that the daily variations in the frequencies of the first two vertically bending modes can be reasonably simulated by modifying the coefficient of the rotational spring merely in a limited range.

Estimators for Structural Damage Detection Using Principal Component Analysis

Structural damage detection is an important issue in conservation. In this research, principal component analysis (PCA) has been applied to the temporal variation of modal frequencies obtained from a dynamic test of a scaled steel structure subjected to different damages and different temperatures. PCA has been applied in order to reduce, as much as possible, the number of variables involved in the problem of structural damage detection. The aim of the PCA study is to determine the minimum number of principal components necessary to explain all the modal frequency variation. Three estimators have been studied: T2 (the square of the vector norm of the projection in the principal component plan), Q (the square of the norm of the residual vector), and the variance explained. In the study, the results related to the undamaged structure needed one principal component to explain the modal frequency variation. However, the high damage configurations need five principal components to explain the modal frequency. The T2 and Q estimators have been arranged in order of increasing damage for all the performed experimental tests. The results indicate that these estimators could be useful to detect damage and to distinguish among a range of intensities of structural damage.

Identification of Joint Discrepancy in Steel Truss Bridge Using Hilbert Transform with root-MUSIC and ESPRIT Techniques

In the present paper, the first three modal frequencies obtained through recorded vibration signal of a steel truss bridge is investigated at three different vehicular speeds. The denoising and extraction of modal frequencies from vibration response signals of steel truss bridge is performed using Hilbert transform (HT) in combination with high-frequency resolution enhancing techniques. The modal frequency extracting techniques applied includes Fast Fourier transform (FFT), multiple signal classification (MUSIC), and estimation of signal parameters by rotational invariance technique (ESPRIT). The comparisons of the outcomes of HT-FFT, HT-root-MUSIC, and HT- ESPRIT are computed. It is observed that HT-FFT computed results with the low resolution which hindered in obtaining distinct modal frequencies while HT-MUSIC and HT-ESPRIT achieved the most denoised, robust and reliable outcomes. The HT-ESPRIT outperforms HT-MUSIC in the elimination of unwanted noise. Further, the application of the sliding window HT-ESPRIT method clearly shows the variation of modal frequencies with the change in vehicular speeds. The first three analytical modal frequencies of 4.56 Hz, 10.44 Hz and 16.66 Hz frequencies are compared with the experimental frequencies obtained through vibrations at 10 km/h, 20 km/h and 30 km/h vehicular speeds, respectively. The joints (also denoted as nodes) 6, 7, and 8 exhibited irregular behaviour with no or minimum frequency peaks due to increased flexibility of member at these locations.

Extra-insensitive shaper with distributed delays: Design and vibration suppress analysis

Distributed delays have proved beneficial in eliminating vibrations in higher frequency ranges compared to the modeled frequency, but not in improving the robustness against the modeled frequency to modeling errors. In this paper, the extra-insensitive shaper with distributed delays is proposed to improve robustness and efficiency for systems with a large variation of modal frequencies. The extra-insensitive shaper with distributed delays is derived by distributing two zeros in the radial direction of the designed zero of the distributed zero-vibration shaper. Two methods of distributing zeros are provided to parameterize the extra-insensitive shaper with distributed delays. Asymmetric extra-insensitive shaper with distributed delays and symmetric extra-insensitive shaper with distributed delays are two types of the extra-insensitive shaper with distributed delays parameterized by the asymmetric distribution method and the symmetric distribution method. Properties of the Asymmetric extra-insensitive shaper with distributed delays and the symmetric extra-insensitive shaper with distributed delays in spectral, sensitivity and step response are analyzed and compared with those of the classical extra-insensitive shaper and distributed zero-vibration-derivative shaper. The results present larger robustness in variations of modeled and higher frequencies, suppressing the vibration of the modeled mode and unmodeled higher multiple modes to a tolerable level. The implement in the time-varying double-pendulum crane verifies the effectivity for vibration suppress of multi-mode systems.

Effects of environmental and operational actions on the modal frequency variations of a sea-crossing bridge: A periodicity perspective

Abstract The modal frequency variations of bridges associated with environmental and operational actions are among the primary research topics in structural health monitoring (SHM). Based on the periodic variations of the monitoring data obtained over 6 years for the Donghai Bridge (DHB), we investigated the effects of environmental and operational factors on the modal frequency variations and identified the main periods and influencing factors of the DHB frequency changes. Partial correlation coefficients and cyclic averaging were applied to compare the contributions of various actions to the frequency changes, and the underlying mechanisms of the frequency changes were preliminarily studied. The modal frequencies of the DHB were found to vary with periods such as 1 year, 1 week, 1 day, and 12.42 h in a manner corresponding to inherent variation cycles of structural temperature, traffic loading, wind loading, and sea level. Structural temperature and traffic loading were the primary factors influencing the DHB frequency changes, and their relative degrees of impact on the frequency changes were different for different cycles. All modal frequencies of the DHB decreased with increasing temperature due to variation in the temperature-dependent elastic moduli of the structural materials. However, as traffic loading increased, the fundamental frequencies of the vertical bending, lateral bending, and torsional modes of the girder decreased, while some higher-order frequencies increased. The influence of traffic on the modal frequencies could be qualitatively explained by employing an equivalent spring–mass model of the traffic flow on the bridge. The results of this study will deepen the understanding of the frequency changes occurring in bridges during operation and can serve as a reference for vibration-based SHM.

Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending

The Acoustic Emission (AE) and Dynamic Identification (DI) techniques were applied simultaneously, in an original way, to examine the stress dependent damage progress in pre-notched concrete beams tested in four-point bending. The damage mechanisms were characterized by analyzing the AE signals registered during the tests, conducted by increasing the specimen’s vertical deflection. In particular, the dominant fracture mode was identified, and correlations between dissipated and emitted energies were investigated. Moreover, variations in the natural bending frequencies, produced by the crack advancement under loading, were detected and put in relation with the cumulated AE energy. Two different types of piezoelectric (PZT) sensors, operating in well distinct frequency ranges, were used to measure AE and modal signals. This study may be of interest with an outlook on possible correlations between a multi-parameter structural monitoring and the solution of inverse problems by numerical models.

Detection of delamination in composite beams using frequency deviations due to concentrated mass loading

Modern composite structures are usually designed to withstand mass loading. The effects of delamination due to concentrated mass loading with respect to modal frequency variations in composite beams have been investigated in the present work numerically and experimentally. A noticeable delamination-induced modal frequency deviation has been observed when a concentrated mass loading is imposed at pre-defined sections of the delaminated composite beams compared to the intact (reference) composite beams. For delaminations of only 10% of the length of a composite beam, modal frequency deviations of about 20% were observed numerically and experimentally. Further investigations of different delamination configurations show that the modal frequency deviations are dependent on the longitudinal location as well as the interlayer positions of the defects. Higher frequency deviations are observed when delamination approaches the clamped boundary of a composite beam. The results suggest that the frequency curve deviations have a local or global characteristic depending on whether the delamination occurs at the near surface or the mid-plane of the composite beam, respectively. Consequently, the frequency curves can be employed as NDT tool for delamination identification and localisation.

Damage assessment of composite plate structures with material and measurement uncertainty

Composite materials are very useful in structural engineering particularly in weight sensitive applications. Two different test models of the same structure made from composite materials can display very different dynamic behavior due to large uncertainties associated with composite material properties. Also, composite structures can suffer from pre-existing imperfections like delaminations, voids or cracks during fabrication. In this paper, we show that modeling and material uncertainties in composite structures can cause considerable problem in damage assessment. A recently developed C0 shear deformable locking free refined composite plate element is employed in the numerical simulations to alleviate modeling uncertainty. A qualitative estimate of the impact of modeling uncertainty on the damage detection problem is made. A robust Fuzzy Logic System (FLS) with sliding window defuzzifier is used for delamination damage detection in composite plate type structures. The FLS is designed using variations in modal frequencies due to randomness in material properties. Probabilistic analysis is performed using Monte Carlo Simulation (MCS) on a composite plate finite element model. It is demonstrated that the FLS shows excellent robustness in delamination detection at very high levels of randomness in input data.

An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure

Piezoelectric shunt damping is a well-known technique to damp mechanical vibrations of a structure, using a piezoelectric transducer to convert mechanical vibration energy into electrical energy, which is dissipated in an electrical resistance. Resonant shunts consisting of a resistance and an inductance connected to a piezoelectric transducer are used to damp structural vibrations in narrow frequency bands, but their performance is very sensitive to variations in structural modal frequencies and transducer capacitance. In order to overcome this drawback, a piezoelectric shunt damping technique with improved performance and robustness is presented in this paper. The design of the adaptive circuit considers the variation of the host structure’s natural frequency as a project parameter. This paper describes an adaptive resonant piezoelectric vibration absorber enhanced by a synthetic negative capacitance applied to a shell structure. The resonant shunt circuit autonomously adapts its inductance value by comparing the phase difference of the vibration velocity and the current flowing through the shunt circuit. Moreover, a synthetic negative capacitance is added to the shunt circuit to enhance the vibration attenuation provided by the piezoelectric absorber. The circuitry is implemented using analog components. Validation of the proposed method is done by bonding the piezoelectric absorber on a free-formed metallic shell.

The iterative complex demodulation applied on short and long Schumann resonance measured sequences

Abstract The precise determination of instantaneous frequency of Schumann resonance (SR) modes, with the possibility of application to relatively short signal sequences, seems to be important for detailed analysis of SR modal frequency variations. Contrary to commonly used method of obtaining modal frequencies by the Lorentz function fitting of DFT spectra, we employ the complex demodulation (CD) method in iterated form. Results of iterated CD method applied on short and long measured sequences are compared. Results for SR signals as well as the comparison with Lorentz function fitting are presented. Decrease of frequencies of all first four SR modes from the solar cycle maximum to solar cycle minimum has been found using also the CD method.

Isomap-based damage classification of cantilevered beam using modal frequency changes

SUMMARY This study adopts the Isomap algorithm that uses the variation of modal frequencies caused by stiffness damage to classify damage locations in a structure. The Isomap algorithm belongs to a nonlinear generalization of classical multidimensional scaling, which makes a new coordinate system for high-dimensional data. And this coordinate system provides good observations for the extraction of the data pattern and for the classification of their nonlinear characteristics. Thus, the Isomap can easily find globally meaningful coordinates and identify the nonlinear structure of complex data sets for many cases, whereas neither the principal component analysis (PCA) nor multidimensional scaling has been successful. This study compares the performances of the PCA and the Isomap algorithm in classifying damage locations in terms of modal frequency changes. The article also investigates the benefits of incorporating the concept of sensitivity enhancing control in the Isomap-based damage classification to improve the level of resolution of a modal frequency shift. It is demonstrated that the Isomap algorithm successfully enhances the quality of patterns and classifications related to damage locations through simulation examples. Copyright © 2013 John Wiley & Sons, Ltd.

Modal identification of spindle-tool unit in high-speed machining

The accurate knowledge of high-speed motorised spindle dynamic behaviour during machining is important in order to ensure the reliability of machine tools in service and the quality of machined parts. More specifically, the prediction of stable cutting regions, which is a critical requirement for high-speed milling operations, requires the accurate estimation of tool/holder/spindle set dynamic modal parameters. These estimations are generally obtained through Frequency Response Function (FRF) measurements of the non-rotating spindle. However, significant changes in modal parameters are expected to occur during operation, due to high-speed spindle rotation. The spindle's modal variations are highlighted through an integrated finite element model of the dynamic high-speed spindle-bearing system, taking into account rotor dynamics effects. The dependency of dynamic behaviour on speed range is then investigated and determined with accuracy. The objective of the proposed paper is to validate these numerical results through an experiment-based approach. Hence, an experimental setup is elaborated to measure rotating tool vibration during the machining operation in order to determine the spindle's modal frequency variation with respect to spindle speed in an industrial environment. The identification of natural frequencies of the spindle under rotating conditions is challenging, due to the low number of sensors and the presence of many harmonics in the measured signals. In order to overcome these issues and to extract the characteristics of the system, the spindle modes are determined through a 3-step procedure. First, spindle modes are highlighted using the Frequency Domain Decomposition (FDD) technique, with a new formulation at the considered rotating speed. These extracted modes are then analysed through the value of their respective damping ratios in order to separate the harmonics component from structural spindle natural frequencies. Finally, the stochastic properties of the modes are also investigated by considering the probability density of the retained modes. Results show a good correlation between numerical and experiment-based identified frequencies. The identified spindle-tool modal properties during machining allow the numerical model to be considered as representative of the real dynamic properties of the system.

A fast method for structural health monitoring of Italian reinforced concrete strategic buildings

The growing number of demand for a widespread of health monitoring for strategic buildings in seismic areas has emphasized the need to realize in-depth scientific studies, in order to verify the feasibility of economic and fast methods to detect anomalous vibrations, to execute post earthquake warning and monitoring, damage assessment and first damage scenarios. Generally, an effective system for structural health monitoring requires an appropriate number of sensors, suitably located in the structures, and complex elaborations of big amounts of data. The simplified method presented in this paper is based on a statistical approach that uses the most significant data recorded on the top floor of the building, with the purpose of extracting information on the maximum inter-story drift, used as damage indicator. The parameters considered in the method are (i) maximum top acceleration, (ii) the first modal frequency variations and (iii) the equivalent structural viscous damping variation. A big amount of experimental data relevant to several tests carried out on scaled R/C models and numerical non linear dynamic analyses have been used to verify the feasibility of this approach.

A novel approach for the structural identification and monitoring of a full-scale 17-storybuilding based on ambient vibration measurements

For reliable and practical application of structural health monitoring approaches inconjunction with dense sensor arrays deployed on ‘smart’ systems, there is a need todevelop and evaluate alternate strategies for efficient problem decomposition to rapidlyand accurately determine the occurrence, location and level of small changesin the underlying structural characteristics of a monitored system based on itsvibrational signature. Furthermore, there is also a need to quantify the level ofuncertainties in the identified system characteristics so as to have a measurablelevel of confidence in the parameters to be relied on for the detection of genuinechanges (damage) in the monitored system. This study presents the results of twotime-domain identification techniques applied to a full-scale 17-story building, based onambient vibration measurements. The Factor building is a steel frame structurelocated on the UCLA campus. This building was instrumented permanently with adense array of 72-channel accelerometers, and the acceleration data are beingcontinuously recorded. The first identification method used in this study is theNExT/ERA, which is regarded as a global (or centralized) approach, since it dealswith the global dynamic properties of the structure. The second method is atime-domain identification technique for chain-like MDOF systems. Since in thismethod the identification of each link of the chain is performed independently,it is regarded as a local (or decentralized) identification methodology. For thesame reason, this method can be easily adopted for large-scale sensor networkarchitectures in which the centralized approaches are not feasible due to massivestorage, power, bandwidth and computational requirements. To have a statisticallymeaningful results, 50 days of recorded data are considered in this study. Themodal parameter and chain identification procedures are performed over timewindows of 2 h each and with 50% overlap. Using the NExT/ERA method, 12dominant modes of the building were identified. It was observed that variations in thefrequency estimation are relatively small; the coefficient of variation is about 1–2%for most of the estimated modal frequencies. Chain system identification wassuccessfully implemented using the output-only data acquired from the Factorbuilding. Probability distributions of the estimated coefficients of displacement andvelocity terms in the interstory restoring functions (which are the mass-normalizedlocal stiffness and damping values) that were found based on the chain systemidentification are presented. The variability of the estimated parameters due totemperature fluctuations is investigated. It is shown that there is a strong correlationbetween the modal frequency variations and the temperature variations in a 24 hperiod.

Small-Amplitude Free-Vibration Analysis of Piezoelectric Composite Plates Subject to Large Deflections and Initial Stresses

A coupled theoretical and computational framework is presented for analyzing the small amplitude-free vibrational response of composite laminated plates with piezoelectric actuators and sensors, subject to nonlinear effects due to large rotations and initial stresses. Coupled laminate mechanics incorporating nonlinear governing equations with mixed-field shear-layerwise assumptions for the piezoelectric laminate are implemented. A finite element method is formulated to yield the linearized discrete dynamic equations of a piezocomposite plate on top of its nonlinear electrostatic response, and a novel eight-node coupled nonlinear plate finite element forms the basis of numerical analyses. The natural frequencies in a beam with a piezoceramic actuator and sensor subject to in-plane mechanical loading, high enough to induce buckling and postbuckling are also experimentally characterized, and comparisons to numerical results show excellent correlation. Additional numerical evaluations quantify the active shifting of natural frequencies in adaptive beams and plates subject to high out-of-plane and in-plane electromechanical loading, and the variation of modal frequencies during buckling and postbuckling response. Finally, the possibility to detect and actively manage buckling in adaptive piezocomposite plates is illustrated.

Vibrational modes of clarinet reeds

The role of the lowest frequency reed resonance in sound production by single reed instruments has been well established [S. C. Thompson, J. Acoust. Soc. Am. 66, 1299–1307 (1979)]. However, the acoustical significance of the reed’s higher vibrational modes remains an open question. Recently, several higher frequency modes have been identified for a clarinet reed [P. L. Hoekje and G. Matthew Roberts, J. Acoust. Soc. Am. 99, 2462(A) (1996)]. The present study examines several reeds and extends Hoekje’s results to higher frequencies. Holographic interferometry was used to locate the frequencies and to image the vibrational patterns of higher vibrational modes of three nominally equivalent commercial clarinet reeds. Dry reeds were clamped to a specially designed reed holder allowing the reeds to vibrate freely when driven by an acoustic sound field. In all, six or seven distinct modes with frequencies below 7.5 kHz were located on each of the three reeds. Four of the modes (including the fundamental) appear to be similar to the one-dimensional modes of a cantilevered beam. The other three modes show two-dimensional vibrations indicating twisting motion. Variations in modal frequencies among the three reeds studied range from 3%–12% over the different modes.

An adaptive input shaping control scheme for vibration suppression in slewing flexible structures

The application of an input precompensation scheme for vibration suppression in slewing flexible structures, with particular application to flexible-link robotic manipulator systems, is considered. The control from such input shaping schemes corresponds to a feedforward term that convolves in real time the desired reference input with a sequence of impulses and produces a vibration-free output. The robustness of such an algorithm with respect to modal frequency variations is not satisfactory but can be improved by convolving the input with a longer sequence of impulses, the tradeoff being a decrease in the transient response speed. An adaptive precompensation scheme that can be implemented by combining a frequency domain identification scheme, used to estimate the modal frequencies online, with a subsequent scheme for adjusting the spacing between the impulses is proposed. The combined adaptive input shaping scheme provides the most rapid slew that results in a vibration-free output. Experimental results for a single flexible link are presented to verify the technique. >

A stochastic operator for interface dynamics and the canonical relation between compliance update and modal frequency variation—I. Modeling of the stochastic stretch-shear-rotation operator for interface dynamics in ordered structures

A model that idealizes an elastic structure as comprising of discrete, statistically homogeneous, close-packed structured mesodomains is developed for the purpose of characterizing the inner foundation and pathology of the compliance influence coefficient variation process. The genesis of approach defines the bond rotation between disturbed contiguous mesodomains (nodes) as the vector that synchronizes the mechanical motions of interior microelements of these structured nodes, with the ingenerate local thermal fluctuations that characterize such mesodomain pairs. It is shown that this bond rotation vector enables the modeling of the desired “Stochastic Stretch-Shear-Rotation Operator”. In principle, this stochastic operator influences the co-operational phenomenon during the mesodomain kineto-elastodynamics, and facilitates the description of nearest-neighbor mesoscopic interactions. An expression for the matrix of correlation associated with this operator is given. The fundamental definition of the latter correlation matrix is such that it provides the topological basis for linking the inner foundations of the random compliance influence coefficient update process to modal frequency changes in a damaged or disordered disturbed structure. In addition, this presentation maintains that the correlation matrix can be conveniently employed for the specification of the statistics of the stress-stiffening effect and the coriolis factor at the mesoscopic level of observation.

A stochastic operator for interface dynamics and the canonical relation between compliance update and modal frequency variation—II. Non-deterministic evolution of modal frequency changes engendered by compliance influenced state-space variations

This paper presents an analytical description of the non-deterministic evolution of modal frequency changes that are engendered by compliance influence state-space variations in a disturbed elastic microstructured medium. In order to access the inner foundation of the random compliance update process which is known to influence predictions on modal frequency state-space variations, the analysis invokes the concept of stochastic stretch-shear-rotation operator which characterizes the microstructure interface dynamics. The analytical results indicate that treating the pathology inherent in the random compliance update process as uncorrelated white and colored noise processes leads to a canonical decomposition that partitions the modal frequency variation as a linear manifold with deterministic and non-deterministic complements. In particular, the formulation shows that the “Paley-Wiener Criterion” can serve as a means of checking the nature of the drift towards non-determinism, once the structure and intensity of the noise-induced transition probability controlling the time-evolution of the modal frequency changes are well defined.