Changes In Natural Frequencies Research Articles

A Study on the Feasibility of Natural Frequency-Based Crack Detection

Owing to the long-standing statement that natural frequency-based crack detection is not sensitive enough to localised damage to identify small cracks, many natural frequency-based crack detection methods are validated by detecting cracks of moderate size. However, a direct comparison between the crack severity causing a measurable natural frequency change and the crack severity reaching the initiation of crack propagation or leading to brittle fracture is constantly ignored. Without this understanding, it is debatable whether the presented crack detection methods are feasible in practical situations. Through natural frequency calculation and linear elastic fracture mechanics, this study is dedicated to filling the above gap in knowledge. To directly utilize the solution of stress intensity factor, common fracture toughness test specimens featuring a single-edge crack are used. These specimens are essentially cracked rectangular plates under uniform uniaxial tension. Considering the stress resultants obtained via the extended finite element method, the natural frequency of the loaded cracked plates is calculated using the Rayleigh–Ritz method incorporating corner functions. In addition, assuming the specimens as structural components under remote uniform tension, the development of critical load versus crack length is derived based on the solution of the stress intensity factor. Thus, critical crack lengths corresponding to a series of safety factors are obtained by equating service load with critical load. After obtaining natural frequencies of the cracked plates with critical crack lengths, the natural frequency drop caused by a critical crack can be computed. Hence, the critical crack length can be compared with the crack length when the frequency drop is measurable. It is found that the brittleness of the employed metals plays a vital role in the feasibility of natural frequency-based crack detection.

Vibration-Based Crack Detection in Plates Using Natural Frequency Degradation.

Abstract Structural cracks reduce the performance and service life of buildings, bridges, and aircraft structures, leading to catastrophic failures resulting in economic losses and fatalities. To avoid such consequences, regular health monitoring and maintenance is required, especially for critical structures that carry high levels of dynamic and fatigue loading and whose failure would be catastrophic. Many techniques are available for structural health monitoring, including visual inspection, ultrasonic testing, acoustic emission, magnetic field, and vibrational-based methods. Any damage causes degradation in the natural frequencies and vibration modes of a structure, which are considered in vibration-based methods to characterize the damage. The focus of this research is to develop a more efficient method for the detection and characterisation of arbitrarily oriented surface cracks in isotropic plates, in terms of five parameters, namely the longitudinal and transverse location, length, depth and orientation. To achieve this objective, an analytical solution based on strain energy is used to generate synthetic data that quantifies changes in the natural frequencies for different crack locations and intensities based on noise-free simulation. The inverse problem, i.e. the determination of the crack parameters based on measured changes in natural frequencies can then be solved based on the use of synthetic data with a gradient based optimisation technique.

Tire vibration analysis of three-dimensional flexible ring with brush model under static contact conditions by using frequency-based substructuring

The use of a simplified physical model of the tire of road vehicles is an efficient and simultaneous method to study the specifications of the entire chassis, including the tire specifications. Therefore, it is important to develop a simplified physical model that can be used in the early design phase when detailed computer-aided design data are not available. In this study, a vibration analysis of tires in road contact is described using frequency-based substructuring in a three-dimensional elastic ring model of a tire that includes a brush model simulating the tread rubber. By modeling the brush as a contact spring between the tire and the road surface, the natural frequencies and mode shapes of the tire under load conditions can be calculated using point-coupled three-way contact spring constraints. The experimental results show that the natural frequency changes significantly with road contact and does not depend on the vertical load. The theoretical analysis also showed that the natural frequency does not change when the stiffness of the contact spring is large enough to limit the displacement of the road contact, which is consistent with the experimental results. Unlike previous studies, this method calculates the mode shape with road contact based on the mode shape without road contact; therefore, the required model parameters can be determined based on the experimental modal analysis for the free-free condition.

Free vibration analysis of a functionally graded porous nanoplate in a hygrothermal environment resting on an elastic foundation

This research investigates the free vibrational behavior of a functionally graded porous (FGP) nanoplate resting on an elastic Pasternak foundation in a hygrothermal environment. The nanoplate is modeled based on the nonlocal strain gradient theory (NSGT) and considering several plate theories including the CPT (classical plate theory), the FSDT (first-order shear deformation theory), and the TSDT (third-order shear deformation theory). Several patterns are investigated for the dispersion of pores, and the surface effects are incorporated to enhance the precision of the model. The governing equations and boundary conditions are derived via Hamilton's principle and an exact solution is provided via the Navier method. The impacts of several parameters on the natural frequencies are inspected such as length scale and nonlocal parameters, surface effects, porosity parameter, hygrothermal environment, and coefficients of the foundation. The results show that the impact of the porosity parameter on the natural frequencies of nanoplates is significantly dependent on the porosity distribution pattern. It is discovered that by increasing the porosity parameter from 0 to 0.6, the relative changes of natural frequencies vary from a decrease of 30 % to an increase of 6 %.

Effect of Magnetorheological Fluid Pockets Energization on Dynamic Response of MR-Laminated Beams under Impulse Loading

Laminated composite beams are being used for many applications due to their high strength to weight ratio. To enhance the performance of laminated composites under dynamic loading, Magnetorheological (MR) and Electrorheological (ER) fluids have been considered to be added as embedded layers/segments to the conventional laminated structures. The present work focuses on the dynamic behavior of laminated composite beams incorporating MR fluid pockets (referred to as MR-laminated beams) under impulse loadings. A modified layerwise displacement theory is employed to account for the varying fluidity of MR pockets along the thickness direction. Four configurations of MR-laminated beams featuring multiple MR pockets distributed through the thickness and along the length have been examined. A parametric analysis explores the impact of magnetic field strength, number and placement of MR pockets, and boundary conditions on the dynamic response of the MR-laminated beams. The changes in natural frequencies concerning the size and location of activated MR pockets have been explored. Time-response analysis is conducted for MR-laminated beams subjected to impulse loading, considering various sizes and locations of activated MR pockets. The investigation highlights the significant influence of the MR pocket's location and size on the vibration response of MR-laminated beams. It is realized that the total stiffness, mass, and activation energy can be optimized according to the desired dynamic response of the beams. The proposed configuration for MR-laminated beam, results in a beam with 7% reduction in total mass while exhibiting fivefold increase in the corresponding natural frequencies, 40% increase in damping and 40% reduction in maximum amplitude.

Influence of agglomeration and waviness phenomena on torsional oscillation of MWCNTs-reinforced composite rods

There are some inevitable challenges during the manufacturing of reinforced composite structures. Agglomeration of reinforcement and wavy reinforcement are in this category. These phenomena possess remarkable effects on the mechanical behavior of reinforced composite structures. In the current research, the effect of agglomeration and waviness of reinforcements on torsional dynamic characteristics of multi-walled carbon nanotubes (MWCNTs) reinforced composite rods subjected to two various boundary conditions have been evaluated. Three dissimilar cross-section shapes have been considered to understand the effect of cross-section shapes on torsional behavior of MWCNTs-reinforced composite rods. A new form of Halpin-Tsai homogenization model has been exerted to estimate the material properties of composite structures. Additionally, Timoshenko-Gere theory in conjunction with the Hamilton’s principle has been employed to derive the partial differential governing equation of MWCNTs-reinforced composite rods. Afterward, the obtained equation was solved using an analytical approach. The precision of the methodology utilized has been evaluated against the results of previous studies documented in the literature. Ultimately, the effects of various significant parameters on the changes in natural torsional frequency have been analyzed and presented in a series of tables and figures. Based on the obtained results, the rectangular rod has the highest torsional frequency and also the effect of MWCNTs’ volume fraction depends on the consideration of waviness and agglomeration factors. At a greater volume fraction of MWCNTs, the agglomeration factor is more effective than the waviness factor and vice versa.

Improving Dynamic Performance of a Small Rhizome Chinese Herbs Harvesting Machine via Analysis, Testing, and Experimentation

The small rhizome Chinese herbal medicine harvesting machine is used for excavating the underground rhizomes of Chinese medicinal plants. The reliability of an existing machine of this type was found to be suboptimal due to high vibration levels, as confirmed by direct measurements. To remedy this issue, the differential equation of motion was derived, solved, and visualized using MATLAB software (R2017a). The impact of various parameters on the equation of motion was analyzed through both time and frequency domain plots, as well as experimental analysis. The parameters studied included the rotational speed of the tractor’s power take-off (PTO) shaft, the machine’s overall mass and stiffness, the transmission ratio, and the excitation force generated by the machine’s reciprocating parts. To reduce vibration in the non-resonant state and avoid resonance as the natural frequency changes, several modifications were necessary: the PTO speed needed to be controlled, the stiffness of the machine had to be increased, and the mass of the reciprocating parts had to be decreased. Additionally, expanding the transmission-ratio range of the operational machinery was essential. Sandbags were added to the machine’s frame to increase its overall mass. The above measures have reduced the vibration speed of the harvester during operation. The vibration speeds Vmax and VRMS of the harvester under both working and non-working conditions have decreased by half compared to their original values, reducing the occurrence of resonance in the harvester and effectively mitigating vibration damage, thereby enhancing operational reliability.

Vibration monitoring of masonry bridges to assess damage under changing temperature

Structural Health Monitoring (SHM) is of utmost importance for the preservation and safe operation of historical arch bridges. This paper presents the development of a SHM strategy aimed at the model-based damage assessment of masonry bridges using frequency data. Structural damage induces natural frequency changes that are strictly related to the damage location. Consequently, a numerical model capable of reproducing the intact dynamic characteristics should allow to simulate damage scenarios, including the observed one, with the anomaly localisation being performed through the similarity between the experimentally detected frequency changes and the numerically simulated ones. The proposed methodology is based on the availability of an appropriate knowledge of the investigated structure, allowing to define a Finite Element (FE) model that accurately reproduces the system dynamic characteristics. Hence, the SHM strategy involves: (a) the use of the calibrated model to simulate different damage scenarios, so that a Damage Location Reference Matrix (DLRM) is defined through the associated frequency shifts; (b) the damage detection through statistical pattern recognition of vibration data; (c) the damage localisation through the comparison between the identified frequency changes and those defined in the DLRM matrix. Pseudo-experimental monitoring data, referring to a historical masonry viaduct, were generated and used to exemplify the reliability and accuracy of the developed algorithms in detecting and localizing damage.

Study on the self-vibration characteristics of non-circular arches with cracks based on the transfer matrix method

As the span of reinforced concrete arch bridges continues to increase, so does the difficulty of construction. The structure is at risk of cracking. Most of the bridges under construction are non-circular arches, and there are few studies on such arches. The current study tried to investigate the self-vibration characteristics of non-circular arches with existing cracks. A computational approach proposed in the original non-circular arch is substituted with multiple infinitesimal arch segments having different radii of curvature, enabling the determination of natural frequencies and mode shapes of the non-circular arches with cracks. Furthermore, a finite element model (FEM) of the reinforced concrete structure with existing cracks is developed to assess the effects of various factors, including axial location, crack depth, and positions within the same cross-section. The results demonstrate the feasibility of the computational method using multiple infinitesimal arc segments with varied radii of curvature, yielding a maximum error of only 1.58 %, which satisfies engineering application standards. An increase in crack depth leads to a reduction in the natural frequencies of specific modes of the structure, while the effect on others is insignificant. For cracks situated at the top or bottom plates within the same cross-section, the impact differs based on the local deformation being convex or concave. If the deformation is convex, the top plate cracks exhibit a higher rate of change in natural frequencies compared to the bottom plate cracks; conversely, with concave deformation, the bottom plate cracks have a greater influence than the top plate cracks.

Application of conical spring to maintain tuning of mass damper for wave-induced vibration control of offshore jacket platform subjected to changes in natural frequency

Offshore jacket platforms are situated in challenging environmental conditions and often experience changes in mass and stiffness, resulting in alteration in its dynamic properties. The tuned mass damper (TMD), known for its effectiveness in vibration control, has been earlier studied for implementation in jacket platforms. However, it is sensitive to tuning and would suffer a performance loss if the structural frequency undergoes modification. This can be overcome by connecting the damper mass to the structure by a conical spring that exhibits multilinear behaviour. This allows the TMD to remain tuned to different values of the structural frequency. In this study, the jacket platform is modelled as a multi-degree-of-freedom (MDOF) system, and the performance of the designed TMD with conical spring (TMD-C) is investigated in both frequency and time domain. Two possible variations in the fundamental period of an example jacket structure are considered and the results of wave-induced vibration control of deck responses achieved by the TMD-C are compared with those by the conventional TMD. Results indicate that despite being a passive device, the TMD-C can maintain the desired tuning to the structural frequency and thereby outperforms the conventional TMD in the reduction of the deck responses.

Investigation of the Natural Frequency Change of the Suspension Bridge Under Operating Conditions

This study addresses the challenge of accurately correlating the bridge natural frequency with influencing factors during ambient vibration by analysing on-site monitored data. This knowledge gap arises from the combined uncertainties of environmental factors and monitoring equipment noise. To tackle this challenge, the Fourier synchrosqueezed transform technique is employed and validated first by the simulated signal, as well as the Welch method. Then the instantaneous frequency of recorded acceleration at the real bridge is tracked, and a distinct diurnal pattern in the natural frequency is revealed. Then the two-stage strategy is adopted for the regression analysis. Firstly, the regression models between the normalised vibration intensity and the normalised frequency change of the vertical mode are established. Building upon these results, the additional factor, namely the effective wind speed, is considered in the second stage. The multiple linear regression model is established between the natural frequency change, the vibration intensity, and the effective wind speed. A thorough comparison of the results from both regression models reveals in-depth statistical insights. This study confirms that vibration intensity has a negative effect on the bridge natural frequency, i.e., higher vibration intensity leads to a decrease in natural frequency. Besides, the study also shows that while the effective wind speed has a statistically significant impact on the frequency change of the vertical modes, vibration intensity (caused by traffic loads) appears to be a more dominant factor.

Damage detection of Kevlar woven fabric using optical fiber multimode interferometer

Kevlar woven fabric is crucial for the lightweight design of aerospace structures due to its unique advantages. However, it is susceptible to damage during operation, making effective damage detection essential for ensuring structural reliability. Nevertheless, conventional sensors used for damage detection have limitations such as complex manufacturing processes and weight. To address this issue, this paper proposed a simple singlemode-multimode-singlemode (SMS) optical fiber sensor to collect vibration signals and construct a damage recognition model based on natural frequency in order to identify the size of damages in Kevlar woven fabrics. To achieve a highly linear and accurate sensor, a length determination criterion for multimode optical fiber segments based on quasi-image, notch, and transmission spectrum loss was proposed. An optical sensor was fabricated based on this criterion. The feasibility and sensitivity of the sensor for vibration signal measurement were verified by constructing a vibration signal measurement device. An experimental study was conducted to detect damage in Kevlar tapes, where the natural frequency changes measured by the SMS sensor were integrated with an optimized multi-variable gray model for damage size detection. The experimental results indicate that the estimated error in damage size is 0.71%. The damage identification system proposed in this paper offers a simple and cost-effective solution for measuring damage in flexible structures using fiber optic sensors.

Numerical Simulation Study on Vibration Characteristics and Influencing Factors of Coal Containing Geological Structure

Accurately determining the natural frequency of coal-containing geological structures is crucial for preventing mine dynamic disasters and utilizing vibration waves to break coal and enhance its permeability. Based on the modal theory of rock, vibration models of coal-containing geological structures, including layering and fractures are established. By analysis, the undamped vibration equation and its characteristic equation for both the layered coal system and the fractured coal system are derived. Subsequently, the Lanczos method is employed to solve the system’s vibration modes using ABAQUS. The effects of the layering position, layering thickness, layering physical properties, crack width, and crack length on the natural frequency and vibration response of coal-containing geological structures are investigated. The results indicate that when a single influencing factor is altered, the displacement response distribution of the coal body vibration system with geological structures remains essentially the same, and these single influencing factors have a minimal impact on the vibration displacement of the coal-containing geological structure. The natural frequency of the system decreases exponentially as the distance between the layering and the geometric center of the coal system with geological structures increases. The presence of layering in the coal system with geological structures significantly reduces the system’s natural frequency. The natural frequency of the coal system with geological structures increases in a power function manner as the layering elastic modulus increases. Conversely, the natural frequency decreases with an increase in crack length. When the change ranges of crack width and bedding thickness are the same, the natural frequency of the fractured coal body system exhibits more significant changes. The natural frequency of the coal system with geological structures initially decreases and then increases as bedding thickness and crack width increase. The trend in the natural frequency changes and the position of the extreme point are related to the ratio of the elastic modulus and density of the geological structure.

An enhanced mathematical model for evaluating grid-to-rod fretting wear under complex boundary

Grid-to-rod fretting wear is a significant cause of fuel failure in pressurized water reactors and poses a challenge in fuel performance evaluation. As burnup increases, neutron irradiation can lead to complex changes in the grid-to-rod system, affecting its dynamic behavior. This paper presents an enhanced mathematical model that can simulate the coupled axial-lateral motion and complex boundary conditions, including relaxation support, friction, and gap constraint. Through multiple parametric studies, the model has revealed valuable results. Notably, grid relaxation of 10%–30% significantly impacts wear. Multiple critical excitation frequencies can cause drastic changes in vibration and wear. The increase in holding force due to rod swelling and the early opening of the gap due to creep down require careful attention. Moreover, the effect of axial force on changes in natural frequency and increased wear should be considered.

Flexoelectric and surface effects on bending deformation and vibration of piezoelectric nanolaminates: Analytical solutions

In this paper, a model of double-layer rectangular piezoelectric nanolaminates with different upper and lower surface properties is established. The bending and vibration behavior of the piezoelectric nanolaminates are evaluated and analyzed, taking into consideration the flexoelectric and surface effects. Utilizing the surface piezoelectric model, flexoelectric theory, and Kirchhoff plate theory, this study provides analytical solutions for the bending deflection and natural frequency of rectangular piezoelectric nanolamination materials under various boundary conditions. The results indicate that the effects of flexoelectric and surface influences on piezoelectric nanolaminates are associated with residual surface stress and flexoelectric coefficients. These effects can enhance the bending stiffness and decrease the natural frequency of the piezoelectric nanolaminates. Furthermore, altering the residual stress on the upper and lower surfaces of the laminates separately will result in different trends in bending deflection, while causing a consistent trend in natural frequency change. When the electric potential direction of piezoelectric nanolaminates is different, the bending deflection of piezoelectric nanolaminates will change accordingly. The natural frequency of piezoelectric nanolaminates is determined by the absolute value of the flexoelectric coefficients, and is independent of their positive or negative values. Both the surface effect and the flexoelectric effect are influenced by size-dependent behaviors. When the thickness of the laminates is sufficiently large, both the surface effect and flexoelectric effect can be disregarded. This paper's research methods and results provide theoretical models and analytical methods for the microstructure design, multi-physical field characterization, and bending deformation behavior of intelligent components containing rectangular piezoelectric nanolaminates.

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.

Development of Modified Rhombus Amplifier of Positioning Stage Compliant Mechanisms

Abstract This paper presents a modified design of rhombus-type amplifier used in positioning stage compliant mechanism. The new rhombus design is introduced to enhance the performance of rhombus and the results are promising. The new approach of rhombus amplifier is based on mixing the concept of rhombus type with the idea of hinges (reduced section portions) existed in bridge type. The performance of the proposed design is investigated by the pseudo rigid body model and validated by the finite element analysis. The new rhombus design improves displacement amplification ratio by (22.3%) with slightly change in master mode natural frequency (1.3%). The pseudo rigid body model for new rhombus design is consistent with the ANSYS results, and hence can be used in modelling and analysis of the new rhombus design.

Active vibration control of a large space telescope based on H∞ control with unilateral and constrained input

The development of the telescope with large aperture is driven by the increasing demand for higher imaging resolution and imaging area. The large membrane diffraction space telescope is particularly attractive due to their lightweight nature, ease of folding and unfolding, and high precision imaging capabilities. However, the flexible and large structure of these telescope makes them prone to long-time, low-frequency vibrations in space. These vibrations can degrade the imaging quality and potentially cause damage to the instrument in the space telescope. Therefore, it is crucial to develop effective active vibration control methods to suppress these structural vibrations. This paper proposes a control method that utilizes cables as actuators. Since cables can only withstand tension and have limited output tension, this constraint is taken into account during the control design process. Firstly, a dynamics model of the membrane diffraction space telescope with hinge flexibility is developed by the beam theory and finite element method. Next, an active controller is designed by combining H∞ control theory and Linear Matrix Inequalities (LMI). Additionally, the optimal positions of cable actuators are determined using the Gram controllability criterion and a particle swarm algorithm. Finally, the effectiveness of the control method is verified through numerical simulations. The simulation results demonstrate that the hinge flexibility significantly influences the structural vibration behavior of the telescope. Furthermore, the proposed control method demonstrates the ability to effectively suppress the vibrations of the telescope while also exhibiting robustness to changes in natural frequencies of the structure.

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.