Quasi-static Component Research Articles

Assessment of aging degradation in rubber using quasi-static components of ultrasonic longitudinal waves

Abstract Aging degradation is the main form of failure of rubber in service, leading to a decline in its physical and mechanical properties. This paper presents an efficient method for assessing the aging degradation of rubber using the quasi-static component (QSC) of ultrasonic longitudinal waves induced by acoustic radiation. The experiments quantitatively observe the response of the QSC pulse to different levels of ageing degradation. A pulse-echo ultrasonic transducer is employed to simultaneously capture the primary longitudinal wave (PLW) and QSC echoes, enabling the determination of the acoustic nonlinearity parameter of QSC with a single transducer excitation. The results suggest that, in comparison to traditional linear ultrasonic techniques based on attenuation coefficient and wave velocity measurements, the relative acoustic nonlinear parameter of QSC proves to be more sensitive to aging degradation in rubber. Particularly, the amplitude of the QSC pulse undergoes a significant change with increasing aging degradation, even when the PLW tone burst is completely attenuated. These findings confirm the effectiveness of QSC as a method for evaluating aging degradation in highly attenuative materials.

A novel approach for state-of-charge estimation of lithium-ion batteries by quasi-static component generation of ultrasonic waves

Lithium-ion batteries content complex internal components, such as porous media and electrolytes, which result in strong scattering and high attenuation of ultrasonic waves in these batteries. The low attenuative feature of the quasi-static components (QSCs) of ultrasonic waves offers great potential for nondestructive assessment of highly attenuating and porous materials. This paper presents an innovative approach for estimating the state-of-charge (SOC) of lithium-ion batteries using QSC of ultrasonic waves. Experimental results demonstrate a clear and repeatable linear relationship between the amplitudes of the generated QSC and the SOC of lithium-ion batteries. In addition, the relationships between different SOCs of the battery and the conventional linear ultrasonic parameters, second harmonic generation (SHG), and the QSC were compared to verify the improved sensitivity of the proposed approach. Notably, compared to linear ultrasonic features and the SHG, the generated QSC shows much higher sensitivity to the variations of SOC. We employ the phase-reversal method to further enhance the signal-to-noise ratio of measured QSC signals. The experimental results demonstrate that the proposed method exhibits a heightened sensitivity to changes in the SOC of batteries, resulting in significantly enhanced detection accuracy and resolution. This method effectively addresses the deficiencies observed in the current detection methods such as limited accuracy and sluggish response times. This method provides a new solution to overcome this challenge. Meanwhile, it also confirms that nonlinear ultrasound promises an alternative method for SOC assessment, providing a foundation for efficient and safe battery management practices.

Collisions between Drones and Rotorcraft: Modeling of the Crash Response of Battery Packs

Drones operating in an urban environment pose a potential collision threat to rotorcraft. In this paper, the battery pack of the DJI MAVIC 2 ZOOM is analyzed since the battery is considered to be the greatest threat due to its high weight and stiffness. Following a pyramid-type building block approach, a high-fidelity model simulation was developed for LSDYNA based on a wide range of experiments, ranging from quasi-static material tests to quasi-static component tests up to high-velocity impact experiments. The high-fidelity model allows the prediction of damage in potential collision scenarios between a high-speed rotorcraft and the battery pack of the drone. For the particular impact configuration analyzed within this paper, the drone battery does not cause catastrophic failure of the windshield of the rotorcraft.

Numerical and experimental investigations on quasi-static component generation of longitudinal wave propagation in isotropic pipes

In this paper, the quasi-static component (QSC) generation of longitudinal waves propagating in an isotropic pipe is investigated numerically and experimentally. The three-dimensional (3D) finite element (FE) simulations are first carried out to gain physical insights into the characteristics of QSC generation from longitudinal wave travelling in an isotropic pipe with weak material nonlinearity. By applying the axial displacement excitation in the FE model, L(0, 1) mode and L(0, 2) mode are excited simultaneously. Then, the generated QSC pulses are extracted using the phase reversal approach for analysis. It is found that the QSC pulses generated by L(0, 2) mode and L(0, 1) mode are L(0, 1) mode. Meanwhile, the shapes of QSC pulses at different locations are extracted and compared. In this study, a data pre-processing method is proposed to handle numerically calculated and subsequent experimentally measured displacement signals, and a nonlinear acoustic parameter is defined to evaluate the incipient damages. After that, an experiment is conducted to measure the QSCs induced by the propagation of longitudinal waves in an aluminum pipe. The experimental results indicate that the propagation of longitudinal waves in the aluminum pipe can induce the QSCs. Different levels of corrosion are created on the surface of the aluminum pipe and are assessed by the generated QSCs. The results show that the nonlinear acoustic parameter has a monotonically increasing trend with the growing severity of corrosion. The QSCs generated by longitudinal wave can be used to detect and evaluate the early-stage surface corrosion in the aluminum pipe.

Quasistatic component generation of group velocity mismatched guided waves in tubular structures for microdamage localization

Quasistatic component (QSC) of guided wave (GW) has relatively low attenuation due to low frequency and high sensitivity to microdamage. The group velocity matching between primary GW and its QSC or higher harmonics usually facilitates the measurement of nonlinear signals due to cumulative effect of amplitude, but it restricts the determination of microdamage location. While group velocity mismatch is general for most of the wave mode pairs in nonlinear GW testing, this study presents a novel method for identifying the location of early stage microdamage using QSC generation of ultrasonic GW propagation in tubular structures under group velocity mismatching condition. A three-dimensional finite element (FE) model is developed to provide insights into the generation and propagation characteristics of the QSC induced by both global material weak nonlinearity and simulated local microdamage in metallic pipes. The FE analysis verifies the L(0,1) mode of the QSC generated from propagations of different fundamental wave modes. The generation efficiency and cumulation feature of the QSC pulse are obtained and discussed. By exploiting the group velocity mismatching condition, a microdamage localization method is proposed based on the L(0,1)-QSC mode pair, which requires one-way excitation of only one primary wave. Experiments are conducted using early corrosion aluminum specimens to investigate the QSC pulse signals and verify the proposed method. The FE and experimental results demonstrate the fundamental properties of QSC generation by GWs in isotropic metallic hollow cylindrical structures. The feasibility of the proposed microdamage localization method is validated experimentally for promising industrial applications.

A novel pulse-echo piezoelectric transducer for detecting quasi-static component induced by an ultrasonic longitudinal wave

For effectively detecting the quasi-static component (QSC) of an ultrasonic longitudinal wave, which is closely related to the elastic nonlinearity of material, we proposed a novel pulse-echo piezoelectric transducer consisting of a high-frequency piezoelectric wafer, a frequency selective isolation layer, a low-frequency piezoelectric wafer, and an acoustic backing. The high-frequency wafer generates the primary longitudinal wave (PLW) tone burst, while the high- and low-frequency wafers receive the pulse echo containing both the PLW component and QSC, respectively. We analyze the pulse-echo formation of the high-frequency PLW tone burst in a specimen, and conduct numerical simulations and experiments to validate the effectiveness of the proposed transducer. The results demonstrate that the low-frequency receiver is more efficient at detecting the QSC, even though the high-frequency wafer can also receive the echo of the QSC pulse. Specifically, the QSC pulse can still be detected by the low-frequency receiver when the high-frequency PLW tone burst is completely attenuated. The novel pulse-echo transducer proposed in this paper expands the design perspectives for transducers used in ultrasonic non-destructive testing.

Influence of ballast heterogeneity on railway induced vibrations and identification of heterogeneous properties of a ballast layer

In the context of railway induced vibration, the excitation induced by a passing train can be separated into a quasi-static and a dynamic component. The quasi-static component is related to the weight of the train transmitted through the wheels to the track. The dynamic component is related to the dynamic train-track excitation resulting from the irregularities of the running surfaces or from the variation of the track stiffness. At sub-Rayleigh speed on a track with longitudinally invariant properties, quasi-static excitation has no significant influence on the far-field vibration. In this paper, a randomly-fluctuating heterogeneous continuum model of the ballast layer is considered. Mechanical properties are represented as 3D random fields. First, the influence of ballast heterogeneity on the vibration field induced by a moving load is studied. The results show that heterogeneity is responsible for the generation of waves propagating away from the track. Then an identification process of the heterogeneous model of the ballast is presented based on experimental measurements of train passages.

Assessment of early fatigue in solid plates using quasi-static component by Lamb wave propagation under group velocity matching

The aim of this study is to investigate the feasibility of evaluating the degree of early fatigue in solid plates by utilizing quasi-static components (QSC) generated by primary Lamb wave (PLW) propagation. The investigation is carried out through theoretical considerations, numerical simulation, and experimental examination. The paper begins by examining the generation of QSCs by PLW propagation under group velocity matching. Subsequently, a suitable mode pair comprising primary and zero-frequency Lamb waves, which satisfy group velocity matching, is chosen for a given aluminum plate to enable the QSC to accumulate and grow with propagation distance. The aluminum plates are then subjected to tension-tension cyclic loading, and experimental measurements are performed. By measuring the amplitudes of the PLW and the generated QSC at different numbers of loading cycles (N), a quantitative relationship between the relative nonlinear acoustic parameter and N is established. The study demonstrates that the relative nonlinear acoustic parameter increases sensitively and monotonically with the increase in fatigue loading cycles. These experimental results confirm the feasibility of utilizing the group-velocity-matching QSC-based approach to evaluate the degree of early fatigue in solid plates.

On the robust experimental multi-degree-of-freedom identification of bolted joints using frequency-based substructuring

Modeling joint dynamics is the bottleneck for precise predictive models of machines. Bolted joints are especially relevant due to their common use in mechanical engineering. Stiffness and damping properties of bolted joints are highly influenced by contact parameters (geometry, surface treatment, preload, …). For high amplitude vibrations, when non-appropriate joint closure is present, even frictional effects can play a role.Substructuring techniques offer a lean solution for isolating dynamical or quasi-static components of joint dynamics. It may be used for an identification of linearized contact parameters for multiple degrees of freedom (dofs). The main limitation of the method is finding a robust workflow to guarantee a proper controllability and observability of the desired joint dynamics, as well as dealing with disturbance/noise in the measurements.In this contribution a robust procedure for the identification of a bolted joint using frequency-based substructuring is presented for a contact in an experimental scenario. The dynamics of the joint are isolated from the assembled system using different substructuring techniques treating the joint as a quasi-static or dynamic component. A simple physical model of the joint is parametrized from the experimental joint dynamics. A validation of the methodology is given by using the identified joint parameters on a modified assembled system.

Theoretical and numerical investigations of acoustic field characteristics of shear-horizontal feature guided waves in a welded joint

This paper investigates acoustic field characteristics of shear-horizontal feature guided waves (SH-FGWs) propagating through topographic waveguides like welds and stiffeners in plate-like structures. It establishes mathematical models of second harmonic and quasi-static component (QSC) generated by SH-FGWs in a welded joint and analyzes their theoretical characteristics. Using two-dimensional semi-analytical finite element and three-dimensional finite element methods, it studies the dispersion characteristics of FGWs and acoustic field distribution at specific frequencies of SH-FGWs, as well as their nonlinear response. This study provides new physical insights into the acoustic field distribution and nonlinear response of SH-FGWs in topographic waveguides.

High-frequency ultrasound-based thickness measurement of highly attenuating materials

This paper investigates an effective method for measuring the thickness of highly attenuating materials using the acoustic radiation-induced quasi-static component (QSC) of a primary longitudinal wave (PLW) at high frequency. The generated QSC features lower attenuation than the high-frequency PLW, so the generated QSC pulse with zero carrier frequency can propagate a longer distance at the same group velocity, even in highly attenuating materials. In addition, the method based on the QSC of a high-frequency PLW has better directivity than the low-frequency PLW-based method, making it more suitable for highly attenuated material local thickness measurement. The thickness of highly attenuating materials can be accurately measured by measuring the pulse-echo time-of-flight of the generated QSC pulse using an ultrasound pulse-echo technique. The experimental examinations conducted for highly attenuating silicone rubber blocks with different thicknesses demonstrate that their thicknesses can be accurately measured with the QSC-based method. This paper provides an effective method for thickness measurements of highly attenuating materials.

A Feasibility Study on Use of an Accelerometer to Measure the Dynamic Forces in Turning

Metal cutting is a highly dynamic process that generates continuously varying forces. Measurement of these forces is essential to characterizing a cutting process and to fully utilize the machine tool. A force dynamometer is often used to measure these varying forces; however, it is limited by the natural frequency of the sensor and can sometimes be hard to set up on a machine. Therefore, this study aims to estimate the dynamic component of the cutting force using an accelerometer placed directly below the cutting edge. The placement of the sensor helps achieving better signal to noise ratio (S/N). The cutting tool is modelled as a single degree of freedom (SDOF) system relative to the workpiece and dynamic loads are experimentally simulated on it. The measured acceleration is numerically integrated to obtain velocity and deflection, which along with the natural frequency (ωn) and damping ratio (ζ), is used to predict the dynamic load using the system equation. The dynamic forces tested over a wide range of frequencies, show good agreement with the data from simultaneous dynamometer measurement and the force estimated using the proposed method. The study shows the feasibility of this method in a real cutting scenario and the capability to apply it to a multi DOF system. One major limitation is the inability to capture the static or quasi-static component of the cutting force.

Horizontal displacement estimation of high-rise structures by fusing strain and acceleration measurements

Monitoring of horizontal displacement is essential for structural health monitoring of high-rise structures. This paper proposes a new technique for estimating the horizontal displacement using fusion measurements including strain and acceleration for high-rise structures. The quasi-static component of structural displacement is first derived from the measured longitudinal strains based on the classical beam theory. The quasi-static displacement is then combined with the resonant displacement determined based on the measured acceleration via a finite impulse response filtering approach to obtain the total horizontal displacement. The effectiveness of the proposed technique is examined through numerical studies, in which two cantilever beams with different sectional shapes are used to verify that the proposed technique can provide accurate estimation of horizontal displacements under different noise levels contained in signals and number of measurement points. Then, a field measurement validation study on a 600 m high skyscraper is presented to demonstrate the applicability and accuracy of the proposed technique for horizontal displacement estimation of high-rise buildings under typhoon conditions.

Experimental Study on the Probability of Different Wave Impact Types on a Vertical Wall with Horizontal Slab by Separation of Quasi-static Wave Impacts

When the fundamental natural frequency of marine structures is comparable to the dominant frequency of incident waves, the response of the load on the structure will be amplified. Accurately quantifying how wave loads can be amplified by incident wave conditions must thus be considered in any structural analysis, given how sensitive these characteristics are to different wave impact types. Systematic physical model tests of wave impacts on the simple horizontal plate and the vertical wall with a horizontal overhanging cantilever slab were performed. By first comparing quasi-static wave load estimates along a simple horizontal plate (obtained by low-pass filtering the pressure time series at different cut-off frequencies) with quasi-static uplift pressures from established predictive formulations, a cut-off frequency of 7 Hz was found to accurately separate the quasi-static component from impulsive wave impacts. By applying the low-pass filtering approach with the selected cut-off frequency to the pressure measurements for the vertical wall with a horizontal cantilever slab case, the impulsive and quasi-static peaks were attained, which were then used to quantify the probabilities of individual impulsive, dynamic, and quasi-static wave impacts. Incoming wave conditions and structural clearance had a significant effect on the probabilities of different wave impacts. With the increasing wave height and wave steepness, wave impacts on the horizontal slab and vertical wall were increasingly of the impulsive type and less frequently of the quasi-static type, while the probability of dynamic impact types were relatively stable. As the overhanging slab was shifted from elevated to submerged, the dominant type of wave impact on the structure was variable, ranging from impulsive to dynamic to quasi-static as its elevation was lowered. The results indicated that up to 90% of the impacts were of the impulsive type when the overhanging slab was on or slightly over the still water level. Moreover, the presence of the vertical wall increased the magnitude of wave loads and the occurring frequency of impulsive wave impacts for the horizontal slab.

Flexibility matrix identification using the moving vehicle induced responses for beam type bridge

Bridge flexibility matrix is widely used in damage detection and condition assessment. As the mass-normalized mode shapes with high spatial resolution are required in formulating the flexibility matrix, the difficult tasks of measuring excitation and arranging a large number of sensors are normally involved. This paper proposes a flexibility matrix identification method by using the moving vehicle induced responses for beam type bridges. Firstly, the proportional relationship between the modal flexibility matrix and the matrix formulated by the bridge influence lines (ILs) of several points is derived theoretically. Then the quasi-static component response of the moving vehicle induced responses is extracted through the analytical mode decomposition (AMD), and the IL of the measurement point is obtained via polynomial fitting accordingly. Finally the flexibility matrix is formulated based on the measured ILs and the derived proportional relationship, and employed to estimate the static displacement of the bridge. Numerical and experimental examples are conducted to verify the accuracy and feasibility of the proposed method. The results indicate that it can identify the bridge flexibility matrix and estimate the static displacement with high accuracy and efficiency at the cost of few sensors. Besides, the proposed method is insensitive to vehicle parameters (velocity, spring stiffness, wheelbase, and weight), road surface roughness and measurement noise.

Wind-induced fatigue analysis of high-rise guyed lattice steel towers

Wind-induced fatigue is a major issue for the design of slender high-rise structures. However, there are still few studies focused on this topic, resulting in a lack of practical design procedures for this type of structures. This paper aims to fill this gap by presenting a complete and practical methodology for the wind-induced fatigue life assessment of high-rise towers and its application to a 120 m cable-stayed steel tower composed by a modular lattice. The wind actions were considered as the sum of the quasi-static component according to international codes and a numerically generated, trough an ergodic stochastic process, turbulent component which is based on the Kaimal wind spectrum. Real wind measurements were also taken for a period of 15 months on a nearby MET station which, when compared with the normative scenario, proved to be much less conservative and were not used for the safety analysis. The wind velocities were used as inputs for a nonlinear dynamic analysis from which stress time histories were derived for 10 potentially critical structural details. The damage in each detail was computed through the application of the Rainflow counting algorithm and Palmgren-Miner’s damage accumulation law, indicating the connection region between the modules as the critical detail with respect to fatigue damage.

A method to estimate peak pressures on low-rise building models based on quasi-steady theory and partial turbulence analysis

A new method for estimating peak area-averaged pressure coefficients on the roof of a low-rise building model is developed. The method relies on the well-known quasi-steady vector model to account for the large-scale, low-frequency fluctuations of the upstream wind. The novel approach is to account for small-scale and body-generated turbulence effects using a stochastic model. Wind tunnel data for a 1/50-scale low-rise building model for six different upstream turbulence conditions are used for the analysis. The fluctuating pressure component induced by the small-scale and body-generated turbulence is obtained by subtracting the quasi-static pressure component from the original pressure signal. It is observed that the small-scale pressure component is highly dependent on turbulence level of the upstream flow, such that normalization by the small-scale components of the upstream turbulence kinetic energy leads to a self-similar distribution. A Monte Carlo simulation was used to combine the small-scale and quasi-steady pressure components. The new model provides good predictions of peak area-averaged pressure coefficients that cannot be captured by the quasi-steady approach.

Inductive Tracking Methodology for Wireless Sensors in Photoreactors.

In this paper, we present a methodology for locating wireless sensors for the use in photoreactors. Photoreactors are, e.g., used to cultivate photosynthetic active microorganisms. For measuring important parameters like, e.g., the temperature inside the reactor, sensors are needed. Wireless locatable floating sensors would enable it to measure the data anywhere inside the reactor and to get a spatial resolution of the registered data. Due to the well defined propagation properties of magnetic fields and the fact that they are not significantly influenced in underwater environments when using low frequencies, a magnetic induction (MI) system is chosen for the data transmission as well as for the localization task. We designed an inductive transmitter and a receiver capable of measuring the magnetic field in every three spatial directions. The transmitting frequency is set at approx. . This results in a wavelength of approx. which clearly exceeds the dimensions of our measurement setup where the transmitter–receiver distances in general are lower than one meter. Due to this fact, only the quasi-static field component has to be considered and the location of the transmitter is calculated by measuring its magnetic field at defined positions and in using the magnetic dipole field equation in order to model its magnetic field geometry. The used measurement setup consists of a transmitter and two receivers. The first measurements were performed without a water filled photoreactor since no differences in the propagation criteria of magnetic fields are expected due to the negligibly low differences in the relative magnetic permeability of water and air. The system is calibrated and validated by using a LIDAR depth camera that is also used to locate the transmitter. The transmitter positions measured with the camera are therefore compared with the inductively measured ones.

ELT-scale elongated LGS wavefront sensing: on-sky results

Context. Laser guide stars (LGS) allow adaptive optics (AO) systems to reach greater sky coverage, especially for AO systems correcting the atmospheric turbulence on large fields of view. However LGS suffer from limitations, among which is their apparent elongation which can reach 20 arcsec when observed with large aperture telescopes such as the European Southern Observatory 39 m telescope. The consequences of this extreme elongation have been studied in simulations and laboratory experiments, although never on-sky, yet understanding and mitigating those effects is key to taking full advantage of the Extremely Large Telescope (ELT) six LGS. Aims. In this paper we study the impact of wavefront sensing with an ELT-scale elongated LGS using on-sky data obtained with the AO demonstrator CANARY on the William Herschel telescope (WHT) and the ESO Wendelstein LGS unit. CANARY simultaneously observed a natural guide star and a superimposed LGS launched from a telescope placed 40 m away from the WHT pupil. Methods. Comparison of the wavefronts measured with each guide star allows the determination of an error breakdown of the elongated LGS wavefront sensing. With this error breakdown, we isolate the contribution of the LGS elongation and study its impact. We also investigate the effects of truncation or undersampling of the LGS spots. Results. We successfully used the elongated LGS wavefront sensor (WFS) to drive the AO loop during on-sky operations, but it necessitated regular calibrations of the non-common path aberrations on the LGS WFS arm. In the off-line processing of the data collected on-sky we separate the error term encapsulating the impact of LGS elongation in a dynamic and quasi-static component. We measure errors varying from 0 nm to 160 nm rms for the dynamic error and we are able to link it to turbulence strength and spot elongation. The quasi-static errors are significant and vary between 20 nm and 200 nm rms depending on the conditions. They also increase by as much as 70 nm over the course of 10 m. We do not observe any impact when undersampling the spots with pixel scales as large as 1.95″, while the LGS spot full width half maximum varies from 1.7″ to 2.2″; however, significant errors appear when truncating the spots. These errors appear for fields of view smaller than 10.4″ to 15.6″, depending on the spots’ elongations. Translated to the ELT observing at zenith, elongations as long as 23.5″ must be accommodated, corresponding to a field of view of 16.3″ if the most elongated spots are put across the diagonal of the subaperture.

Train-induced ground vibration due to the irregularities of the soil

Many measurements of train induced ground vibrations show high amplitudes for a certain mid-frequency range. This ground vibration component cannot be well explained by dynamic loads of the train. Many characteristics indicate that the axle impulses, which are scattered by an irregular soil, are the excitation. This new understanding of railway-induced ground vibration is verified by numerical analysis. The response of the regular homogeneous and irregular inhomogeneous soils has been calculated by the finite-element method in frequency domain. A specific superposition of the impulse responses has been invented including time shift, axle sequence, track filter and hanning filter. The superposition yields the quasi-static component of the ground vibration which is restricted to very low frequencies and to the close near-field of the track. In case of an irregular soil of which the stiffness varies randomly in space, the superposition yields a mid-frequency ground vibration component from the scattering of the axle impulses. The existence and the importance of this component can thus be demonstrated by the calculations. Some rules of the influence of distance, train speed, soil stiffness, strength and width of the stiffness variation have been derived from the calculations. Many measurements show the unique explanation of the mid-frequency ground vibration component by the scattered axle impulses.