Changes In Natural Frequencies Research Articles

A statistical and reliability approach to vibration-based health monitoring in composite structures

In this paper, a novel statistical vibration-based damage detection method is developed considering uncertainties in measured resonance frequencies. The proposed method is based on the application of resonance frequencies as the most accurate and easiest measurable vibration feature. For proof of efficiency of the proposed method, case studies were undertaken using two identical composite plates, one delaminated and the other pristine. In this respect, the frequency response functions (FRFs) were measured and used as the main input to the Resonance Detection Algorithm as the proposed method. Applying these FRFs to a Resonance Detector Function can determine the resonant frequencies and their statistical distribution. Through the statistical distributions of the corresponding resonant frequencies, their reliability of detecting damage has been obtained via the beta distribution. By observing the damage detection reliability of the two sets of corresponding resonant frequencies, it has been determined that the changes in natural frequencies are due to structural changes and not random errors through measurement.

Health monitoring of ultra high fiber performance reinforced concrete communication tower using machine learning algorithms

Within the last decades, the needed for communication towers has accelerated with the requirements for effective communication, especially for radio, radar, and television. The complexity configuration of the tower and limit access to the structure body especially inner part of the tower with hollow section is led the health monitoring of tower as the main challenging issue to maintenance during its function. The change of natural frequencies can be considered as one of the prevalent damage detection methods in structural assessment procedures. Therefore, the main aim of present research is to develop health monitoring system for Ultra High Fiber Performance Reinforced Concrete (UHPFRC) communication tower based on frequency domain response. Since the frequency data of tower is mostly noisy and interpreting of frequency in different modes in variant case of tower damage. The hybrid algorithm based on the Adaboost, Bagging and RUSBoost algorithms are implemented to identify the damage in the UHPFRC communication tower using frequency domain data. The training samples for the algorithm are obtained from a finite element simulation and full-scale experiment testing is also performed to generate the testing samples. The finite element simulation dynamic frequency results are verified through conducting a full-scale experimental test on 30 m height UHPFRC communication tower. For this propose, frequency Response Functions (FRF’s), for healthy and damaged structures were obtained by exciting of tower by an impact hammer and the acceleration response recorded by three accelerometers sensors attached in suitable positions. The developed hybrid algorithm to identifying the damage is tested and verified by considering the part of tower segments 2–3 and conducting experimental testing on the healthy structure as well as a damaged structure which caused using dynamic actuator. The testing results proved the accuracy of the developed optimized hybrid algorithm to identify damage in the tower structure in variant condition.

Outlier analysis combined with Gaussian mixture model for structural damage detection

Damage diagnostic techniques based on changes in natural frequency has two major problems, limiting their applicability to practical structures. The limitations are low sensitivity to smaller-size damage and the influence of ambient and operational factors (temperature, humidity, wind, traffic, etc.). The change in natural frequency due to environmental and operational factors may be even larger than the change due to damage. A reliable vibration-based structural damage detection distinguishing damage and other confounding factors is needed to avoid false alarm of damage. This paper presents an enhanced approach combining the gaussian mixture model (GMM) and outlier analysis for damage detection considering the effect of changing environmental and operational conditions. In the proposed work, GMM is first applied to classify the feature vectors (first two natural frequencies) into different clusters. The natural frequencies obtained under similar environmental and operational conditions were classified into the same cluster by satisfying the same probability distribution. Outlier analysis is then performed for each different cluster using the Mahanabolis Distance (MD) measure. The MD is a measure of the distance between a point and a distribution. In the current study, the MD between the current data sample and the reference data of each mixture is computed and the minimum MD among all the clusters is used as the damage index (DI). The threshold to conclude the presence of damage (DI > threshold) is established based on Generalized Extreme Value Distribution using the datasets of the healthy structure with various environmental and operational conditions. The proposed method is verified using benchmark examples of numerically simulated simply supported beam and experimental wooden bridge structure. The results of the investigations concluded that the proposed DI considering the patterns in the data using GMM proves better in decoupling the damage and other confounding factors following the conventional outlier analysis of damage detection.

Modal parameter calculation and vibration characteristic analysis of transmission line conductor

AbstractStructural damage identification technology based on modal parameters is an extremely effective monitoring method. Because of the structural characteristics of the conductor, with its small diameter and long span, it is not easy to obtain the modal parameters by manual excitation. Here, a method for structural health monitoring of the conductor under wind load excitation is proposed. Firstly, the natural frequency change law of the conductor after broken strand damage is obtained by analyzing the conductor modal parameters calculation formula and IEEE standards. Then, the vibration characteristics are calculated by vibration experiments and finite element methods. Finally, through the broken strand experiment, this paper demonstrates how to determine the damage degree of the conductor using the modal parameters. And it is applied to online monitoring in the field. The results show that this method is convenient, fast, and accurate.

Dynamic performance analysis based on the mechatronic system of power transmission line inspection robot with dual-arm

Dynamic performance of the power transmission line inspection robots (PTLIRs) is of great importance, which would heavily affect the stability of the robot during obstacle avoidance. In this paper, a detailed dynamic performance analysis method of PTLIR is presented by considering the effect on the mechatronic system caused by obstacle avoidance. First, the dynamic modeling of the robot and control system model of the revolute joint are given based on the mechatronic modeling. Then, dynamic characteristics of mechanical subsystem are analyzed by studying the change of the inertia matrix during obstacle avoidance. Next, to analyze the control subsystem performance, three kinds of pole assignment methods which used to tune the controller parameter are compared. Finally, a series of numerical simulations are performed, which prove the time-varying characteristic of load inertia during obstacle avoidance has a great influence on the dynamic performance of the robot, moreover, the changes of natural angular frequency and damping coefficient parameters could be used to evaluate dynamic performance. The main results of the paper can provide an effective tool to analysis dynamic performance of the PTLIR, which is meaningful to improve inspection stability.

Effect of the Stiffness of the Turntable Bearing Joint on the Dynamic Characteristics of the Five-Axis Machine Tool Rotary System

The positioning accuracy and machining performance of the five-axis machine tool are significantly impacted by the dynamic characteristics of the rotary system of the two-axis rotary table machine. In this study, first, the stiffness of the joint bearing of the rotary table system is calculated, and the effect of bearing clearance and external load on the stiffness is analyzed. Second, considering the stiffness characteristics of the joint, the natural frequency and mode shapes of the turntable system are calculated. Finally, the influence of turntable angle and bearing stiffness on the dynamic characteristics of the turntable system is analyzed. The results show that the natural frequency of the rotary table system does not change obviously with the axial stiffness of the turntable bearing joint, but increases significantly with the increase in the radial stiffness. The first order natural frequency of the turntable decreases with the increase in the swing angle, and the change in the first order natural frequency is 77.43 Hz. The research results provide theoretical basis and guidance for machine tool design and use.

Study on Staged Damage Behaviors of Rock-like Materials with Different Brittleness Degrees Based on Multiple Parameters

Understanding the brittle fracture behavior of rock is crucial for engineering and Earth science. In this paper, based on acoustic emission (AE) and laser Doppler vibration (LDV) monitoring technology, the staged damage behaviors of rock-like materials with different brittleness degrees under uniaxial compression are studied via multiple parameters. The results show that the brittleness degree determines the fracture mode. As the specimen's brittleness degree increases, the tensile failure increases and shear failure decreases. AE activity is enhanced at the crack damage point. With an increasing specimen brittleness degree, different instability precursor information is shown during the unstable crack growth stage: the AE b value changes from the fluctuating to continuously decreasing state, and the natural frequency changes from the stable fluctuation to upward fluctuation state. The AE b value near the stress drop is the smallest, and it decreases with an increasing brittleness degree. The natural frequency reduction indicates the rock-like fracture. The natural frequency is a symbolic index that reflects staged damage characteristics and predicts the amount of energy released by brittle failure. These findings provide guidelines for rock stability monitoring and provide support for better responses to stability evaluations of rock slopes, rock collapses, and tunnel surrounding rock in engineering.

Experimental Study on the Vibration Characteristics of Dangerous Rock Mass under Constant Micromotion

In mountainous areas, dangerous rock mass collapse is a serious threat to human life and property safety. However, how to effectively prevent and control the instability of dangerous rock mass is still an urgent unsolved problem. In this study, the dynamic characteristics of dangerous rock mass under constant micromotion were analysed from the perspective of elastic wave propagation. When the slip plane of the dangerous rock mass is damaged, many micropores and cracks will appear in the medium composed of the slip surface. With constant micromotion as the vibration source, the elastic wave propagates to the dangerous rock mass through the damaged slip plane. The high-frequency components of elastic waves scatter in pores and fissures, where energy dissipates. According to this characteristic, a laboratory simulation experiment was designed. In the experiment, the damage process of the slip plane was simulated by the freeze‒thaw process of frozen hydrosol. The experimental analysis showed that the centre frequency of the high-frequency part of the dangerous rock mass model and bedrock mass model decreased as the frozen surface continued to melt. As the dangerous rock mass model and the bedrock mass model continued to fit, the centre frequency of the high-frequency part of the two rock mass models rebounded. This phenomenon showed that the damage degree of the slip plane between the dangerous rock mass and the bed rock mass can be effectively reflected by the centre frequency of the high-frequency part of the two rock mass models. During the experiment, the dangerous rock mass did not slide in the whole process, indicating that the deformation index has difficulty reflecting the stability of the hidden dangerous rock mass. In addition, the application conditions of using the natural frequency characteristics of dangerous rock mass and the scattering characteristics of elastic wave in the damage identification of structural plane were analysed: (1) when the structural plane has macrofracture, the change of natural frequency of dangerous rock mass should be used to analyse the damage degree of structural plane; (2) when there is no macrofracture of the structural plane, the characteristics of elastic wave scattering should be used to analyse the damage degree of the structural plane. This study provided a new idea for the prevention and control of dangerous rock masses and is expected to provide a useful reference for the automation of dangerous rock mass prevention and control.

Spectral element formulation for rock-socketed mono-pile under horizontal dynamic loads

The current study entails a thorough investigation of the dynamic response of a mono-pile foundation in homogeneous soil and varied layered soil–rock conditions under horizontal dynamic loads. A sequence of visco-elastic springs linked along its length represents the mono-pile immersed in elastic half space. The frequency dependent stiffness and damping of a mono-pile foundation embedded in layered elastic half space are developed using spectral element formulation. The variations in stiffness and damping with frequency for various soil–rock systems are demonstrated. The dynamic response characteristics of the pile were found to be influenced by the depth of the rock-socketed pile. The presence of the underlying layer of stiffer layer of rock enhances the overall stiffness of the system. The frequency versus amplitude responses of a mono-pile supported heavy mass block for both horizontal translation and rocking motion are calculated using the stiffness and damping of the mono-pile under various soil rock conditions. The horizontal amplitude of the pile decreases with increasing pile rock socketing depth. The resonant amplitudes for rocking motion increases as the pile’s rock socketing depth increases. Finally, the changes in natural frequency and peak amplitudes with varied pile slenderness ratios are investigated for diverse pile–soil–rock conditions.

Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: An experimental validation

Owing to ever-increasing complexity of engineering structures, developing a methodology for the early detection of defects has become crucial to ensure their long-term safety and reliability with the least amount of expense. There are always discrepancies between experimental and numerical modal data because of unknown structural parameters and uncertainties. The finite element (FE) model updating techniques attempt to minimize the differences by adjusting the unknown parameters of the FE model. Therefore, the FE model updating methods are essential for developing a baseline model and accurate damage identifications in subsequent steps. This paper employs the semi-rigidly connected frame element (S-RCFE) instead of the standard Euler-Bernoulli beam element for assembling the FE model of the experimental beam and establishing a high-fidelity numerical model. The S-RCFE with extra design parameters, including the end fixity factor of all connections, enables us to achieve a reasonable agreement between experimental and numerical models through the optimization-based procedure. In FE model updating step, two objective functions based on modified total modal assurance criterion (MTMAC) and changes in natural frequencies are used to minimize by three optimization algorithms, viz, grey wolf optimizer (GWO), gradient-based optimization (GBO), and an improved version of GWO (IGWO). The influence of the S-RCFE and standard Euler-Bernoulli beam on the model updating accuracy is also examined, and the efficiency of S-RCFE is evaluated. The statistical results reveal that GWO-MTMAC and IGWO-MTMAC can be successfully implemented for FE model updating with almost the same performance. However, IGWO provides the most reliable results with a relatively extensive computation time for damage identification in all scenarios. In some damage scenarios, the GWO and GBO perform comparably with very similar running time. Data used in this article can be found at https://github.com/Samir-Khatir/Data-modal-analysis-of-healthy-and-cracked-beam.git

A novel multi-objective optimization of mass dampers for controlling the vortex-induced vibration in bridges

This paper investigates an optimization framework of the four mass dampers for controlling the vortex-induced vibration (VIV) in long-span bridges, including the tuned mass damper (TMD), the series double tuned mass dampers (DTMD) and the inerter-equipped tuned mass damper (ITMD). The equations of motion of the bridge-damper system subjected to the vortex-induced force are established. The vortex-induced amplitude of the girder is analytically given. Furthermore, the optimal design is implemented by taking the vortex-induced amplitude as the constraint condition. Introducing two optimization objectives, the stroke index and the robustness index, a novel bi-objective optimization framework with constraints is proposed and then solved by multiple objective particle swarm optimization (MOPSO). A comparative analysis of the four mass dampers with varying total mass ratios is performed. The results show that the vortex-induced amplitude of the girder is greatly reduced to satisfy the requirement after installing the four optimized mass dampers. Both performances of the two optimization objectives are improved with the increase of the total mass ratio. The inertial device parallel to the spring and dashpot provides no advantage in controlling the VIV in bridges. The DTMD has dramatic robustness to changes in the bridge natural frequency and cannot strongly amplify its stroke, especially under the condition of a small mass ratio. The framework provides an excellent balance between control effect and stability in the VIV of bridges for the optimal design of the mass dampers.

Torsional vibration of Timoshenko-Gere non-circular nano-bars

The displacement field and governing equation completely depend on the cross-section shape in the torsion of nano-bars. Due to the torsion of structure and warping of its cross-section, axial strain is created. A review of the literature demonstrates that the effect of the normal strain in the torsional analysis of nanostructures with non-circular cross-sections is ignored for the sake of simplicity and causes a computational error. While in the torsion of short nano-bars due to the great warping of the cross-section the normal strain appears and it shouldn’t be ignored. Therefore, for the first time, the effect of normal strain based on the torsion of Timoshenko-Gere theory is considered in this research. In this theory, the twist rate of non-circular sections in the axial direction is not considered constant, unlike studies in the literature. The governing equation of torsional vibration is extracted using the Hamilton principle, and the nonlocal strain gradient theory is used to show the size-dependent effects. The fundamental frequency is calculated for the arbitrary cross-section shape by using Galerkin’s method. The effect of parameters such as size effects, the thickness of nano-bar, mode number, and dimensions changes of cross-section versus natural frequency of nano-bar for both the Timoshenko-Gere and typical theories are investigated. Results indicate that neglecting normal strain due to warping the cross-section causes a significant error in the short nano-bars, especially at higher mode numbers. Also, a comparison is made between the obtained natural frequencies and those of the results reported in the literature.

A rapid evaluation method based on natural frequency for post-earthquake traffic capacity of small and medium span bridges

To improve the efficiency of evaluating the traffic capacity of bridges after the earthquake, a rapid method based on natural frequency for evaluating post-earthquake traffic capacity of small and medium-span bridges is proposed. Firstly, OpenSees software is selected to establish the seismic numerical analysis model of the pier, and the pressure of the main girder on the pier is equivalent to concentrated mass to extract the dynamic characteristics of the pier. The horizontal thrust on the pier top is adopted to simulate seismic action by the pseudo-static method, and the horizontal thrust is controlled by the maximum horizontal displacement. The value range of pier parameters is determined according to the definition of the regular bridge and relevant design data, then the design parameters and maximum horizontal displacement of each pier are sampled by the Latin hypercube sampling method to obtain various combined working conditions. Subsequently, the natural frequency, residual displacement and bearing capacity of the pier under different working conditions are obtained through numerical simulation. The relationship between natural frequency and residual bearing capacity of the pier after the earthquake is established in light of the simulation results of pier models. Then, the vehicle load is arranged on the basis of the most unfavorable loading principle, and the bearable maximum vehicle weight of the bridge is estimated from the bearing capacity of each pier, so that the traffic capacity of the bridge after the earthquake can be quickly evaluated by the change of natural frequency of piers. Finally, the reliability of the pier numerical model and residual displacement calculation method are verified by the test results of piers. The application process of the evaluation method proposed in this paper is illustrated by two typical examples of a simply supported beam bridge and a continuous beam bridge, which proves the feasibility of this method.

Free Vibration Characteristics of Multi-Material Lattice Structures

This paper presents a modal analysis of honeycomb and re-entrant lattice structures to understand the change in natural frequencies when multi-material configuration is implemented. For this purpose, parallel nylon ligaments within re-entrant and honeycomb lattice structures are replaced with chopped and continuous carbon fibre to constitute multi-material lattice configurations. For each set, the first five natural frequencies were compared using detailed finite element models. For each configuration, three different boundary conditions were considered, which are free–free and clamping at the two sides that are parallel and perpendicular to the vertical parts of the structure. The comparison of the natural frequencies was based on mode-shape matching using modal assurance criteria to identify the correct modes of different configurations. The results showed that the natural frequency of the multi-material configurations increases from 4% to 18% depending on the configuration and material.

Stapes vibrations induced by piezoelectric floating mass transducer

The paper presents a problem of nonlinear vibrations in the human middle ear stimulated by a piezoelectric floating mass transducer. The transducer is connected to the malleus by means of a coupler that is nonlinear. This nonlinearity together with the transducer has a key meaning for the middle ear behaviour because the improved model of piezoelectric transducer is used compared to previous papers. Nonlinear coupler stiffness and the applied voltage to the transducer produce a change of middle ear natural frequency. Moreover, a bistability effect of periodic solution and irregular vibrations are observed as well. The chaotic motion can exist in the hearing range that is especially harmful for patients who use implants with piezoelectric floating mass transducer.

Effects of temperature on modal characteristics of non-uniform rigid-frame bridges

The effect of temperature on structural modal characteristics plays an important role in structural health monitoring and evaluation. Herein, the free vibration analysis of rigid-frame bridge is conducted by taking into account the effect of temperature. Firstly, the non-uniform rigid-frame bridge is divided into several members to develop the flexural and axial vibration equations for members under the effect of temperature in accordance with Hamilton’s principle. Secondly, each member is further divided into several segments, and the transfer relationship between segments is established to obtain the generalized dynamic stiffness matrix of the member. Then, the generalized dynamic stiffness matrix of each member is constructed by using the numerical assembly method similar to the finite element method so as to obtain the characteristic equation of rigid-frame bridge. Furthermore, the natural frequency and mode shape of the whole rigid-frame bridge are calculated by using the algorithm of Wittrick-Williams. Finally, the dynamic characteristic test of Yong-an bridge and the numerical calculation of the rigid-frame bridge are carried out to verify the generality and accuracy of the proposed method. The results indicate that the change of temperature will lead to the secondary internal force and the change of Young’s modulus, which together affect the modal characteristics of the structure, and the change of natural frequency caused by the change of Young’s modulus is greater than that caused by the secondary internal forces. In addition, there is a negative correlation between temperature and natural frequency of the rigid-frame bridge, and different temperature gradient modes also have certain influence on the mode shape of rigid-frame bridge.

ДОСЛІДЖЕННЯ НЕРЕЗОНАНСНИХ КОЛИВАНЬ СИСТЕМИ «ТЕЛЕСКОПІЧНИЙ ГВИНТ – СИПКЕ СЕРЕДОВИЩЕ»

In the article it is substantiated the value of the angular speeds of rotation of the auger screw, which leads to the breakdown of its lateral vibrations. The dependences describing the law of change of amplitude or natural frequency at slowly variable length of the telescopic screw are deduced. Based on the Van der Paul’s method, in the developed system differential equations are obtained that determine the laws of change of amplitude and frequency of the wave process in the system of a telescopic propeller. It is established that for nonresonant oscillations for this system the main parameters of bending oscillations are a continuous flow of bulk medium - the screw does not depend on its small torsional oscillations and external periodic perturbation. The analysis of the given regression equations shows that to reduce the torque of the auger it is necessary to reduce the frequency of its rotation and the angle of the conveyor. The constructive diagram and the results of theoretical calculations for assessing the influence of constructive-kinematic parameters on the torque indicators of the telescopic screw conveyor are presented.

ОЦЕНКА ЭФФЕКТИВНОСТИ ИСПОЛЬЗОВАНИЯ ТРАДИЦИОННЫХ КОНСТРУКЦИЙ ПОДВЕСОК В СПЕЦИАЛИЗИРОВАННОМ АВТОМОБИЛЬНОМ ТРАНСПОРТЕ

In order to identify the reasons for the decrease in the efficiency of vehicles equipped with traditional suspension designs and to identify promis-ing areas for improving their efficiency, an analysis was made of the results of a review of studies obtained in the scientific field under consideration by foreign and Russian scientists. The article substantiates the relevance of increasing the efficiency of suspensions of specialized trucks and road trains operated in difficult changing climatic and road conditions. The main disadvantages that appear during the operation of vehicles equipped with traditional suspension designs are given. The consequences of the operation of such vehicles equipped with traditional suspension designs in conditions of a low level of road infrastructure are listed. The advantages of hydropneumatic suspensions, leaf springs made of composite materials in comparison with steel springs, independent suspension structures over dependent ones, semiactive air suspensions over passive and active ones, as well as regenerative suspensions are considered. The dependences of the change in the time between failures of the elements of the spring suspension, the estimated durability of the spring on the speed of movement, the acceleration of the sprung mass of the trailer of a road train when driving over bumps, the resistance forces of the hydraulic shock absorber on the ambient tem-perature are presented. The dependences of the change in natural frequencies and the damping coefficients of oscillations of the sprung and un-sprung masses of the car with an increase in the mass of its sprung part are given. The perspective directions for increasing the efficiency of suspensions of timber trucks and road trains identified as a result of the analysis are given.

Artificial neural network based delamination prediction in composite plates using vibration signals

Dynamic loading on composite components may induce damages such as cracks, delaminations, etc. and development of an early damage detection technique for delaminations is one of the most important aspects in ensuring the integrity and safety of composite components. The presence of damages such as delaminations on the composites reduces its stiffness and further changes the dynamic behaviour of the structures. As the loss in stiffness leads to changes in the natural frequencies, mode shapes, and other aspects of the structure, vibration analysis may be the ideal technique to employ in this case. In this research work, the supervised feed-forward multilayer back-propagation Artificial Neural Network (ANN) is used to determine the position and area of delaminations in GFRP plates using changes in natural frequencies as inputs. The natural frequencies were obtained by finite element analysis and results are validated by experimentation. The findings show that the suggested technique can satisfactorily estimate the location and extent of delaminations in composite plates.

An experimental investigation on the effectiveness of damping changes for damage detection in a Fibre Reinforced Plastic Plate

Fibre reinforced plastics (FRP) are extensively used because of their high specific strength and stiffness. However, throughout their service life, such materials are susceptible to damages, which when accumulated may result in catastrophic failure. Studies on effects of stiffness loss due to damage has been exercised by quite a large number of researchers but very less investigators have involved the variations in dissipative behaviour in combination with such stiffness loss. However, damage in these structures not only causes local reduction of stiffness but is also observed with increased dissipation behaviour. One of the most convenient ways to carry out health monitoring exercise to detect damages is to conduct systematic vibration testing. The present study investigates the likely changes in natural frequencies and mode shapes of a rectangular FRP composite plate along with damping factors due to the induced damage. The FRP plate considered has been modal tested and dynamic responses i.e., natural frequencies, mode shapes and modal damping factors are derived through curve-fitting technique from the frequency response function measurements. In this study, changes in dynamic responses due to a locally induced damage in the FRP plate is studied. For this, in order to maximize the effects of local reduction in the stiffness on the modal parameters, a partial-cut is provided in a localised region of the plate in the first damage case. In the second damage scenario, the partially-cut area has been filled with epoxy resin matrix to create a region with localised change in material properties and with limited stiffness loss. Damping changes has been observed to be significant and more sensitive than variations in natural frequencies and mode shapes. The study suggests that damping parameters along with stiffness changes together can be put into practice to develop an effective vibration-based health monitoring scheme