Natural Frequency Drop Research Articles

An experimental and numerical effort on the vibration behavior of additively manufactured recycled polyethylene terephthalate glycol components

AbstractThe importance of recycling engineering components and thus obtaining low‐cost production solutions has become prominent in today's world. In this study, the mechanical and dynamic behaviors of three‐dimensional‐printed recycled polyethylene terephthalate glycol (RePET‐G) beams were investigated numerically and experimentally for the first time in the literature. Initially, the governing equations of the beams were determined according to the Bernoulli–Euler beam theory, and these equations were numerically solved using the differential quadrature method and ANSYS program. Subsequently, to validate the accuracy of the numerical models, the obtained natural frequencies were compared with experimental results. It was observed that the numerical results showed good agreement with the experimental results. Finally, the effects of beam length, infill rate, and building direction on the natural frequencies of RePET‐G beams were investigated. The outcomes showed that as the beam length changed, natural frequencies were significantly affected. Increasing the infill rate, especially for beams with vertical building direction, from 20% to 100% led to a slight decrease in the natural frequency values of the structure. Moreover, it was found that for beams with an infill rate of 100%, the natural frequency values obtained in the horizontal building direction were higher than those obtained in the vertical building direction.Highlights Printable recycled filaments have great potential for vibration applications. Sample length affects the first natural frequency value of RePETG parts. Differential quadrature and ANSYS methods can be utilized for the vibration. For the 3D‐printed samples, rising infill rate causes a natural frequency drop.

Progressive deterioration of reinforced concrete structures: effect on dynamic properties of flexural members

PurposeThe main purpose of this study is to examine the damage behavior of flexural members under different loading conditions. The finite element model is proposed for the prediction of modal parameters, damage assessment and damage detection of flexural members. Moreover, the analysis of flexural members has been done for the sensor arrangement to accurately predict the damage parameters without the laborious work of experimentation in the laboratory.Design/methodology/approachBeam-like structures are structures that are subjected to flexural loadings that are involved in almost every type of civil engineering construction like buildings, bridges, etc. Experimental Modal Analysis (EMA) is a popular technique to detect damages in structures without requiring tough and complex methods. Experimental work conducted in this study concludes that a structure experiences high changes in modal properties once when cracking occurs and then at the stage where cracks start at the critical neutral axis. Moreover, among the various modal parameters of the flexural members, natural frequency and mode shapes are the viable parameters for the damage detection.FindingsFor torsional mode, drop in natural frequency is high for higher damages as compared to low levels. This is because of the opening and closing of cracks in modal testing. When damage occurs in the structure, there is a reduction in the magnitude of the FRF plot. The measure of this drop can also lead to damage assessment in addition to damage detection. The natural frequency of the system is the most reliable modal parameter in detecting damages. However, for damage localization, the next step after damage assessment, mode shapes can be more helpful as compared to all other parameters.Originality/valueEffect on Dynamic Properties of Flexural Members during the Progressive Deterioration of Reinforced Concrete Structures is studied.

Diagnostics of a Clamping Joint System

Abstract The article describes a diagnostic method, on the basis of which it is possible to assess whether there is a loose connection in the clamping system (detection) and to determine which of them is loose (localization). The diagnostic method is based on comparing the drops in the natural frequencies of a measured system with respect to a reference system, which simulates the desired state. When analysing the drop in natural frequencies in order to locate the loosening, it is necessary to relate this drop to the position of the clamping joints within the considered mode shape.

A molecular dynamics study on the vibrational behavior of perfect and defective hybrid carbon boron-nitride heteronanotubes

In this paper, the free vibration of hybrid carbon boron-nitride heteronanotubes (CBNNTs) is analyzed through molecular dynamics (MD) simulations. In the vibration analysis, various CBNNTs (Cx ∣ (BN)y and C-BN models) according to two geometrical arrangements of constituent segments are considered. By introducing vacancy defects in nanotubes, the influence of defects on the vibrational response is studied in terms of the weight percentage and distribution pattern. The highest vibration frequency is reported and CBNNTs' results are compared with those of carbon nanotubes (CNTs) and boron-nitride nanotubes (BNNTs). It is observed that CBNNTs possess natural frequencies which lie between the values for CNTs and BNNTs. The natural frequency is found to be reduced by increasing the defect percentage. At each defect percentage, the defective C-(BN) model I and C1.5 ∣ (BN)1.5 experience almost the same natural frequency in both distribution patterns. Vibration frequencies of defective C-(BN) model II and C4.5 ∣ (BN)4.5 are nearly close together at a defined percentage of defects. Despite the minor differences between natural frequencies in either distribution pattern, regularly defected CNTs tend to have a bit higher frequency than randomly defected CNTs, however, the results are opposite in the regularly and randomly defected BNNTs. Moreover, the C-(BN) model II vibrates at a higher natural frequency than that of the C-(BN) model I. It is found that the vibrational behavior of the C-(BN) model I is mostly affected by the BN segment than the C segment. Further, the natural frequency's drop in the defected C1.5 ∣ (BN)4.5 is found to be more significant than other CBNNTs by rising the defect percentage. C-(BN) model I and defective C-(BN) model I experience higher deformations in comparison with the Cx ∣ (BN)y configurations when vibrating at their natural frequency.

Effect of Elevated Temperature on Harmonic Interlaminar Shear Stress in Graphite/Epoxy FRP Simply Supported Laminated Thin Plate Using Finite Element Modeling

Graphite/Epoxy Fiber Reinforced Polymer (FRP) plates are used widely due to their high strength to weight ratio. Current work is concerned about investigating the harmonic interlaminar shear stresses existing between laminates in a simply supported composite Graphite/Epoxy FRP plate under elevated temperatures and for different fiber orientation schemes using finite element modeling. Interlaminar shear stress which is affected by temperature plays a major role in composite material delamination. The simply supported composite plate under study consists of eight laminated layers with different orientation schemes ([0°]8, [0°/15°]4, [0°/30°]4, [0°/45°]4, [0°/60°]4, [0°/75°]4, and [0°/90°]4). Modal analysis is performed to find the natural frequencies for all fiber orientations and temperatures considered. However, harmonic analysis is carried out to study the transverse deflection and interlaminar dynamic shear stress for orientation schemes and temperatures considered at the interfacial of the 7th ply. It is found that increasing temperature leads to slight drop in natural frequency at each orientation scheme but leads to higher deflection and shear stress. Furthermore, it is observed that orientation scheme [0o/45o]4 is the best case for all the temperatures considered since minimum transverse deflection and interfacial shear stress are obtained for almost all the driving frequency range.

Experimental study on vibration characteristics of fluid-solid coupling cantilever thin aluminum plate

Compared with the general environment, the modal characteristics of structures under fluid-solid coupling will show great differences. Reasonable experimental methods can provide reliable conclusion support for fluid-solid coupling research. In order to explore the modal characteristics of structures under the action of fluids, the interference and finite element numerical calculation methods are used to study the dry and wet modal characteristics of the cantilever aluminum plate under fluid-solid coupling. According to the amplitude fluctuation resonance discrimination method, the resonant frequency and mode of the cantilever aluminum plate under different working conditions are obtained accurately. Experiments show that the effect of the fluid will greatly reduce the natural frequency of the structure and have little effect on the vibration mode. With the gradual increase of the fluid-solid coupling interface, the natural frequency drop rate and the amplitude at the gas-liquid interface remain consistent, and slightly ahead of the amplitude characteristics. At the same time, for each mode with the same characteristics, the frequency decreasing trend is linear, such as the first few pure bending vibration modes, and the first few bending and twisting combined vibration modes contain first-order twisting vibration. The experimental results and the finite element numerical results are in good agreement, which shows that the electronic speckle method is a good test method for studying fluid-solid coupling modes. Most importantly, the experimental conclusion has reliable reference value for practical engineering applications.

Vibration analysis of rotating composite blades with piezoelectric layers in hygrothermal environment

In this study, vibration of a rotating composite blade with piezoelectric layers subjected to a tip mass in hygrothermal environment is investigated. The general composite equations for the single layer materials are expanded under varying temperature and humidity concentrations. The governing equations are derived based on the Hamilton principle based on the Euler-Bernoulli beam theory. Applying Galerkin’s procedure, the resulting equations are converted into a set of eigenvalue equations. The effects of temperature, humidity, angular velocity, fiber orientation angle, voltage and piezoelectric layers on the natural frequency of system are explored. The results show that by increasing the angular velocity, the natural frequencies increases. It was also found that increasing temperature and humidity causes a drop in the non-dimensional natural frequency. Besides, it can be concluded that heat and humidity have significant effects on the natural frequency of rotating composite blades. Applying positive and negative voltages results in a raise and drop in the natural frequency, respectively. It was also found that as the angular velocity of the composite beam increases, the non-dimensional natural frequency decreases. Furthermore, the lowest natural frequency is achieved when the tip mass is located at the end of the beam. The results show that as the fiber orientation angle increases, the natural frequencies increase which is related to enhancing the bending stiffness of the composite blades.

The effect of a crack near the fixed end on the natural frequencies of a cantilever beam

The paper examines how a transverse crack near the fixed end of a beam affects the natural frequency drop. It is known that the decrease in the frequency due to a crack depends on the position of the damage and its severity. This happens because the slice of the beam on which the crack is located changes its stiffness. Consequently, the damaged beam is no longer able to store the identical amount of energy as the healthy one. In addition, the field of stresses and deformations on an extended area around the crack is disturbed. This alteration can manifest freely for most positions of the crack along the beam. For this case, there is a direct relationship between the defect position and the frequency change, given by the modal curvature of the beam. Close to the fixed end, the field of stress and deformation is hindered on one side of the crack by the fixed end condition. In this way, the crack will produce a lower frequency drop compared with what it is expected. We performed simulations to obtain the frequency drop if the crack is located very close to the fixed end. With these values, we plot the regression curve and estimate the frequencies which should result for a crack located exactly on the fixed end of the beam if symmetric fields of stress and strain are possible. The results are necessary because the frequency drop characterizes the damage severity, further used in the damage detection processes.

Failure criterion of titanium alloy irregular sheet specimens for vibration-based bending fatigue testing

The failure moments of vibration-based fatigue tests are usually defined based on the natural frequency drops of specimens. But the selections of the critical values of the frequency drop have been very arbitrary in the previous tests, lacking of convincing reasons. The present paper aims to propose a failure criterion of titanium alloy irregular sheet specimens tested in a vibration-based bending fatigue experiment. A novel three-dimensional finite element model of the specimen is built, with a cohesive zone model employed to simulate the fatigue dangerous zone (FDZ) and the semi-elliptic crack propagation process of the specimen. A failure criterion to define the critical natural frequency drop is subsequently proposed based on the obtained computational results. Furthermore, a vibration-based bending fatigue test for the specimens is conducted to verify the computational model and the proposed failure criterion. After comparing the present testing results with the results of a similar bending fatigue test, the two types of the testing results are found very close. The vibration-based bending fatigue test with the proposed failure criterion provides an effective way for obtaining accurate fatigue life of irregular specimens.

Rotordynamic Computational and Experimental Characterization of a Convergent Honeycomb Seal Tested With Negative Preswirl, High Pressure With Static Eccentricity and Angular Misalignment

Hole-pattern or honeycomb seals have been commonly used for many years in the Oil & Gas industry as damper seals for turbomachinery. The main motivation has been to introduce additional damping to improve the shaft rotordynamic stability operating under high-pressure conditions. Experience has shown that the dynamic and even static characteristics of those seals are very sensitive to the operating clearance profile as well as the installation tolerances. Rotordynamic stability is related not only to the seal effective damping but to the effective stiffness as well. In fact, for this kind of seal, the effective stiffness can be high enough to alter the rotor system's natural frequency. The seal stiffness is strictly related to the tapering contour: if the clearance profile changes from divergent to convergent, the effective stiffness may change from a strong negative to a strong positive magnitude, thus avoiding the rotor natural frequency drop as it is detrimental for the stability. Unfortunately, the effective damping is reduced at the same time but this effect can be mitigated using proper devices to keep the preswirl low or even negative (e.g., swirl brakes and shunt holes). This paper presents the results from an extended test campaign performed in a high-speed rotor test rig equipped with active magnetic bearings (AMBs) working under high pressure (14 krpm, 200 bar gas inlet pressure), with the aim to validate the rotordynamic characteristics of a negative preswirl, convergent honeycomb seal and demonstrate its ability to effectively act as a gas bearing as well as a seal. The test plan included variations of inlet pressure, differential pressure (given the same inlet pressure), as well as rotational speed in order to fully validate the seal behavior. This kind of test was performed in a “dynamic mode” that is to say exciting the spinning test rotor through a pair of AMBs along linear orbits. Additionally, the impact of the seal to rotor static eccentricity and the seal to rotor angular misalignment were both experimentally investigated and compared to relevant computational fluid dynamics (CFD) simulations. This kind of test was performed in a “static mode,” that is to say imposing through the AMBs the required eccentricity/angular misalignment and then measuring the forces needed to keep the rotor in the original position. Dynamic mode test was also performed in order to check the impact of the seal static eccentricity on its dynamic behavior. Finally, the test results were compared with predictions from a state of the art bulk-flow code in order to check the predictability level for future design applications.

Effect of concrete carbonation on natural frequency of reinforced concrete beams

We carried out an experimental investigation to study the influence of concrete carbonation on the natural frequency of simply supported reinforced concrete beams. A total of 10 reinforced concrete test beams and 12 concrete-carbonation test specimens were subjected to different accelerated carbonation stages for 0, 7, 14, 21, and 28 days. Modal tests were performed on reinforced concrete test beams after the accelerated carbonation stages. In order to reduce the effect of other factors on the modal tests, constant temperature, relative humidity, and boundary conditions of the test beams were maintained in the experimental process. The experimental results show a trend of the natural frequencies of reinforced concrete test beams to decrease with the increase in concrete-carbonation depths. With statistical analyses of experimental data, this study established the relationship between concrete-carbonation depths and natural frequencies. Fitting lines for the drop in natural frequencies and carbonation depths are obtained for the first four modal frequencies. Based on the analysis of the physicochemical processes of concrete carbonation, the main reason behind the drop in natural frequencies is the increase in mass after concrete carbonation. The percentage composition of increase in mass after complete carbonation is obtained based on the analysis of the physicochemical process. This analysis demonstrates part of the reason for the drop in natural frequencies and proves that the experimental results are reliable and credible. This study provides further insight into the use of modal parameters to assess damage in concrete structures in structural health monitoring.

Pre-emptive Rotor Blade Damage Identification by Blade Tip Timing Method

The blade tip timing (BTT) method uses the differential arrival timings of the blades at case-mounted sensors to effectively characterize the vibrations of all blades in a rotor. This paper studies the use of the BTT method for pre-emptive prediction of rotor blade damage; through a careful monitoring of blade natural frequencies in conjunction with the blade tip position during an engine test. In the current study, the low pressure turbine stage of a developmental aero engine is instrumented with a combination of eddy current and optical sensors located circumferentially on the casing. This instrumentation effectively captures the engine order resonances of interest for the blade bending mode. During one of the normal engine tests, one of the blades in the LPT stage suddenly showed a drop in natural frequency beyond the allowable scatter and an abrupt change in the blade tip position. As the engine test was continued further, this drop in blade natural frequency and change in blade tip position progressively increased towards blade failure limits. Suspecting a propagating crack in the particular blade, the test was aborted and the engine was withdrawn for detailed inspection. Inspection of the rotor blades confirmed the presence of significant aerofoil crack in the suspect blade.

Dynamic characteristics and model updating of damaged slab from ambient vibration measurements

This paper reports a field investigation using ambient vibration testing on a damaged floor slab of a reinforced concrete frame building. Due to unexpected heavy rainfall, the hill slope at the rear of building failed triggering a major landslide and causing major damage to the perimeter beams and parts of the slab on the first floor. The modal parameters namely natural frequencies and mode shapes were acquired using output only identification technique and the results obtained from the undamaged and damaged floor slabs were compared. It was observed that there was a 25–53% drop in natural frequencies of the damaged slab compared to the undamaged slab, with a much bigger drop for the lower modes. The irregularities in mode shapes identified correlates with the location of the cracks as revealed from visual examination on the damaged slab. Two finite element models of the slab were created using a finite element software package. The damaged slab was updated manually so as to match the modal parameters obtained experimentally. The results from this study further highlight the possibility and feasibility of using non-destructive vibration testing for condition monitoring of structures over more conventional testing techniques.

The development of a resonance type gear fatigue tester.

A resonance type gear fatigue tester has been developed to evaluate tooth root fatigue strengths rapidly and efficiently. The tester operates on the resonance condition. One of a pair of test gears is held stationary to the tester bed and the other, fastened to the vibratory shaft, is oscillated against the stationary gear. The torsional vibration of the vibratory shaft is excited by the rotating eccentric on the end of the lever arm fixed to the shaft. Torque amplitude is controlled by varying the rotational speed of the eccentric, which is rotated with a 1.5 kW induction motor driven by a frequency converter. If the test frequency is slightly below the natural frequency of the vibrating system containing the test gears, sudden overloading occurs with the natural frequency drop due to slip on the tooth face and so on. To prevent overloading, a tester is designed so that the frequency can be set above the natural frequency. The test frequency range of the tester is 1000-3000 cpm and the torque capacity is 1200 N·m.