Changes In Natural Frequencies Research Articles

Development of Environmental Monitoring Sensor for Steel Corrosion in Concrete based on Micro-Electro-Mechanical Systems (MEMS)

Many bridges located near marine environments usually have high risk to lose their structural performance due to corrosion of reinforcing bars with chloride attack. While a huge amount of budget to maintain may be consumed for the structural maintenance methodologies, an efficient monitoring system for Reinforced Concrete (RC) structures in the corrosive environment is strongly demanded. Thus, structural health monitoring in real situations is significant for bridge asset management. The alternative way for preventing severe damage propagation is proactively monitoring the environmental condition containing chloride ion and its effect on the durability of concrete structures, for which numerous methods have been conventionally suggested such as dry gauze method to capture chlorides in air. In this study, Micro Energy Harvester (MEH) based on Micro-Electro-Mechanical Systems (MEMS) is technically applied to develop a sensor to identify the corrosion environment with chlorides in the exposure condition. MEMS is a rapidly evolving device, which enables to monitor the changes in natural frequency and amplitude at nodal locations of the targeting structure due to vibration-based electrostatic power generation induced by the corrosive environment. The purpose of this research is to develop a system for detecting the high corrosion-prone areas and finding the suitable metal sheet material for various chloride ion conditions, using the metal sheet as a cantilever structure for the MEMS device. 4 types of metal, aluminium, copper, iron and zinc are considered for the parametric experiments. Several scenarios are considered including chloride ion concentration, temperatures, and wet and dry conditions to compare the dominant frequency changes of each metal sheet and determine their sensitivity to corrosion environment. From the preliminary results, iron and zinc have a significant drop in frequency with the elapsed exposure period, which indicates that they are highly sensitive to the external chloride ion environment. These results offer an innovative and proactive approach to structural health monitoring for further developed applications. It enables prompt maintenance and early detection of potential issues for corrosion of steel bars in concrete, ensuring the longevity and safety of RC bridge structures.

The study of the natural frequency evolution and numerical simulation of retrogressive landslides

A retrogressive landslide is influenced by the cyclical fluctuations in reservoir water levels is considered a common natural disaster. Tension cracks are important indicators for assessing landslide status in the case of retrogressive landslides. Displacement monitoring is a commonly used method and provides an intuitive reflection of the landslide deformation; however, it does not directly indicate the depth of the tension cracks. Based on the principles of vibrational dynamics, a retrogressive landslide is proposed to be initially classified as a single-mass spring oscillator model before the development of cracks. Following the development of tension cracks, the model can be classified as a double-mass spring oscillator model. The model patterns are verified through numerical simulations using ABAQUS. Based on the numerical simulations, with an increase in the number of reservoir water cycle fluctuations, the displacement and stress of the landslide exhibit periodic growth. However, during displacement growth, the tension cracks do not necessarily increase. As the tension cracks deepen, the landslide transitions from a single-mass spring oscillator model to a double-mass spring oscillator model, with the appearance of a second-order natural frequency. Moreover, as the tension cracks deepen, the numerical values of the natural frequency change. The maximum change in first-order natural frequency is 3.5 Hz. The maximum change in second-order natural frequency is 4.5 Hz. The variation in the natural frequency can reflect the depth of development of the landslide's tension cracks and, consequently, indicate changes in the stability state of the landslide.

Change of Natural Oscillation Frequencies of Buildings and Structures Depending on External Factors

Abstract —This work is devoted to the development of the engineering seismic monitoring method created in Geophysical Survey of the Russian Academy of Sciences (GS RAS). In previous years, the “method of standing waves” was created and put into practice. It helps to separate natural oscillation modes of buildings and other engineering structures. The natural oscillations of hundreds of various objects (buildings, bridges, dams, etc.) had been studied and identified. We assumed that the physical condition of studied constructions could be controlled during exploitation by measuring the changes of natural oscillation frequencies. That would help to identify the appearance of defects in constructions, to prevent the risk of their destruction. However, it turned out that not everything is that simple: changes in frequency values are logically affected by changes in the environment around the studied objects. This article provides examples of these relations, influence of changes in environmental temperature, mass of objects and precipitation on the frequencies of natural oscillations.

Vibration-based detection of non-overlapping delaminations in FRP beams using frequency shifts

Extensive research has been carried out on the detection of single delamination in fibre-reinforced polymer (FRP) structures using different structural health monitoring (SHM) approaches, including the vibration-based assessment methods. However, there are limited studies that on the detection of multiple delaminations, which could occur in many real-world scenarios. To address this research gap, this paper aims at developing a vibration-based method to assess the two non-overlapping delaminations in FRP beams based on changes in natural frequencies. A theoretical model of vibrating FRP beams with two non-overlapping delaminations was constructed and used for generating the multiple frequencies of the delaminated beams. By analysing the frequency shifts of the FRP beams before and after the occurrence of damage, the delamination characteristics (location and severity) can be inversely predicted using optimisation algorithms. The accuracy and efficiency of the frequency-based inverse algorithm were verified experimentally by modal testing on FRP beam specimens with one and two non-overlapping delaminations. It is interesting to observe that using the proposed vibration-based method, the single delamination in FRP specimens can also be predicted as two non-overlapping delaminations, with a major one matching the original single delamination and a minor one that can be neglected. Thus, the current vibration-based delamination assessment approach is flexible in identifying the prediction of either single or double non-overlapping delaminations in FRP beams, and therefore, it potentially has wider applicability than the existing single delamination detection methods.

Prediction of multiple transverse cracks in a composite beam using hybrid RNN-mPSO technique

The presence of faults is common in engineering composite structures. Precise detection of faults prior to failure has been the focal point for researchers working in this domain. Detection of damage from the modal characteristics is an age-old promising technique besides the artificial intelligence techniques such as neural network (NN), Artificial neural network (ANN), recurrent neural network (RNN), and particle swarm optimization (PSO) methods. However, multiple detection techniques combined can give better results. In this regard, recurrent neural networks (RNN) and modified particle swarm optimization (mPSO) are combined to detect damages in a glass fiber reinforced polymer (GFRP) composite cantilever beam. The proposed hybrid model consists of two stages; indices of relative natural frequencies applied to locate crack parameters (position and severity) by recurrent neural network technique and optimization of the results (position and severity) by mPSO. The results illustrate this method can be implemented to predict multiple transverse cracks and their parameters in a composite beam, manifested in the change of natural frequencies where the error is limited to 0.97% only.

Nonlinear dynamic modelling and analysis of a rotating composite thin-walled beam considering ice coating

For rotating structures operating in severe weather conditions, ice coating phenomenon is an established issue that impairs the reliability and effectiveness of the structures by changing the dynamic behaviors. To explore the influence mechanisms of ice coating on the dynamic behaviors of rotating structures, this work presents an analytical dynamic model for nonlinear forced vibration of a composite thin-walled beam under both rotating and ice coating conditions. The ice coating is considered as C-shaped configuration which can affect the system parameters of the beam, especially aerodynamic performance. With effect of out-of-plane warping taken into account, the nonlinear dynamic equation of the beam is established using Hamilton's principle. The Galerkin discrete method together with the incremental harmonic balance method (IHB) as well as pseudo arclength continuation technique are adopted to obtain the periodic response of the nonlinear system. Then, a detailed parametric study on natural frequency, frequency-response and bifurcation behaviors is numerically conducted. Special attention is paid to the effects of ice coating, rotating angular velocity, inflow velocity and design parameters on the linear and nonlinear dynamic behaviors of the beam. Results reveal a prominent change in natural frequency, vibration amplitude and cusp bifurcation of multivalued region under the combined effects of ice coating and rotating motion. Such ice-induced changes exhibit the requirement of vibration control and optimization design consideration for rotating structures operating in icing coating conditions.

Dynamic characteristics of stone masonry walls before and after damage: Experimental and numerical investigations

Seismic behavior of masonry walls has been heavily investigated, especially by means of laboratory experiments employing cyclic tests to determine the mechanical parameters and seismic capacity. Nevertheless, the dynamic properties of the tested walls often remain unknown, even though the nature of the seismic response is dynamic and profoundly affected by the structure's dynamic properties. This paper presents an investigation on the dynamic properties of three different masonry wall panels in healthy and damaged states, and examines if damage quantification via tracking the changes in dynamic properties is feasible. Ambient vibration and impact measurements are used for the dynamic identification of wall panels, before and after they are tested in reversed-cyclic in-plane shear-compression tests. The natural frequencies, damping ratios, and mode shapes of the walls are determined and compared to each other. Moreover, the damage progression and its effect on the dynamic features of the URM wall panel is investigated using a discrete element model of the benchmark wall that is validated in terms of the force-displacement response and damage pattern of the wall. The results of the study indicate that changes in natural frequencies and mode shapes are traceable, although it is difficult to infer damage quantification relationships from these changes. The outcomes of this study also highlight that numerical models verified with the nonlinear quasi-static behavior do not necessarily match the wall's dynamic behavior, and that more research is required to update nonlinear numerical models. Overall, the results contribute to the knowledge regarding the dynamic characteristics of masonry walls in healthy and damaged conditions, and to quantify the damage in masonry walls as well as the changes in their dynamic properties.

Heteroscedastic Gaussian processes for data normalisation in probabilistic novelty detection of a wind turbine

This study investigates the data normalisation of modal parameters of an operating concrete–steel hybrid onshore wind turbine tower considering also the identification uncertainty. In order to take into account the Environmental and Operational Condition (EOC)-dependent variance, sparse heteroscedastic Gaussian processes (GPs) are used for the data normalisation. Following a typical vibration-based Structural Health Monitoring (SHM) scheme, data normalisation of the natural frequencies and the mode shapes is performed first. Subsequently, a metric is defined which takes into account both the identification uncertainty and the operation-dependent uncertainty in order to enable novelty detection.The data normalisation methods must be able to handle uncertainties of different magnitudes due to EOCs in the data. In this context, GPs can be a suitable tool. However, standard GPs assume homoscedasticity, which is an unrealistic assumption in the case of EOC-dependent variance. Using a heteroscedastic GP instead, the variance of the data is better mapped and allows comparison with the identification uncertainties of Bayesian operational modal analysis (BAYOMA), taking into account the specifics of closely spaced modes of the tower structure. This leads to a better interpretation of the data and enables the introduction of a probabilistic novelty metric.This data normalisation approach, taking into account EOC-dependent uncertainties using heteroscedastic GPs, is being applied for the first time to a tower of a full scale 3.4 MW wind turbine in operation. Following this approach, it is possible to detect smaller changes in natural frequencies and second-order modal assurance criterion (S2MAC) compared to the assumption of homoscedasticity within the GP. In addition, a novelty was detected using the S2MAC during the period under study. Therefore, it can be illustrated that mode shape-based metrics tend to be more sensitive than purely frequency-based ones. However, it is difficult to assess the significance of such changes for structural integrity without further information.

A study of the vibrations of a rotor bearing suspended by a hybrid spring system of shape memory alloys

Abstract The study of rotor-bearing vibration is crucial across various fields, encompassing applications such as rotating machinery, wind turbines, washing machines, and elevators. However, operational challenges can arise from these machines’ propensity to vibrate under specific conditions. To address this issue, the current research investigates the utilization of shape memory alloy (SMA) springs as intelligent materials in the rotor suspension system. SMA’s unique property of changing stiffness with temperature-induced phase shifts is harnessed, leading to the construction of a test rig for validating vibration characteristics. A novel hybrid bearing is devised to effectively manage vibrations, particularly in resonance zones. To the authors’ knowledge, this new model is never reported in the literature. Then, an accelerometer is employed to measure the rotor shaft response corresponding to disc position vibration signals. Furthermore, a numerical model is developed to validate experimental results, taking into account the phase change of SMA springs and the disc’s influence on the rotor bearing’s natural frequency. Temperature variations from 20 to 80°C resulted in a 13% change in natural frequency for the hybrid spring configuration. The experimental findings align closely with ANSYS simulations, displaying an acceptable error ratio, with the highest error remaining within 20% thresholds.

Research on the Influence of Disc–Drum Connection Bolt Preloading Rotor Assembly Modal Characteristics and Diagnosis Technology

The drum rotor of an aero-engine is connected by one or multiple mounting edges through bolts, and their dynamics are significantly influenced by the preload state of the bolts. Long working hours in challenging environments can result in the deterioration of bolt pre-tightening during assembly or service, which impacts the rotor’s dynamic stability and overall performance. Currently, there are no available methods for detecting the dynamic characteristics of the drum connection components. This paper analyzes the impact of the natural characteristics of the drum composite structure of a high-pressure aero-engine turbine based on the refined finite element method when the preloading state changes. Two conditions of deviation and uneven stiffness distribution were applied to the connected components of the drum. The analysis focused on the impact of the pre-tightening state on its natural frequency. After analyzing the feasibility of identifying the pre-tightening state, two methods are proposed. These methods focus on changes in natural frequency and mode shape, specifically the sensitive natural frequency change method and the mode step change method. The methods proposed in this paper can serve as a reference for evaluating the quality of assembling complex disc–drum structures with multiple bolt connections.

Intermolecular forces and surface stress residual effects on the size-dependent performance analysis of nanocrystalline micro/nano gyroscopes

This work investigates an electrostatically-actuated vibrating beam micro/nano-gyroscope made of nanocrystalline silicon material. The comprehensive size-dependent micro/nanogyroscope model is developed by couple stress and surface elasticity theories. Then, considering the effects of intermolecular forces (Casimir force and van der Waals force) and surface stress residual, an in-depth investigation was conducted on the performance of the micro/nanogyroscope. The calculation results display that the maximum static deflection, pull-in voltage and natural frequency change obviously with the increase of surface stress residual as the scale varies from micrometer to nanoscale. However, the effect of intermolecular forces on the performance of gyroscopes is exactly the opposite, which improves the prediction of system structural softening deformation phenomenon. Considering the influence of the Casimir and van der Waals forces in micro/nano gyroscopic system will help gyroscopes to obtain reliability and functionality sensitivity, increase the accuracy of predicting static deformation, natural frequency and differential frequency. Moreover, a frequency-domain method using the difference between the two vibration natural frequencies is studied, with changing the scale of the gyroscope under the effect of the intermolecular forces. The numerical simulations exhibit that when considering smaller structure sizes of the gyroscope, strong coupling occurs between the intermolecular forces and surface stress residual, which is helpful for the design of micro/nano gyroscopes.

Determination of the Natural Frequency Change of Different Bayburt Stone (Tüfit) Sizes During the Transportation in the Screw Conveyor

The mechanism that carries the powder or tiny granular particles with the rotational movement of the spiral shaft is called the screw conveyor. The working principle of screw conveyors is transporting dust particles due to rotating the screw shaft placed in a cylindrical pipe with engine power. The transport process transfers the powder particles to the conveyor from the feed pipe at the top of the mechanism to the wings (helix) of the helix shaft. In this study, a scaled prototype of the screw conveyor was produced. Different Bayburt stone (Tüfit) sizes were transported utilizing the prototype, and natural frequency changes were measured during transportation. Consequently, it is observed that the different micron sizes of stone particles affect the natural frequency of the screw conveyor.

IDENTIFICATION OF DAMAGE IN STEEL BEAM BY NATURAL FREQUENCY USING XGB MODEL

Beams have played a significant role in engineering applications and they have been commonly used for modelling civil problems. Different models and methods have been developed to identify the damage to the beams. In this article, the extreme gradient boosting (XGB) model was developed to predict the location, width and depth of the saw-cut of steel beams by the change of natural frequencies. The natural frequencies of a steel beam in different scenarios were identified by the finite element method (FEM). The criterions to evaluate the accuracy of the models were the R squared (RSQ) and the mean square error (MSE). The result indicated that combining the FEM method with XGB would hold significant potential for applications in structural health monitoring.

Determining the temperature using natural frequencies and artificial intelligence

"The current paper explores a novel approach for determining temperature variations by integrating the modal parameters and AI techniques. The research focuses on the development of a comprehensive dataset for training an AI model encompassing an analytical method that considers thermal conditions and natural frequencies. Traditional methods of temperature measurement, like infrared and platinum resistance thermometers, often face limitations in terms of accuracy, especially in complex or dynamic environments having an uncertainty of ±3.6 °C [1], respectively ±0.2 °C [2]. In this study, we propose a methodology that harnesses the inherent relationship between axial loads caused by temperature variations and the change in natural frequencies of a double clamped steel beam. The measured natural frequency data is collected and fed into the AI model, specifically, for a robust temperature estimation, obtaining a maximum predicted temperature deviation of 0.386 °C. Keywords: temperature, natural frequency, artificial intelligence, finite element method, thermal condition"

A novel surrogate-based crack identification method for cantilever beam based on the change of natural frequencies

A novel crack identification method is presented in this paper for cantilever beam-type structures within the scope of vibration-based damage identification. Natural frequencies are more easily to be measured yet are weakly sensitive to damage in comparison to other dynamic parameters such as mode shape and damping ratio. Therefore, this paper develops a surrogate-based crack identification method in order to overcome the low sensitivity of frequency to damage. The surrogate model was constructed using radial point interpolation method (RPIM) and subsequently trained with the frequency shift database established from parametric finite element analysis (FEA) modeling of cracked/ non-cracked cantilever beams. On this basis, the crack identification problem had been converted to a standard optimization model with crack length and location as design variables. Subsequently, genetic algorithm (GA) was employed for solving the optimization model to achieve crack parameters. In the end, numerical examples and experimental test have been conducted to validate the developed method, revealing maximum relative errors within 0.5% and 2.5%, respectively.

Key trends in the response of suction bucket foundations to extreme axial cyclic loads

The offshore wind industry is currently expanding into emerging markets at a rapid pace. Some of these markets are located in areas characterized by frequent extreme events. From a geotechnical perspective, this results in new design challenges, as foundations must withstand severe loads repeatedly throughout their intended lifetimes. Jacket structures resting on suction buckets represent a new foundation concept that still requires research to become a potential optimal solution. The vertical cyclic response of bucket foundations constitutes the main topic of this article. The current study is based on observations of the behavior of a scaled model installed in dense sand. Both normal and extreme conditions were simulated by applying axial cyclic loads of varying amplitudes, means, and frequencies. High amplitude and low frequency cause significant stiffness degradation and permanent displacement. These scenarios occur due to build-up of excess pore pressure, with subsequent triggering of liquefaction. A criterion for liquefaction occurrence is identified and may be readily used for practical applications. Considerable levels of tensile loading lead to a high rate of heave, regardless of frequency. For one-way compressive forces, after an extreme loading sequence, stiffness returns to its initial level, as long as no liquefaction develops priorly. This bears essential implications in predicting the change of natural frequency of the system.

Investigating Damage in Reinforced Concrete Members by Using Vibrating Wire Strain Gauge

Recently the use of vibrating wire strain gauges has increased to find out the damage in a reinforced concrete structure. The assembly and functioning of this acoustic strain gauge are presented. This gauge provides numerous benefits including its sensitivity to measure strain (up to 1micron) and its property of being easily attached on any concrete surface. The gauge apparatus can be made in a lab due to its low cost which gives it an edge over the conventional systems. The gauge was calibrated after considering the variations in temperature. The purpose of the experimentation was to set up a low-cost vibrating wire strain gauge, calibrate it and use it for static strain damage assessment of a reinforced concrete beam. The strain readings from the vibrating wire strain gauge were cross-checked using a Demec gauge. Discrete Fourier transforms moving window was utilised to analyse the vibration signals specifically the change in natural frequency with respect to time. The gauge setup provided a cheap and accurate way for measuring long-term static strain in reinforced concrete structures. The results are presented and reviewed.

Identification of damage in steel beam by natural frequency using ANNS models

Beams have played a significant role in engineering applications and they have been commonly used for modelling civil problems. In fact, different models and methods have been developed to identify the damage to the beams. In this paper, the artificial neural network (ANN) model was developed to predict the location, width and depth of the saw-cut of steel beams by the change of natural frequencies. The natural frequencies of a steel beam in different scenarios were identified by the Finite Element Method (FEM). In order to validate the accuracy of FEM model, the natural frequencies of the steel beam in the case of no saw-cut determined by this model were compared with those determined by the Frequency Domain Decomposition (FDD) method. The results indicated that, the combination of FEM method, FDD method and ANN model would have great significance in structure health monitoring.

A novel analytical-based viewpoint for MEMS mass spring system: systematic design guideline for dimensional tolerance and footprint reduction powered by dimensionless analysis

Mass-spring is one of the most used structures in sensors and actuators of MEMS technology, including accelerometers, gyroscopes, harvesters, etc. Some of the major design parameters of the structure are natural frequency and displacement sensitivity. The limitations of microfabrication processes should be considered in the design process. The optimized geometry topology can reduce the area occupied by the structure in the fabrication and increases the number of possible structures per wafer. This study aims to provide a novel systematic design and optimization of a MEMS mass-spring system by using a dimensionless design flowchart. Based on the dimensionless design, this algorithm provides the designer with the optimized dimensions of the mass-spring by following the provided dimensionless diagrams, taking into account stress, displacement sensitivity, natural frequency, and fabrication limitations. Also, the optimized dimensions of the mass-spring system are obtained using the dimensionless design flowchart with respect to the desired natural frequency and displacement sensitivity. In addition, genetic algorithms and dimensionless diagrams present a procedure to minimize the footprint of the structure while keeping the desired natural frequency and displacement sensitivity. Results demonstrate that up to a 3% change in both natural frequency and displacement sensitivity, leads to a 45% reduction in the structure area compared to the related literature of MEMS accelerometers.

Evaluating the effect of spinal cord stimulation on patient with disorders of consciousness: A TMS-EEG study

ObjectiveThe application of spinal cord stimulation (SCS) in the treatment of disorders of consciousness (DOC) has attracted attention, but its effect on brain activity is still unknown. Transcranial magnetic stimulation combined with EEG (TMS-EEG) can measure cortical activity, which can evaluate the effect of SCS on DOC. MethodsWe record 20 DOC patients' CRS-R values and TMS-EEG data before and after one-session SCS (Pre-SCS and Post-SCS). 20 DOC patients including 10 patients with unresponsive wakefulness syndrome (UWS) and 10 patients with minimally conscious states (MCS). TMS evoked potential (TEP) was used to measure the changes of cortical activity in DOC patients between Pre-SCS and Post-SCS. Firstly, we used the global mean field potential (GMFP) and fast perturbational complexity index (PCIst) to compare the temporal changes of patients' cortical activity. Then, we obtained the frequency feature (natural frequency, NF) based on the TEP time-frequency analysis, and compared the changes of natural frequency between Pre-SCS and Post-SCS. Finally, the study explored the relationship between the patient's baseline CRS-R values and changes of TMS evoked cortical activity in time and frequency domains. ResultsAfter SCS, MCS and UWS groups almost have no changes of CRS-R values (MCS: 9.9 ± 1.52 at Pre-SCS, 10.2 ± 1.48 at Post-SCS; UWS: 5.6 ± 1.26 at Pre-SCS, 5.7 ± 1.34 at Post-SCS). MCS group showed significant increases of GMFP amplitude (around 100 ms and 300 ms) and PCIst values at Post-SCS (p < 0.05). UWS group had no significant changes (p > 0.05). Besides, SCS induced the significant increases of natural frequency for MCS group(p < 0.05), but not for UWS group. At last, the study found that all patient's baseline CRS-R values were significantly correlated with ΔPCIst (r = 0.67, p < 0.005), and ΔNF (r = 0.72, p < 0.001). ConclusionsSCS can modulate cortical activity of DOC patient, including temporal complexity and natural frequency. The changes of cortical activity caused by SCS are related to patients’ consciousness level. TMS-EEG can evaluate the effect of SCS on DOC patients.