Lowest Natural Frequency Research Articles

Comparison Study on the Fatigue Damage of a Container Ship Applying Hydroelastic Fatigue Analysis Procedures of LR and BV Classification Societies

<i>Container ships, which have hatch openings, are subject to low natural frequencies and exhibit elastic behavior due to wave loads, a phenomenon referred to as the hydroelastic effect. Classification societies have established hydroelastic fatigue analysis procedures to address the increased fatigue damage caused by this effect. This study compares the fatigue damage increase ratios at the hatch coaming top corners according to the procedures provided by Lloyd's Register (LR) and Bureau Veritas (BV). The weight distribution was adjusted using mass and interpolation elements, and normal mode analysis was conducted to obtain the natural frequencies and mode shapes of the ship, which were then used in frequency-domain hydroelastic motion analysis. The fatigue analysis was performed based on LR and BV procedures, using mode response amplitude operators (RAOs) and hydrodynamic coefficients derived from the hydroelastic motion analysis. Despite the differing methodologies between LR and BV, similar stress RAOs were obtained, with the midship showing a higher fatigue damage increase ratio than the forward and aft ends. For the LR procedure, more modes are needed for greater accuracy at the aft end, and for the BV procedure, further investigation is required to address the unreasonable response of the dynamic stress RAO in the low-frequency region, which is distant from the resonance frequency.</i>

Development of vibration isolation system for halls and report on sound insulation and vibration experiment

Rubber and polyurethane have been widely used as vibration isolation materials in halls and studios. In this project, we have developed a floor-mounted coil spring vibration isolator with improved vibration isolation and sound insulation characteristics, while keeping the installation height equivalent or lower than rubber and polyurethane. In this paper, we evaluate the vibration isolation performance of the developed device by measuring vibration transmission loss, and confirm that the device can suppress surging, which is a weak point of metal springs, while achieving a low natural frequency. The sound transmission loss measurement also confirmed that the floating slab incorporating the device has sufficient sound insulation performance, and these results indicate that the device can be applied to acoustic spaces such as concert halls, where quietness is required.

Dynamic response and vibration suitability analysis of the large-span double-connected structure under coupled wind and pedestrian loads

Modern buildings increasingly utilize lightweight, high-strength materials and feature high-rise, large-span structural designs. These structures often exhibit low natural frequencies and are susceptible to resonance from low-frequency dynamic loads such as wind and pedestrian loads. This paper focuses on a large-span double-connected structure and analyzes its dynamic response under the combined effects of wind and pedestrian loads. First, a finite element model of the structure was created using ANSYS, and model validity verification and modal analysis were performed. Second, a Fourier-based pedestrian model was used to simulate pedestrian loads and generate time-range data. The pulsating wind speed was generated from the Davenport spectrum using the harmonic superposition method. Wind load time-range data were calculated for different heights using Bernoulli’s theorem. Finally, the solution yields information about the dynamic response of the structure. The study revealed maximum vertical comfort ratings in the connecting corridor were achieved when crowd density did not exceed 0.3 persons/m2. The connecting corridor’s most unfavorable horizontal comfort level was evaluated as a medium, except for the 0-degree wind angle condition. This paper provides experience in studying the dynamic response and vibration suitability assessment of the large-span double-connected structure under wind and pedestrian loads.

An Investigation of the Effects of a Dynamic Vibration Absorber (DVA) to the Comfort of a Bus's Driver Seat

The frequency weighted acceleration, relative displacement, and Seat Effective Amplitude Transmissibility (SEAT) of a bus driver's seat are investigated by a 4 degrees of freedom (4DOF) vertical dynamic model, including a dynamic vibration absorber (DVA). The Root Mean Squared (RMS) values of the gain responses in the frequency domain are analyzed in the DVA damping ratio domain to help determine the optimal value of the DVA' s suspension. The obtained results show that the comfort evaluation index, in the case of a bus driver's seat with DVA, can be improved by more than 15% and nearly 10%, respectively, with the seat suspension natural frequency of 1~Hz and 4~Hz respectively. The comfort is better with the lower seat suspension natural frequency and vice versa. Especially in the case of both the seat and the DVA suspensions with low natural frequencies, all the three mean of evaluation indexes in the whole damping ratio domain of the DVA, have improved by more than 12%. This is the case with all three evaluation indexes which are the best when the damping ratio of the DVA is greater than 0.6.

Aging evaluation of fuse holders of BWR nuclear power plant

The aging evaluation of a typical fuse holder, which is used in a BWR-5 nuclear plant, is discussed in this paper. This evaluation considered the guidelines of the NUREG-1760. A fuse holder, class R, has been considered. It has a wire gauge in the 500 kcmil – 4 Cu/Al range. It is used for a nominal current between 201 A and 400 A. It has 3 poles with a box-type terminal and a reinforcing clip, for blade-type fuses. The evaluation was carried out in two steps using the ANSYS® code. In the first, the operation of the fuse holder without aging was simulated. A three-dimensional model was used. The numerical solution requires the coupling of electrical, thermal, and mechanical analyses. It can be done with a single model. The mesh elements are Solid 232, Solid 291, and Solid 187. The model was refined at the clip holder and connector terminals. The model has 3,379,780 nodes and 2,387,463 elements. Its natural frequencies and the distribution of temperature, voltage, and stresses were obtained. The aging analysis was carried out in the second step after sixty years of operation. The loss of 1 mm in the thickness of the fastener, caused by corrosion or wear in the fuse assembly, was considered. The results showed that the vibration modes occurred with lower natural frequencies when inadequate contact occurred. Besides, changes in the other operating parameters were observed.

FPSO ROLL MOTIONS DRIVEN BY SECOND-ORDER FORCES AND THE IMPACTS ON SLWR RISER DESIGN

Abstract The dynamic behavior of risers is highly influenced by the FPU motions, associated with environmental loads, caused by waves, current and wind. Particularly, as well known, under potential flow modelling, wave loads may be represented through power series expansions, with respect to a small parameter ε. First-order wave forces pulsate in the frequency range of the incident wave spectra, whereas second-order wave forces are related to sum or difference frequencies of the same spectra. The so-called second-order difference frequencies forces may then be responsible by resonating motions of the vessel in that range. Significant low-frequency motions due to second order forces are commonly observed in the horizontal plane, resonating low natural frequencies of moored floating systems characterized by low mooring stiffnesses. Recently, however, this phenomenon was also observed for roll motions in several new FPSOs that will operate in the Pre-Salt of Santos Basin. The phenomenon had already been detected in a deep draft semi-submersible in Campos Basin, but only more recently in FPSOs. The new floating units are characterized by high roll natural periods, above the typical wave period range in the pre-salt region, and the roll response to the second-order difference frequencies forces can be significant. This phenomenon was indeed detected in model tests and confirmed by numerical studies. In fact, this additional FPSO roll behavior occurs in typical periods slightly above 20 s, imposing displacements and accelerations that can directly affect the dynamics of the riser top region. The present paper addresses this phenomenon and its possible impact on steel lazy-wave riser (SLWR) designs.

The novel Vogel's approximation method integrated with a random forest algorithm in the vibration analysis of a two-directional functionally graded taper porous beam: Assessment

A functionally graded material is a class of composite materials characterized by gradual variations in composition and microstructure, which further induces the respective changes in the material properties. This study focuses on evaluating the vibration behavior of two directional functionally graded taper porous beams (FGTPB). This approach adopts a rectangular cross-section in order to deal with the challenges related to fluctuating material characteristics and geometric tapering in both thickness and width dimensions. The research employs a novel approach that merges Vogel's approximation technique with the Random Forest algorithm, an approach that has not been used in analyzing structural vibrations, establish boundary conditions and solve equations of motion. Comparative results of the suggested beam theory with the existing literature on FGTPB materials such as alumina and SUS304 at various taper, porosity, gradient and width ratios verified it. The material gradation and porosity developed a uniform pattern in the first three modes of fundamental frequencies. Higher gradient indices increased the rigidity and natural frequencies of the beams whereas the porosity index decreased the rigidity, resulting in lower natural frequencies. By combining Vogel's approximation method with machine learning techniques, the study improved vibration behavior analysis in FGTPB. The disciplines of materials and structural engineering are significantly impacted by this.

Experimental and numerical analyses on the modal behaviour of an aluminium alloy sheet

Abstract The study of modal behaviour for vehicle body panels represents a field of interest for automotive engineering, having a major influence on automotive comfort, with respect to vehicle noise, vibration and harshness, but also concerning the durability of vehicle body. The investigation of natural frequencies and vibration mode shapes is crucial in the design phase, because essential information can be obtained concerning the behaviour of the components in dynamic conditions. The current paper focuses on the investigation of vibration modes and frequency response function on an aluminium alloy sheet. The aim of the paper is to perform the study of modal behaviour both experimentally and theoretically, through measurements using the impact hammer method and respectively through finite element analysis. The CAD model of the aluminium alloy sheet has been developed in Catia V5 environment in view of elaborating the finite element model, which has been used for investigation of modal behaviour, taking into account the case of free vibrations. Through the modal finite element analysis performed in Ansys Workbench, the natural frequencies of the aluminium alloy sheet, as well as the corresponding mode shapes have been obtained. Experiments have been performed on an aluminium alloy sheet, mounted on an elastic support with low natural frequency. The impact hammer method has been used for obtaining the natural frequencies, through frequency analysis of accelerations measured with two piezoelectric accelerometers mounted on the aluminium alloy sheet. The frequency response function has been computed from the response acceleration measured on the aluminium alloy sheet and the impact force measured using the force transducer of the impact hammer. Virtual instruments have been developed in LabVIEW environment for data acquisition, time domain and frequency analysis, as well as for determining the frequency response function using the measured signals. The natural frequencies obtained from the finite element analyses have been compared to the results of measurements and very good similarities have been ascertained. The experimental investigation of modal behaviour contributed to the validation of the finite element model, but further research is required to investigate the possibilities of improving the modal behaviour of the aluminium alloy sheet.

Tunable High-Static-Low-Dynamic Stiffness Isolator under Harmonic and Seismic Loads

High-Static-Low-Dynamic Stiffness (HSLDS) mechanisms exploit nonlinear kinematics to improve the effectiveness of isolators, preserving controlled static deflections while maintaining low natural frequencies. Although extensively studied under harmonic base excitation, there are still few applications considering real seismic signals and little experimental evidence of real-world performance. This study experimentally demonstrates the beneficial effects of HSLDS isolators over linear ones in reducing the vibrations transmitted to the suspended mass under near-fault earthquakes. A tripod mechanism isolator is presented, and a lumped parameter model is formulated considering a piecewise nonlinear–linear stiffness, with dissipation taken into account through viscous and dry friction forces. Experimental shake table tests are conducted considering harmonic base motion to evaluate the isolator transmissibility in the vertical direction. Excellent agreement is observed when comparing the model to the experimental measurements. Finally, the behavior of the isolator is investigated under earthquake inputs, and results are presented using vertical acceleration time histories and spectra, demonstrating the vibration reduction provided by the nonlinear isolator.

Hardware-in-the-Loop experiments in model ice for analysis of ice-induced vibrations of offshore structures

The study investigated the use of a Hardware-in-the-Loop (HiL) technique applied in model ice experiments to enable the analysis of offshore structures with low natural frequencies under dynamic ice loading. Traditional approaches were limited by facility capacities and ineffective downscaling of the geometry of the offshore structures. The goal of the present study was to overcome these challenges and to enhance the understanding and explore the applicability of a hybrid testing technique in model ice experiments. To achieve the objective, 204 Hardware-in-the-Loop simulations in model Ice (HiLI) were analyzed. Results showed robust behavior and good performance of the HiLI due to minimal variation in measured delay, normalized root mean square error, and peak tracking error and low magnitudes of such parameters despite alterations in factors such as the choice of the numerical structural model, physical prototype, measurement system, and ice type. Notably, the performance of the HiLI was affected when testing with warm model ice or scaling for harsh ice conditions, attributed to a reduced signal-to-noise ratio and instability of the system, respectively. Experimental identification of the critical delay, along with the application of an analytical stability criterion, revealed that the instability observed, was likely induced by reducing the structural stiffness of the numerical structural model to fulfil the scaling requirements when testing for harsh ice conditions. Additionally, the study showed improved HiLI performance when the physical prototype was in contact with the model ice. This observation was further analyzed and is assumed to be caused by the coupling between the ice and physical prototype, causing a coupled and thus increased eigenfrequency of the physical prototype-ice system.

OPTIMIZING THE PRODUCTION OF LAYERED SYSTEMS INCORPORATING MFC TRANSDUCERS AND MODELING BOLT JOINT LOOSENING DETECTION WITH THEIR APPLICATION

This article offers a concise overview of cutting-edge techniques for monitoring bolt joint looseness and optimizing Macro Fiber Composite (MFC) based structure manufacturing for structural health monitoring emphasizing MFC-host structure attachment methods, optimal MFC placement, and the impact of adhesive layers between MFC and the host structure. The study also employs Ansys software to conduct Multiphysics modelling and characterization of bolt joint conditions using MFC piezoelectric transducers. Emphasizing joint looseness under varying pretension loads, the results demonstrate that increasing preload, up to the full tightening torque value (14.5 Nm), increases the natural frequency, indicating enhanced joint stiffness. Conversely, looser connections result in lower natural frequencies, signifying decreased joint stiffness. The article focuses on assessing the effectiveness of Macro-Fiber Composite (MFC) for monitoring the health of bolt joints, providing a simple and efficient method for modelling the structural response of MFC-integrated bolt joints, facilitating convenient and rapid engineering analysis and testing.

Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System: A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles, pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system. However, traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles. To address this issue, a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension (GIQZSPS) is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes. This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension. It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers. Firstly, a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system. By the nonlinear mechanical model of GIQZSPS system, the force transmissibility rate is chosen as the evaluation index to analyze characteristics. Furthermore, a testing bench simulating 1/4 GIQZSPS system is designed, and the testing analysis of the model validation and isolating performance is carried out. The results show that compared to traditional pneumatic suspension, the GIQZSPS designed in the article has a lower natural frequency. And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

Nd-, La-induced precipitate/defect in cobalt-iron magnetic alloy for strong and broadband microwave absorption

Soft magnetic microwave absorbents have merits of sufficient magnetic loss and unique magnetism-frequency response characteristics, yet are limited by the low natural resonance frequencies and simplex loss mechanism. Introducing second phase has been proven to be efficient in evoking structure, magnetism and conductivity changes, but the effects on the microwave absorption is still unbeknown. In this work, the Co0.72Fe0.28 alloy magnetic absorbents with dispersedly distributed NdCo5/LaCo5 nano precipitates were prepared. By fine-tuning the doping ratios of the rare earth (RE) of Nd/La, the coercivity and conductivity show an upward trend with enhanced magnetic and dielectric losses on 2–18 GHz. On one hand, the high magneto-crystalline anisotropic RECo5 phases uplifted the holistic resonance frequency ranges and enhanced the C/X/Ku band attenuations. On the other hand, the as-spawn vacancies, heterogeneous interfaces and dislocations boosted the conductive/polarization losses of the individual magnetic alloys. As a result, the high-frequency performance was significantly improved when ensuring the impressive low-frequency loss. A remarkable minimum reflection loss (RLmin) of −76 dB was achieved in the S band, and the effective absorption bandwidth (EAB) of 7.34 GHz was obtained at only 1.7 mm, covering most of the X/Ku bands. The performance sets it apart as the highest among the reported RE-transitional alloy absorbents so far. Overall, this work provides a feasible way and novel strategy for improving the microwave absorption properties for the traditional metal alloys and their compounds.

Studying the mode shape participation factor of wave loads for offshore wind turbine structures

This paper introduces a method for analyzing resonance between Offshore Wind Turbine (OWT) structures and wave loads using Wave Participation Factor ratios (WPFs). Despite temporal fluctuations in WPFs due to wave loads, they prove effective for identifying key modes influencing wave load behavior in both fixed and floating OWT structures. For fixed OWT foundations, nonlinear soil behavior causes some natural frequency variations under wave forces, but they typically remain within a limited range. Lower natural frequency modes show minor WPFs, reducing the risk of resonance with wave loads. Modes with higher natural frequencies have substantial WPFs and are less prone to resonance. However, precautions are needed to avoid rotor-induced wind load resonance. Floating OWT structures have large WPFs in their first six near-rigid body motion modes, while mooring line stiffness leads to substantial variations in these modes. It's crucial to control the first six nonlinear frequencies outside the dominant wave load range. Beyond these six modes, natural frequencies significantly exceed wave load frequencies, reducing resonance concerns. In summary, this study presents an effective method for assessing resonance between OWT structures and loads, providing valuable insights for structural design and operational safety.

Research on bionic foldable spray aircraft wings

In this paper, the hind wing of Coccinella septempunctata is selected as the research object to design the bionic foldable spray aircraft wing. The structure of the bionic wing, the related flapping mechanism, the folding mechanism and other aircraft components are designed, and the two key parts of the bionic wing and arm are statically analyzed and optimized. To reduce the vibration in flight, modal analysis of the bionic wing and arm is carried out, and the natural frequencies and modes of the two parts are explored. The results show that the lower natural frequency has the greatest influence on the dynamic characteristics of the components. The influence of the material properties on the modal characteristics is studied by changing the material characteristics of the components. The flow around the bionic wing is simulated by FLUENT software. The velocity distribution and pressure distribution of the flow field around the bionic wing are obtained. The influence of aerodynamics with attack angle α is analyzed to clarify the flight principle of the bionic wing.

Experimental Testing on Tuned Liquid Dampers for Implementation in Industrial Chimneys.

A TLD is a passive damping device that works by dissipating energy through the sloshing of the liquid and the effect of wave breaking, thereby controlling the vibrations of the structure. One of the applications where TLDs are of great interest is in the case of industrial chimneys since these structures often have a very low natural frequency, which can be easily achieved in a control device of this type. The main objective of this study is to evaluate the behaviour of an annular TLD composed of multiple cells through laboratory tests and investigate if it is adequate to design it as an agglomeration of smaller rectangular TLDs. The influence of the amplitude of displacement on the behaviour of the annular TLD will also be analysed. The tests were performed on a shaking table and recurring with pendulums of the same length but of different masses. Three reservoirs were studied as TLDs: a rectangular one, a cell of an annular TLD and a quarter-ring of an annular TLD. This study concluded that the analytical methods developed in previous studies were, in general, adequate for the design of a rectangular TLD and that it was reasonable to design the annular TLD studied as a combination of rectangular ones, as its cells were a close match to a rectangle of similar dimensions. It was also concluded that a compartmentalised annular TLD is an adequate solution for the vibration control of structures with high displacements.

Simulation and experimental study of notched cantilever beam for improved vibration energy harvesting

This research paper addresses the design and analysis of a Notched Cantilever Beam Energy Harvester (NCBEH) aimed at enhancing vibration energy harvesting. The voltage output from Lead Zirconate Titanate (PZT) piezoelectric material is directly related to the strain it experiences. Therefore, numerical simulations using ANSYS were conducted to investigate the variations in natural frequency and stress–strain distribution with respect to slot length in a slotted cantilever beam. Additionally, a notch was introduced into the beam to further enhance strain distribution. The study found that, with precise PZT placement, an NCBEH with a 55 mm slot length can generate 15% more voltage output at lower natural frequencies compared to existing Piezoelectric Cantilever Beam Energy Harvesters (PCEH) [1]. Experimental tests were also conducted to compare the voltage output response of the NCBEH and the PCEH, with the results showing good agreement with the numerical simulation findings.

Characterizing Natural Frequencies of the Hybrid III and NOCSAE Headforms

The vibrational characteristics of the Hybrid III and NOCSAE headforms are not well understood. It is hypothesized that they may perform differently in certain loading environments due to their structural differences; their frequency responses may differ depending on the impact characteristics. Short-duration impacts excite a wider range of headform frequencies than longer-duration (padded) impacts. While headforms generally perform similarly during padded head impacts where resonant frequencies are avoided, excitation of resonant frequencies during short-duration impacts can result in differences in kinematic measurements between headforms for the matched impacts. This study aimed to identify the natural frequencies of each headform through experimental modal analysis techniques. An impulse hammer was used to excite various locations on both the Hybrid III and NOCSAE headforms. The resulting frequency response functions were analyzed to determine the first natural frequencies. The average first natural frequency of the NOCSAE headform was 812 Hz. The Hybrid III headform did not exhibit any natural frequencies below 1000 Hz. Comparisons of our results with previous studies of the human head suggest that the NOCSAE headform’s vibrational response aligns more closely with that of the human head, as it exhibits lower natural frequencies. This insight is particularly relevant for assessing head injury risk in short-duration impact scenarios, where resonant frequencies can influence the injury outcome.

Experimental Study on Dynamic Characteristics of Damaged Post-Tensioning Concrete Sleepers Using Impact Hammer.

Concrete sleepers in operation are commonly damaged by various internal and external factors, such as poor materials, manufacturing defects, poor construction, environmental factors, and repeated loads and driving characteristics of trains; these factors affect the vibration response, mode shape, and natural frequency of damaged concrete sleepers. However, current standards in South Korea require only a subjective visual inspection of concrete sleepers to determine the damage degree and necessity of repair or replacement. In this study, an impact hammer test was performed on concrete sleepers installed on the operating lines of urban railroads to assess the field applicability of the modal test method, with the results indicating that the natural frequency due to concrete sleeper damage was lower than that of the undamaged state. Furthermore, the discrepancy between the simulated and measured natural frequencies of the undamaged concrete sleeper was approximately 1.87%, validating the numerical analysis result. The natural frequency of the damaged concrete sleepers was lower than that of the undamaged concrete sleeper, and cracks in both the concrete sleeper core and the rail seat had the lowest natural frequency among all the damage categories. Therefore, the damage degrees of concrete sleepers can be quantitatively estimated using measured natural-frequency values.

Train–Bridge Coupled Vibration of a Long-Span Steel Truss Suspension Bridge Under Complex Driving Conditions

To investigate the vibration characteristics of long-span suspension bridges under the impact of high-speed trains, a method for conducting a time–frequency domain analysis of the dynamic response of a coupled system is presented in this study. First, the finite element model of a suspension bridge is established to conduct modal analysis, and simulation results are compared with measured data to validate the correctness of the bridge model. Subsequently, a multi-body dynamics model of a high-speed train is developed. Then, two approaches, the dummy method and flexible-track method, are employed to create the train–bridge coupled system. Finally, the flexible-track method is used to perform time–frequency domain analysis of the system under complex operational conditions. The research revealed that large-span suspension bridges exhibit lower natural frequencies. The vertical bending vibrations of the main beam have the potential to significantly impact train operations. Under the combined impact of cable tension and wheel–rail forces, the vibration patterns of large-span suspension bridges become notably intricate. The number of trains and their loading configurations both exert influence over the dominant frequencies and amplitudes in the PSD of bridges. In the complex traffic of large-span suspension bridges, the rational arrangement of travel lanes can reduce the possibility of resonance in the bridge–train system.