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The use of tuned liquid dampers (TLDs) as an alternative to reduce the response of flexible structures with a low amount of structural damping is a viable option. The correct characterization of the dynamic properties of the TLD plays an important role in the performance of the TLD-main structure system. This work presents the results of an experimental study to evaluate the dynamic properties of a scaled rectangular TLD using high-speed videos. For the experimental investigation, a scaled rectangular TLD is subjected to lateral displacement of the sinusoidal type with amplitudes that range from 5 to 40 mm and frequency equal to 0.625 Hz. The dynamic properties of the TLD system are identified with the use of high-speed videos with a duration of 28.96 s and recorded at 500 frames per second (fps). The recorded videos are analyzed with the software Tracker to extract time histories of wave elevation at predefined locations. The frequency and damping of the TLD system are identified from the time histories of wave elevation through Fourier analysis and free-vibration decay. The findings of this study revealed that the identified dynamic properties of the TLD by using high-speed videos presented small differences with respect to the target values, with errors that range from 0.93 to 2.9% for frequency and from 1.6 to 8.8% for damping, indicating that the use of high-speed videos can be an alternative to evaluate the dynamic properties of TLD systems. [ABSTRACT FROM AUTHOR]

The energy amplification factor transmitted from the excitation source to the response end cannot be identified quickly and accurately using the method of obtaining modal frequency combined with damping through modal frequency resonance. As a result, the above method cannot be used to further evaluate the effect of structural improvement. In this paper, a frequency difference sensitivity method is proposed in order to improve the efficiency of the above identification and evaluation processes while also guaranteeing accuracy. Firstly, a theoretical model suitable for the damping and rigid-body-mode frequency range of the cooling module is established according to the frequency difference between the excitation frequency,.system mode frequency, and vibration response sensitivity. Then, the accuracy and effect of the model are studied from the perspective of a simulation and experiment. The model can be used to identify and evaluate the resonance problem of the vehicle cooling module quickly and accurately. The energy amplification factor of the fan to the passive end of the cooling module can be efficiently predicted using the frequency difference sensitivity method proposed in this paper while ensuring accuracy. The quantized noise-reduction effect of the interior before and after the improvement can be efficiently predicted and evaluated using said model. The literature shows that the resonance of a vehicle cooling module can be identified and evaluated quickly and accurately via the frequency difference sensitivity method, which can overcome the problems that the conventional modal frequency resonance method encounters in identifying and evaluating quickly. [ABSTRACT FROM AUTHOR]

Natural fiber composites (NFC) exhibit good specific mechanical properties in comparison to synthetic fiber composites (SFC). The study investigates interlaminar glass (G) fiber hybridized jute (J) and flax (F) reinforced epoxy composites designated as JGGJ, GJJG, FGGF, and GFFG along with their virgin counterparts. Composite laminates of four plies are manufactured by hand-layup followed by compression molding to investigate tensile, flexural, and interlaminar shear properties. Further the effect of hybridization is also investigated for modal frequencies and damping ratio obtained from experimental modal analysis. Glass fiber hybridization as extreme layers shows significant improvement in flexural and shear properties as compared to tensile. Glass fiber reinforcement, as core layers improve the damping by 155.55% and 101.31% for JGGJ and FGGF, respectively, over pure glass epoxy. However with increase in bending stiffness of GJJG and GFFG, the bending modal frequency is improved. Also, the modal frequency and damping ratio increases following a power-law variation with a decrease in the free length. Finite element and analytical validations are presented to the experimental frequencies and flexural modulus, respectively. These studied hybrid composites can serve as semi-structural members like interior trim panels in automotive applications that possess significant strength and dissipate in-service vibrations effectively.

The use of tuned liquid dampers (TLDs) as an alternative to reduce the response of flexible structures with a low amount of structural damping is a viable option. The correct characterization of the dynamic properties of the TLD plays an important role in the performance of the TLD-main structure system. This work presents the results of an experimental study to evaluate the dynamic properties of a scaled rectangular TLD using high-speed videos. For the experimental investigation, a scaled rectangular TLD is subjected to lateral displacement of the sinusoidal type with amplitudes that range from 5 to 40 mm and frequency equal to 0.625 Hz. The dynamic properties of the TLD system are identified with the use of high-speed videos with a duration of 28.96 s and recorded at 500 frames per second (fps). The recorded videos are analyzed with the software Tracker to extract time histories of wave elevation at predefined locations. The frequency and damping of the TLD system are identified from the time histories of wave elevation through Fourier analysis and free-vibration decay. The findings of this study revealed that the identified dynamic properties of the TLD by using high-speed videos presented small differences with respect to the target values, with errors that range from 0.93 to 2.9% for frequency and from 1.6 to 8.8% for damping, indicating that the use of high-speed videos can be an alternative to evaluate the dynamic properties of TLD systems.

The energy amplification factor transmitted from the excitation source to the response end cannot be identified quickly and accurately using the method of obtaining modal frequency combined with damping through modal frequency resonance. As a result, the above method cannot be used to further evaluate the effect of structural improvement. In this paper, a frequency difference sensitivity method is proposed in order to improve the efficiency of the above identification and evaluation processes while also guaranteeing accuracy. Firstly, a theoretical model suitable for the damping and rigid-body-mode frequency range of the cooling module is established according to the frequency difference between the excitation frequency, .system mode frequency, and vibration response sensitivity. Then, the accuracy and effect of the model are studied from the perspective of a simulation and experiment. The model can be used to identify and evaluate the resonance problem of the vehicle cooling module quickly and accurately. The energy amplification factor of the fan to the passive end of the cooling module can be efficiently predicted using the frequency difference sensitivity method proposed in this paper while ensuring accuracy. The quantized noise-reduction effect of the interior before and after the improvement can be efficiently predicted and evaluated using said model. The literature shows that the resonance of a vehicle cooling module can be identified and evaluated quickly and accurately via the frequency difference sensitivity method, which can overcome the problems that the conventional modal frequency resonance method encounters in identifying and evaluating quickly.

Bridge modal frequency is an important parameter reflecting its overall property change and widely used for bridge condition assessment. However, the effects of multiple environmental conditions on the modal frequency will mask the variation induced by structural damage. Traditional single regression models cannot quantify measurable and unmeasurable environmental effects simultaneously, resulting in poor prediction and separation performance. Therefore, a two-stage elimination model (TSEM) integrating regression analysis and trend decomposition technique was developed. Environmental principal components (PCs) sensitive to the single-order modal frequency were extracted based on partial least-squares analysis. To quantify the nonlinear effects of measurable environmental factors, the baseline predictor with respect to modal frequency and environmental PCs was constructed through relevance vector machine technology. An error compensation model based on singular spectrum analysis was established to extract trend-related components and remove the part of residual modal variability unknot considered by the baseline model. On this basis, exponential weighted moving average control chart was established to highlight slight abnormal changes in modal frequency. A cable-stayed bridge case verified its validity and accuracy. The results indicate that the proposed TSEM has better modeling, generalization, and separation performance than the baseline model, and the variation of normalized frequency tends to be more stable. Additionally, the significant differences of damage sensitivity of different orders were determined. [ABSTRACT FROM AUTHOR]

Freezing weather can introduce challenges in long-term structural health monitoring of civil structures, particularly bridges. A noticeable impact of freezing temperature is the emergence of sudden and sharp increases in structural modal frequencies, causing false alarm and mis-detection errors in change detection of civil structures. This paper proposes an innovative unsupervised data normalization method to mitigate freezing effects. The proposed method integrates locally robust principal component analysis (LRPCA) with Gaussian density distance (GDD) clustering, called GDD-LRPCA, which automatically determines the number of clusters. Initially, a training set of original modal frequencies is partitioned via the GDD clustering. Subsequently, an individual LRPCA model is fitted to each partition to extract new normalized modal frequencies insensitive to freezing effects. The groundbreaking nature of this research relies on developing an integrated unsupervised data normalizer by leveraging advanced machine learning algorithms such as local learning, robust learning, and hybrid unsupervised learning. The major advantage of the proposed method is its non-parametric nature obviating any supplementary technique for hyperparameter optimization. The validity of this method is benchmarked by real-world bridge structures along with several comparative analyses. Results demonstrate that GDD-LRPCA effectively removes the freezing effects from structural modal frequencies and outperforms its counterparts in unsupervised data normalization. • Proposing an unsupervised data normalizer for removing freezing effects from modal frequencies under statistical learning. • Leveraging cutting-edge machine learning algorithms including local learning, robust learning, and hybrid learning. • Suggesting a non-parametric framework for unsupervised data normalization without any hyperparameter optimization • Lacking the need for temperature sensor installation and measurement for removing freezing effects. [ABSTRACT FROM AUTHOR]

Cylindrical roller bearing is an important component of the airflow root blower of a power generation plant, and its malfunction has been identified as one of the root causes of poor quality demineralized water produced during operation. Hence, there is need to study the dynamic behaviour of a typical cylindrical roller bearing of an airflow root blower. In this study, the dynamic analysis of a cylindrical roller bearing subjected to different rotational speeds was simulated using finite element analysis software, Abaqus. The frequency response of the bearing was determined experimentally and analytically, and the modal frequency results obtained from both analyses were compared. The outcome of the dynamic analysis showed that the maximum temperature and Hertzian stress was developed on the outer ring of the bearing during operation, thus making this component most prone to failure. It was observed that the value of the temperature and stress developed increase with an increase in rotational speed. However, at a rotational speed greater than 503 rad/s, a drop in the Hertzian stress was developed due to the stress relaxation the bearing experience at the higher temperatures. A good agreement was obtained when the modal frequency of the frequency response obtained numerically was compared with those obtained experimentally.

A method to estimate modal frequency based on empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) is proposed. This method can decrease the difficulties in identifying modal frequency of combine harvesters. First, we used 16 acceleration sensors installed at different test points to collect vibration signals of a corn combine harvester under operating conditions (mass time-varying conditions). Second, we calculated mean value, variance and root mean square (RMS) value of the vibration signals, and analyzed its stationarity of vibration signals. Third, the main frequencies of the 16 points were extracted using the EMD and EEMD methods. Finally, we considered modal frequencies identified by the SSI algorithm as standard, and calculated the fitting degrees of the EMD and EEMD methods. The results show that in different time periods (0~60 s and 60~120 s), the maximum differences of the mean value, variance and RMS value of signals were 0.8633, 171.1629 and 11.3767, and the vibration signal under the operating condition of field harvesting can be regarded as a typical non-stationary random vibration signal. The EMD method had more modal aliasing than EEMD, and when we obtained the fitting equations of EMD, EEMD and SSI methods, the value of the Euler distance between the EMD fitting equation and the SSI fitting equation was 446.7883, while that for EEMD and SSI was 417.2845. The vibration frequencies calculated by the EEMD method is closer to the modal frequencies identified by SSI algorithm. The proposed method provides a reference for modal frequency identification and vibration control in a complex working environment. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) has been widely used for the performance assessment of bridges, especially the methods based on dynamic characteristics. Meanwhile, bridge modal frequency is influenced significantly by environmental factors, such as temperature and humidity. Combined with SHM, a reliability assessment of bridges with the temperature and humidity effects eliminated is proposed. Firstly, the bridge deflection verification coefficient is adopted as the evaluation indicator for bridge condition, which is the ratio of deflection-measured value to deflection-calculated value. It is obtained from the relationship between verification coefficient and modal frequency through theoretical derivation. Secondly, a back propagation (BP) neural network is improved by using an artificial bee colony algorithm and employed as a surrogate model to eliminate the effect of temperature and humidity on frequency. Thirdly, a dynamic Bayesian network is applied to establish the reliability analysis model combined with the monitoring results, so that the probability distribution of bridge parameters is updated to improve the accuracy of the reliability analysis. Finally, a simply supported bridge is used as the case study, based on the proposed method in this work. The results indicate that the proposed method can eliminate the temperature and humidity effect on frequency precisely and effectively. With the effect of temperature and humidity on frequency eliminated, the bridge condition assessment can be evaluated accurately through the reliability analysis based on SHM and the dynamic Bayesian network. [ABSTRACT FROM AUTHOR]

Cylindrical roller bearing is an important component of the airflow root blower of a power generation plant, and its malfunction has been identified as one of the root causes of poor quality demineralized water produced during operation. Hence, there is need to study the dynamic behaviour of a typical cylindrical roller bearing of an airflow root blower. In this study, the dynamic analysis of a cylindrical roller bearing subjected to different rotational speeds was simulated using finite element analysis software, Abaqus. The frequency response of the bearing was determined experimentally and analytically, and the modal frequency results obtained from both analyses were com- pared. The outcome of the dynamic analysis showed that the maximum temperature and Hertzian stress was developed on the outer ring of the bearing during operation, thus making this component most prone to failure. It was observed that the value of the temperature and stress developed increase with an increase in rotational speed. However, at a rotational speed greater than 503 rad/s, a drop in the Hertzian stress was developed due to the stress relaxation the bearing experience at the higher tempera- tures. A good agreement was obtained when the modal frequency of the frequency response obtained numerically was compared with those obtained experimentally. [ABSTRACT FROM AUTHOR]

Metallic-ceramic functionally graded materials have potential application value in the design of thermal barrier systems for aircraft panels due to their ultrahigh temperature resistant and high strength properties. In this article, the FGMs plate was used as the object to study the influence of parameters such as the volume fraction index, the geometric size of the plate and the thermal environment on the modal frequencies of a FGMs plate. Firstly, the power law distribution function was employed to discuss the influence of thermal environment on the physical properties of FGMs plates. Thereafter, the FGMs linear layered model dependent on temperature field was established by using the temperature continuously changing with the spatial position trait in the finite element, and the validity of this model in dynamic analysis was verified. Finally, the effects of ceramic volume fraction index, FGMs plate length-to-width ratio, temperature gradient and other variables on the modal frequencies of a FGMs plate were comprehensively analyzed and discussed. Results indicate that the higher order modes are mostly impacted by the uniform temperature field, while the linear and nonlinear temperature fields have the greatest impact on the first-order modes. In linear and nonlinear temperature fields, the volume fraction index is the most sensitive one to the effects of modal frequency drop ratio, while the modal frequency drop ratio is mainly affected by the coupling effect of the volume fraction index and the temperature gradient in uniform temperature field.

In this article, a magnetic suspension technique was introduced into the field of vibration absorption. Using the advantage of adjustable control parameters of a magnetic suspension system, a type of a magnetic suspension dynamic vibration absorber that can achieve broadband vibration suppression was designed. First, the theoretical model of a magnetic suspension dynamic vibration absorber was established. Then, the cantilever beam with sinusoidal excitation is seen as the main system of vibration suppression; combined with the fixed point theory (Seto K (2013) Dynamic Vibration Absorber and its Application. Mechanic Industry Press), the specific structure of the magnetic suspension dynamic vibration absorber was designed. Based on that, the simulation study of vibration suppression performance of the magnetic suspension dynamic vibration absorber was carried out. The results indicated that the vibration of the main system at the 1st modal frequency was reduced by 65.38% under the action of the magnetic suspension dynamic vibration absorber, compared with that without the action of the magnetic suspension dynamic vibration absorber. Furthermore, the vibration of the main system can be suppressed in the frequency band of [16 Hz, 32 Hz]. Finally, a vibration test rig of the magnetic suspension dynamic vibration absorber was built up for experimental study. And the results showed that the absorber can decrease the vibration of the main system by 43.03% at the 1st modal frequency compared with that without the action of magnetic suspension dynamic vibration absorber and had a certain suppression effect (decrease varies from 0 to 43.03%) on the vibration of the main system in the frequency band of [20 Hz, 32 Hz]. [ABSTRACT FROM AUTHOR]

Modal frequencies are often used in structural model updating, based on the finite element model, while the metamodel approach is often used in the respective optimization process. In this work, the Kriging model is adopted as the metamodel. First, the influence of different correlation functions of Kriging model is inspected, followed by the investigation of the approximate capability of Kriging model by inspecting the approximate accuracy of nonlinear functions. Next, a model updating procedure is proposed, based on the Kriging model, constructed using samples generated via the method of Optimal Latin Hypercube. Finally, a typical frame structure is taken as a case study, demonstrating the feasibility and efficiency of the proposed approach. The results show that, the Kriging model can match the target functions very well, while the finite element model can achieve accurate frequencies and can reliably predict the frequencies after model updating. [ABSTRACT FROM AUTHOR]

In field harvesting conditions, the non-stationary random vibration characteristics of the harvester are rarely considered, and the results of vibration frequency calculated by different time–frequency transformation methods are different. In this paper, the harvester’s vibration characteristics under the time-varying mass were studied, and the correlation between vibration frequency and modal frequency was analyzed. Firstly, under the conditions of time-varying mass (field harvesting conditions) and non-time-varying mass (empty running condition), the non-stationarity characteristics of vibration signals at 16 measurement points of a combined corn harvester frame were studied. Then, fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT) were used to calculate the vibration frequency distribution characteristics of the corn harvester. Finally, based on the EFDD (enhanced frequency domain decomposition) algorithm, the correlation between the primary vibration frequency and the operating mode frequency is studied. The results show that the mean, variance, and maximum difference of the vibration amplitude under harvesting conditions (mass time-varying system) are 0.10, 26.5, and 1.0, respectively, at different harvesting periods (0~10 s, 10~20 s, 20~30 s). The harvesting conditions’ vibration signals conform to the characteristics of non-stationary randomness. The FFT algorithm is used to obtain more dense vibration frequencies, while the frequencies based on STFT and CWT algorithms are sparse. The correlation between the FFT method and the EFDD algorithm is 0.98, and the correlation between the STFT, CWT, and the EFDD algorithm is 0.99 and 0.98. Therefore, the primary frequency of the STFT methods is closer to the modal frequency. Our research laid the foundation for further study and application of mass time-varying combined harvester system non-stationary random vibration modal frequency identification and vibration control.

Quantifying the uncertainty in the dynamic properties of large-scale complex engineering structures presents significant computational challenges. Monte Carlo simulation (MCS) method is extensively employed to perform uncertainty quantification (UQ) because of its generality, stability, and easy implementation. However, a brute-force MCS approach may be unaffordable and impractical when the target model contains a large number of uncertain parameters. In this circumstance, MCS requires a potentially burdensome (if not computationally intractable) number of model evaluations to obtain a credible estimate of the global statistics. In this study, a general framework for analytical UQ of model outputs using a Gaussian process (GP) metamodel is presented, where case inputs are characterized as normal and/or uniform random variables. A detailed derivation of important low-order statistical moments (mean and variance) is given analytically. This analytical method is adopted to characterize the uncertainty of modal frequencies of two bridges with assumed normally- and uniformly-distributed parameters. Meanwhile, the brute-force MCS approach is used for comparison of GP metamodel-derived statistics. Results show that the GP method outperforms the MCS methodology in terms of computational cost, with consistency in the "true" values obtained by MCS. It demonstrates that this GP method is feasible and reliable for modal frequency UQ of complex structures. © 2014 Elsevier Ltd.

Quantifying the uncertainty in the dynamic properties of large-scale complex engineering structures presents significant computational challenges. Monte Carlo simulation (MCS) method is extensively employed to perform uncertainty quantification (UQ) because of its generality, stability, and easy implementation. However, a brute-force MCS approach may be unaffordable and impractical when the target model contains a large number of uncertain parameters. In this circumstance, MCS requires a potentially burdensome (if not computationally intractable) number of model evaluations to obtain a credible estimate of the global statistics. In this study, a general framework for analytical UQ of model outputs using a Gaussian process (GP) metamodel is presented, where case inputs are characterized as normal and/or uniform random variables. A detailed derivation of important low-order statistical moments (mean and variance) is given analytically. This analytical method is adopted to characterize the uncertainty of modal frequencies of two bridges with assumed normally- and uniformly-distributed parameters. Meanwhile, the brute-force MCS approach is used for comparison of GP metamodel-derived statistics. Results show that the GP method outperforms the MCS methodology in terms of computational cost, with consistency in the "true" values obtained by MCS. It demonstrates that this GP method is feasible and reliable for modal frequency UQ of complex structures. © 2014 Elsevier Ltd.

A method to estimate modal frequency based on empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) is proposed. This method can decrease the difficulties in identifying modal frequency of combine harvesters. First, we used 16 acceleration sensors installed at different test points to collect vibration signals of a corn combine harvester under operating conditions (mass time-varying conditions). Second, we calculated mean value, variance and root mean square (RMS) value of the vibration signals, and analyzed its stationarity of vibration signals. Third, the main frequencies of the 16 points were extracted using the EMD and EEMD methods. Finally, we considered modal frequencies identified by the SSI algorithm as standard, and calculated the fitting degrees of the EMD and EEMD methods. The results show that in different time periods (0~60 s and 60~120 s), the maximum differences of the mean value, variance and RMS value of signals were 0.8633, 171.1629 and 11.3767, and the vibration signal under the operating condition of field harvesting can be regarded as a typical non-stationary random vibration signal. The EMD method had more modal aliasing than EEMD, and when we obtained the fitting equations of EMD, EEMD and SSI methods, the value of the Euler distance between the EMD fitting equation and the SSI fitting equation was 446.7883, while that for EEMD and SSI was 417.2845. The vibration frequencies calculated by the EEMD method is closer to the modal frequencies identified by SSI algorithm. The proposed method provides a reference for modal frequency identification and vibration control in a complex working environment.

This paper examines the influence of the equipment considered as a DVA (Dynamic Vibration Absorber) upon the mode of vertical vibrations of the car body in high-speed vehicles. The car body is represented as an Euler-Bernoulli beam to minimize flexible vibration. The DVA approach is used to find the appropriate suspension frequencies for various types of equipment. A vertical mathematical model with a flexible car body and equipment is developed to investigate the effect of equipment mass, suspension stiffness, damping, and mounting location on car-body flexible vibrations. A three-dimensional, rigid-flexible coupled vehicle system dynamics model is developed to simulate the car body and equipment’s response to track irregularities. The experimental result was considered to verify the theoretical analysis and dynamic simulation. The mathematical analysis demonstrates that the DVA theory can be used to design the suspension parameters of the equipment and that it is suitable and effective in reducing the flexible vibration of the car body in which the vertical bending mode is greatly affected. Heavy equipment should be mounted as close to the car body’s center as possible to achieve significant flexible vibration reduction, whereas light equipment contributes very little flexible vibration reduction.

Structural health monitoring represents an efficient way to diagnose the condition of cable-stayed bridges. Most studies assessing the condition of cable-stayed bridges and detecting damage to them have been developed to monitor the longitudinal performance of bridge bearings. However, few studies have aimed to detect the damage to tension pendulums, which are usually tie-down cables that resist girder uplift from auxiliary piers. This study aims to develop an effective method for detecting the damage of tension pendulums in cable-stayed bridges using structural modal frequencies. First, the sensitivity of the bridge frequency to tension pendulum damage is derived according to the Rayleigh method. Then, a finite-element simulation of a cable-stayed bridge is conducted to validate the rationality of the frequency index. Finally, a case study on tension pendulum damage is carried out for the cable-stayed Yonghe Bridge. The results indicate that the frequency change is far more sensitive to the damage of the tension pendulums than to the damage of the stay cables. The failure of tie-down cables will result in a substantial decrease in the bridge frequency, up to approximately 35% for the first vertical bending mode of the bridge. In practice, the damage of tension pendulums can be effectively detected by a sudden decrease in the measured frequency of cable-stayed bridges. [ABSTRACT FROM AUTHOR]

In the vibration based structural health monitoring (VBSHM) field, the modal frequency of a structure is commonly used as an indicator for the global health condition of the structure. However, field measurements have shown that the modal frequency of a bridge varies with structural anomalies and the operational and environmental actions, e. g., temperature and traffic loading. Moreover, the latter variation usually exceeds the frequency shifts induced by the small and medium structural anomalies. To highlight the anomaly-induced frequency changes, the variability of modal frequencies of bridges with the operational and environmental actions must be investigated, and then, the action-induced frequency variations need to be eliminated. According to the periodic characteristics of the six-year monitoring data of the Donghai Bridge, this research identified the main actions that affected the modal frequencies of the first vertical/lateral bending modes and torsional mode of the girder of this bridge, and further, it compared the relative contributions of actions to the variability of frequencies through the partial correlation coefficients and the proposed cyclic averaging method. The results show that the modal frequencies of the Donghai Bridge vary at cycles as 1 a, 1 week, 1 d, and 12.42 h, which coincide with the inherent predominant cycles of structural temperature, traffic loading, wind loading, and sea levels, respectively. Structural temperature and traffic loading are the most influential factors for the frequency variation, and their relative importance is different for each individual cycle. The results also show that the cyclic averaging method can effectively separate the components in periods of 1 a, 1 week, and 1 d and can disclose the inherent correlation between actions and modal frequencies. This study helps in enhancing the understanding of the frequency variability for operational bridges and may lead to a more reliable evaluation of structural performance.

[Objectives] In order to improve the overall bending mode frequency of the structure and reduce the acceleration level at the end of the stiffened cone in the low frequency range, a mathematical model of a multi-objective optimization design for the vibration characteristics of a stiffened conical shell is established. [Methods] Finite element software ANSYS is used to model a vertical and horizontal stiffened conical shell. The vibration modal frequency and structural response under the vertical downward unit concentrated force at the end of the stiffened conical shell are analyzed. Based on Matlab, the vibration characteristics of the stiffened conical shell are optimized by a genetic algorithm and the tolerance sorting method. [Results] The results show that with the increase of tolerance and target weight, the acceleration level of the optimal structural scheme decreases. With single objective optimization for the same target value, there can be multiple schemes. [Conclusions] The research results of this paper can provide useful references for the acoustic design of reinforced conical shell structures.

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Fine grain particles such as sugar, sand, salt etc. form Chladni patterns on the surface of a thin plate subjected to acoustic excitation. This principle has found its relevance in many scientific and engineering applications where the displacement or response of components under the influence of vibration is vital. This study presents an alternative method of determining the modal shapes on vibrating plate in addition to other existing methods like the experimental method by Ernst Chladni. Three (3) finite element solvers namely: CATIA 2017 version, ANSYS R15.0 2017 version and HYPERMESH 2016 version were employed in the modelling process of the 0.40 mm x 0.40 mm plate and simulation of corresponding mode shapes (Chladni patterns) as well as the modal frequencies using Finite Element Method (FEM). Result of modal frequency obtained from the experimental analysis agreed with the FEM simulated, with HYPERMESH generated results being the closest to the experimental values. It was observed that the modal frequencies obtained from the FEM and experimental approach increased as the excitation time increased. ANSYS R15.0 and HYPERMESH software clearly represented the modal lines and mode shapes for each frequency which CATIA software was somewhat limited. This study has shown that FEM is an effective tool that can save time and energy invested in acoustic experiments in determining modal frequencies and patterns. [ABSTRACT FROM AUTHOR]

Dynamic response control of a wind-excited tall building installed with distributed multiple tuned mass dampers (d-MTMDs) is presented. The performance of d-MTMDs is compared with those of single tuned mass damper (STMD) and MTMDs installed at top of the building. The modal frequencies and mode shapes of the building are first determined. Based on the mode shapes of the uncontrolled and controlled building, the most suitable locations are identified for the dampers, in that the TMDs are placed where the modal amplitude of the building is the largest/larger in a particular mode, with each tuned to the modal frequency of the first five modes. The coupled differential equations of motion for the system are derived for the cases with the STMD, MTMDs, and d-MTMDs and solved numerically. Extensive parametric studies are conducted to compare the effectiveness of the three control schemes using STMD, MTMDs, and d-MTMDs by examining the variations in wind-induced responses. The mass ratios, damping ratios of the devices, number of TMDs, and robustness of the TMDs are the parameters of investigation. It is concluded that the MTMDs exhibit improved performance when compared with the STMD. The use of d-MTMDs is most efficient among the three schemes because it can effectively control wind-induced response of the building, while reduced space is required in the installation of the TMDs, as they are placed at various floors. [ABSTRACT FROM AUTHOR]

A modified masking empirical mode decomposition (EMD) for effectively improving the mode separation capability of standard EMD while analysing power system signals with closely spaced modes of frequency is proposed here. A multi‐frequency test signal resembling the dynamic power system signal and the actual data recorded by wide area measurement systems (WAMS) from Northern Grid, India, on 1 June 2010 due to generation loss are analysed by both the existing method and the proposed method. Various components of modal frequency extracted by masking signal base EMD are compared with extracted components by the proposed modified masking EMD. Further, the time–frequency representation of extracted modes by Hilbert spectral analysis is implemented to know mode behaviour with time reference. Simulation results prove that the EMD with proposed modification is capable of separating various modes of frequencies present in the WAMS signal. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposes a two-stage damage detection method for truss structures. • First stage focused on the damage localization and in the second stage, the damage severities are evaluated. • To localize the suspected damaged elements, using the concept of residual force vector, a new index is proposed. • To evaluate the damage severities, the damage detection problem formulated as an optimization problem and solved by GA. Abstract Use of optimization search algorithms is recognized as an efficient method for solving structural damage identification problems. Although these algorithms demonstrated their robustness to identify the location and extent of multiple damages in structural systems, they impose so much computational efforts to the damage assessing process that it reduces their attraction. In this paper by utilizing the concept of residual force vector, an efficient approach based on a Truss Element Damage Index (TEDI) is defined to assist in a fast and reliable prediction of damaged elements. Based on the proposed technique, the first step focuses on location detection of most probable damaged members. The healthy members will then be eliminated from the total list of variables. This can reduce the computational effort significantly. In the second step to identify damaged locations and severities, the Genetic Algorithm is employed to search for the optimum solution in the new search space resulted from the first step. Three test examples are considered to investigate the efficiency of proposed method for damage identification. [ABSTRACT FROM AUTHOR]

This study investigates the relationship between the temperature and the modal frequencies of bridges through a series of model experiments using a concrete continuous beam bridge model and a steel cable-stayed bridge model in a controlled-temperature chamber. The experimental results show that, for a given boundary condition and in the absence of freezing, a change in temperature affects the structural frequencies of the bridge as it alters the elastic modulus of the bridge materials. The structural frequency tends to linearly decrease with increasing temperature and with the decrease in the frequency of steel bridges smaller than that of concrete bridges. For the particular case of wet concrete bridges, the temperature dependencies of modal frequencies vary dramatically near the freezing point, which is attributable to the freeze–thaw process of concrete pore water. The effect of air humidity on structural frequency is less significant than that of temperature when the boundary conditions remain unchanged. Furthermore, temperature changes may alter the boundary conditions of bridges, thereby affecting the structural frequencies. [ABSTRACT FROM AUTHOR]

• A case study for failure scenarios assessment in a steel truss railway bridge is described. • Monitoring results are given in terms of deflections and modal frequencies. • Finite Element Analysis (FEA) was validated to simulate failure scenarios. • The most severe failure scenarios were identified. • Long-term monitoring recommendations for failure detection is proposed. The latest studies on failures in steel truss-type bridges found that they are highly vulnerable to damage and thus prone to potential local or total collapse. Many authors recommend monitoring the critical elements in the existing steel truss-type bridges in real time to anticipate any failures in local members. Although mechanical strain is the most frequently used variable for this purpose, this method also happens to be the most expensive monitoring strategy. This paper describes a case study of failure scenarios assessment in a steel truss-type railway bridge after extensive long-term monitoring conducted by the authors, based on measuring vertical deflections and modal frequencies. The structure has both an isostatic and a hyperstatic configuration, and was assessed by means of a combination of: (i) long-term monitoring results, and (ii) a finite element analysis to simulate several failure scenarios. A sensitivity study of the different failure scenarios has been carried out, identifying those that can be detected. The results are used to define practical recommendations for failure detection by measuring vertical deflections and modal frequencies. [ABSTRACT FROM AUTHOR]

The structural health monitoring of power transmission towers (PTTs) has drawn increasing attention from researchers in recent years; however, no long-term monitoring of the dynamic parameters of PTTs has previously been reported in the literature. This study performed the long-term monitoring of an instrumented PTT. An automated subspace identification technique was used to extract the dynamic parameters of the PTT from ambient vibration measurements taken over approximately ten months in 2017. Ten target modal frequencies were selected to explore the effects of environmental factors, such as temperature and wind speed, as well as the root-mean-square (RMS) acceleration response of the PTT. Variations in the modal frequencies of approximately 2% to 8% were observed during the study period. In general, among the environmental factors, the temperature was found to be the primary cause of decreases in the modal frequencies, except in the case of some of the higher modes. Typhoon Nesat, which affected the PTT on July 29th, 2017, seems to have decreased the modal frequencies of the PTT, especially for the higher modes. This reduction in the modal frequencies seems to have lasted for approximately two and a half months, after which they recovered to their normal state, probably due to a seasonal cool down in temperature. The reduction percentages in the modal frequencies due to Typhoon Nesat were quantified as approximately −0.89% to −1.34% for the higher modes, but only −0.07% to −0.46% for the remaining lower modes. Although the unusual reductions in the modal frequencies are reported in this study, the reason for this phenomenon is not clear yet. Further studies would be required in the future in order to find the cause.

Vision-based techniques are frequently used to compute the dynamic deflections of bridges but they are rather computationally complicated and require demanding instrumentation. In this article, we show that it is possible to reconstruct the 2-D kinematics of flexible bridges using a simplified algorithm to analyze common video imagery. The only requirements are that the movement of the control points is clearly visible on the images and that next to each control point, there exist vertical and horizontal bridge elements defining the image scale. We applied this technique during controlled, forced excitations of a timber bridge that was stiff in the vertical but very flexible in the lateral axis because of cumulated damage. We used videos from low-cost cameras, in which the changes of the pixel coordinates of several control points during excitation events and their attenuation were clear. These videos were obtained during two annual structural health monitoring surveys using numerous sensors (Global Navigation Satellite Systems (GNSS), robotic total station (RTS), accelerometers), and hence the output of the video analysis was fully controlled. Because of various errors, the transformation of the video image coordinates into bridge coordinates yielded spurious deflections along the main axis of the bridge, which were used to control the uncertainty of our results. We found that the computed lateral deflections (i) were statistically significant, (ii) satisfied structural constraints, and (iii) were consistent with structural estimates derived from other sensors. Additionally, they provided accurate estimates of the natural frequency and the damping factor of the bridge. This approach can be applied in other cases of monitoring of flexible structures if the requirements for planar deformation, pixel resolution and scale definition are satisfied.

The modal frequencies of a structure are affected by continuous changes in ambient factors, such as temperature, wind speed etc. This study incorporates nonlinear principal component analysis (NLPCA) with support vector regression (SVR) to build a mathematical model to reflect the correlation between ambient factors and modal frequencies. NLPCA is first used to eliminate the high correlation among different ambient factors and extract the nonlinear principal components. The extracted nonlinear principal components are input into the SVR model for training and predicting. The proposed method is verified by the measured data provided in the Guangzhou New TV Tower (GNTVT) Benchmark. The grid search method (GSM), genetic algorithm (GA) and fruit fly optimization algorithm (FOA) are applied to determine the optimal hyperparameters for the SVR model. The optimized result of FOA is most suitable for the NLPCA-SVR model. As evaluated by the hypothesis test and goodness-of-fit test, the results show that the proposed method has a high generalization performance and the correlation between the ambient factor and modal frequency can be strongly reflected. The proposed method can effectively eliminate the effects of ambient factors on modal frequencies.

In this article, the mechanical properties of large-scale rack structures are analysed by MSC Marc analysis software is verified through the modal test. The modal frequency and modal shape are obtained through the finite element analysis and LMS data acquisition system for modal test verification. It is showed that the modal shape of the modal test and the calculation by finite element analysis are consistent, which verifies the inherent characteristics of the frame structure effectively and provides reliability parameters of the manipulator for the space station in the zero-gravity test.

To obtain some basic laws for bird-strike resistance of composite materials in aeronautical application, the high-velocity impact behaviors of composite laminates with different materials were studied by numerical methods. The smoothed particle hydrodynamics (SPH) and finite element method (FEM) coupling models were validated from various perspectives, and the numerical results were comparatively investigated. Results show that the different composite materials have relatively little effect on projectile deformations during the bird impact. However, the impact-damage distributions can be significantly different for different composite materials. The strength parameters and fracture energy parameters play different roles in different damage modes. Lastly, modal frequency was tentatively used to explain the damage behavior of the composite laminates, for it can manifest the mass and stiffness characteristics of a dynamic structure. The dynamic properties and strength properties jointly determine the impact-damage resistance of composite laminates under bird strike. Future optimization study can be considered from these two aspects.

This paper aims to develop a new probabilistic monitoring-based framework for damage detection of long-span bridges, by eliminating the temperature effects from the measured modal frequencies, probabilistic modeling of modal frequencies using kernel density estimate, and detection damage using the control chart. A methodology is presented to address the issue of modal frequencies' non-normal distribution, which has been neglected in the past studies using the control chart to detect the modal frequencies' abnormality caused by structural damages. The efficiency of the proposed framework is validated through a case study of long-term monitoring data of a long-span suspension bridge. The results show that after elimination of the temperature effects, the selected modal frequencies are not normally distributed, while the Q statistics transferred from the modal frequencies follow the standard normal distribution. The abnormality of modal frequencies can be detected when the data points of the Q statistics exceed the limits of the control chart. Further, the control chart has sufficient sensitivity and thus can be used to detect minor abnormalities of the prototype bridge's modal frequencies. It is concluded that the proposed probabilistic monitoring-based framework offers an effective technique for structural health monitoring of long-span bridges. [ABSTRACT FROM AUTHOR]

To identify the location and severity of structural damages precisely, a two-stage damage detection method is proposed here. In the first stage, the most probable elements that maybe damaged are determined using the modal strain energy concept of structure. For such purpose, an efficient modal strain energy conversion-based index is proposed. In the second stage, the structural damage identification problem is defined as an optimization problem that to be solved by a modified genetic algorithm. In the optimization problem, the damage extents of structure’s elements which are determined in the previous stage are considered as the variables. An efficient objective function considering the first few modal frequencies of the structure, before and after damage occurrence, is utilized for optimization. The robustness of the proposed method is assessed by several benchmark examples. The numerical results exhibit the effectiveness of the proposed method for precisely determining the location and severity of multiple structural damages. [ABSTRACT FROM AUTHOR]

High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes (k ≤ 12) are solvable for i-step (i ≥ 0) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory. [ABSTRACT FROM AUTHOR]

• Proposing a novel unsupervised meta-learning method for long-term SHM with large data and profound environmental effects. • Proposing a locally unsupervised feature selection approach called nearest cluster selection. • Proposing a locally robust Mahalanobis distance via local metric learning and robust statistics for anomaly detection. • Accurate warning of damage occurrence under severe environmental variability caused by freezing weather. Long-term monitoring brings an important benefit for health monitoring of civil structures due to covering all possible unpredictable variations in measured vibration data and providing relatively adequate training samples for unsupervised learning algorithms. Despite such merits, this process may encounter large data with missing values and also yield erroneous results caused by severe environmental changes, particularly those emerge as sharp increases in modal frequencies during freezing weather. To address these challenges, this article proposes a novel unsupervised meta-learning method that entails four steps of an initial data analysis, data segmentation, subspace searching by a novel approach called nearest cluster selection, and anomaly detection. The first step intends to initially analyze measured data/features for cleaning missing samples. Next, the second step exploits spectral clustering to divide clean data into some segments. In the third step, the proposed nearest cluster selection is utilized to measure dissimilarities between the segments by a distance metric and select a cluster with the minimum distance as the representative of the main segment. Finally, a locally robust Mahalanobis-squared distance is applied by merging the concepts of robust statistics and local metric learning for online anomaly detection. The key innovations of this research contain developing a new unsupervised learning strategy alongside a locally robust distance and proposing the idea of nearest cluster selection. Long-term modal frequencies of full-scale concrete and steel bridges are used to verify the proposed method. Results demonstrate that this method succeeds in mitigating severe environmental effects and accurately detecting damage. [ABSTRACT FROM AUTHOR]

The paper deals with the results of an experimental campaign carried out on a post tensioned concrete beam with the aim of investigating the possibility to detect early warning signs of deterioration based on static and/or dynamic tests. The beam was tested in several configurations aimed to reproduce 5 different phases of the ‘life’ of the beam: in the original undamaged state, under increasing loss of tension in the post tensioning cables, during and after the formation of cracks at mid span, after a strengthening intervention carried out by means of a second tension cable, during and after the formation of further cracks on the strengthened beam. Responses of the beam were measured by an extensive set of instruments consisting of accelerometers, inclinometers, displacement transducers, strain gauges and optical fibers. In this paper data from accelerometers and displacement transducers have been exploited. The paper presents the test program and the dynamic characterization of the beam in the different damage scenarios in terms of the first modal frequency, identified from dynamic tests and of the bending stiffness monitored during static tests. [ABSTRACT FROM AUTHOR]

The transformation of a 30 m long timber pedestrian bridge into a wobbly (laterally swaying) bridge with a dramatically reduced first lateral modal frequency has been monitored by seven annual, multi-sensor surveys. This evidence, in combination with analysis of the wind record, observations of local damage and evidence of wind-induced excitations from other bridges, is used to present a multi-stage scenario of the extraordinary structural weakening of our study bridge in only a few years. Our analysis is constrained by observations of asymmetric damage (longitudinal splitting cracks around metallic connections along the south side of the deck, not explained by ordinary, essentially symmetric lateral oscillations) and over-threshold analysis of strong northerly wind events, including gusts. The proposed scenario is that an unexpected for the area icing event took advantage of construction vicissitudes and produced damage that reduced the lateral stiffness of the bridge, especially of the arch superstructure. In addition, strong winds sharing common direction with gusts produced a combination of semi-static lateral bending and of dynamic oscillations, leading to numerous cycles of asymmetric high amplitude lateral deflections producing tensile stress normal to grain, cracks localized in connections, and fatigue. The vertical stiffness of the bridge was only slightly affected.

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. [ABSTRACT FROM AUTHOR]