Displacement Spectra Research Articles

Full-field measurements of high-frequency micro-vibration under operational conditions using sub-Nyquist-rate 3D-DIC and compressed sensing with order analysis

High-speed imaging is essential for high-frequency vibration measurement techniques that utilize images, such as digital image correlation (DIC). However, it poses challenges, including reduced displacement resolution due to decreased image resolution, increased measurement and calculation costs, and greater data volume. A previous method used compressed sensing to reconstruct time information from images captured with a high-resolution, low-speed camera, allowing high-frequency vibration measurements. However, this method was limited to steady vibrations since waveforms were reconstructed using the Fourier basis. In this study, order analysis is introduced into compressed sensing to measure operational vibrations, including rotation speed fluctuations, such as those in automobile engines. An out-of-plane vibration experiment on an aluminum plate confirmed the method’s accuracy in identifying mode shapes and displacement spectra of operational vibrations. The proposed method reconstructed vibrations (amplitude: several μm to several hundred μm, frequency: 33.3–133.2 Hz) using images captured at 10 fps. The modal assurance criterion (MAC) indicated 0.98 accuracy compared with finite element analysis. The mean squared error below 1 % compared to the frequency spectrum obtained with a laser Doppler vibrometer. Applied to automobile engine vibrations (amplitudes of a few μm), the method achieved errors under 2 % over a 1225 mm × 960 mm field of view. However, error increased for vibrations below the DIC displacement resolution. This method shows promise for analyzing vibrations in rotational machinery, such as engines and motors, through the full-field measurement of high-speed operational vibrations. In addition, the developed compressed sensing with order basis is expected to contribute to the advancement of the recovering missing signals and data compression.

The Dynamic Soil–Foundation–Structure Interaction Problem in the Time Domain Using a Discrete Element Model

This study investigates the influence of the soil–structure interaction (SSI) on the seismic performance of structures, focusing on the effects of foundation size, soil type, and superstructure height. While the importance of SSI is well recognized, its impact on structural behavior under seismic loads remains uncertain, particularly in terms of whether it reduces or amplifies structural demands. A simplified dynamic model, incorporating both the mechanical behavior of the soil and structural responses, is developed and validated to analyze these effects. Using a discrete element approach and the 1940 El Centro earthquake for validation, the study quantitatively compares the response of soil-interacting structures to those with fixed bases. The numerical results show that larger foundation blocks (20 m × 20 m and 30 m × 30 m) increase the seismic response values across all soil types, causing the structure to behave more like a fixed-base system. In contrast, reducing the foundation size to 10 m × 10 m increases the flexibility of structures, particularly buildings built on soft soils, which affects the displacement and acceleration response spectra. Softer soils also increase natural vibration periods and extend the plateau region in regard to spectral acceleration. This study further finds that foundation thickness has a minimal impact on spectral displacement, but structures on soft soils show more than a 15% reduction in spectral displacement (SD) compared to those on hard soils, indicating a dampening effect. Additionally, increasing the building height from 7 to 21 m results in a more than 20% decrease in SD for superstructures with natural vibration periods exceeding 2.4 s, while taller buildings with longer natural vibration periods exhibit opposite trends. Structures built on soft soils experience larger foundation-level displacements, absorbing more seismic energy and reducing earthquake accelerations, which mitigates structural damage. These results highlight the importance of considering SSI effects in seismic design scenarios to achieve more accurate performance predictions.

Displacement-Based Seismic Design of Multi-Story Resistance Capacitance-Coupled Shear Wall Buildings with Energy-Dissipation Dampers

This research aims to apply the displacement-based design method (DBDM) for the seismic design of reinforced concrete-coupled shear wall buildings equipped with energy dissipation dampers. The DBDM offers design simplicity by focusing on structural design based on a target design displacement, where the building converts into a single degree of freedom (SDOF) system. The implementation of dampers aims to reduce repair costs and downtime for buildings following significant seismic events. Two types of dampers are utilized in this study: metallic damper and viscoelastic damper. The DBDM procedure begins with determining the target displacement, which corresponds to the specific story drift ratio of the structural system, using a nonlinear static pushover analysis. For the structural wall system considered in this study, a target drift ratio of 1/250 is selected due to the inherent rigidity of the structure. The effective damping factor is then determined from the average energy absorption, which is based on the ductility factor of each structural member. Additionally, the effective period of the building is obtained from the displacement spectrum of the design-level earthquakes. Finally, the required damper shear capacity for the SDOF system is calculated based on the target deformation and effective stiffness. The design earthquakes are generated from the acceleration response spectrum for Level 2 earthquakes, as specified in the Japanese seismic code, utilizing three different sets of phase information: Kobe, El Centro, and random phase records. The effectiveness of the DBDM is scrutinized through a comparison with results obtained from time history analysis. The results obtained for 6-, 12-, and 18-story RC-coupled shear walls with energy dissipation dampers indicate that the proposed design methodology effectively meets the specified design objectives.

Coda-derived source properties estimated using local earthquakes in the Sea of Marmara, Türkiye

Abstract. Accurate estimates of the moment magnitude of earthquakes that physically measure the earthquake source energy are crucial for improving our understanding of seismic hazard in regions prone to tectonic activity. To address this demand, a method involving coda wave modelling was employed to estimate the moment magnitudes of earthquakes in the Sea of Marmara, northwestern Türkiye. This approach enabled us to model the source displacement spectrum of 303 local earthquakes efficiently recorded at 49 regional seismic stations between 2018 and 2020 in the region. The coda wave traces of individual events were inverted across 12 frequency ranges between 0.3 and 16 Hz. The resultant coda-derived moment magnitudes were found to be in good accordance with the conventional local magnitude estimates. However, the notable move-out between local magnitude and coda-derived moment magnitude estimates for smaller earthquakes less than a magnitude of 3.5 likely occurs due to potential biases arising from incorrect assumptions for anelastic attenuation and/or the finite sampling intervals of seismic recordings. Scaling relations between the total radiated energy and seismic moment imply a non-self-similar behaviour for the earthquakes in the Sea of Marmara. Our findings suggest that larger earthquakes in the study area exhibit distinct rupture dynamics compared to smaller ones, resulting in a more efficient release of seismic energy. Hence, we introduce an empirical relationship obtained from the scatter between local magnitude and coda-derived moment magnitude estimates.

Vibration response of nanobeams subjected to random reactions

Nanobeams composed of materials exhibiting flexoelectric properties have been successfully used in advanced technological equipment, including electronic circuits and very sensitive sensors, owing to their remarkable unique effects. Therefore, it is essential to determine their mechanical behavior as a practical need. This study employs an analytical methodology to provide a precise solution to the vibration issue of nanobeams under random stationary loads. Under such circumstances, the nanobeam is influenced by both the temperature and moisture conditions simultaneously. Additionally, the beam is supported by a viscoelastic foundation that considers both the viscous resistance parameter and the elastic parameter. Analytical formulations are derived by integrating classical beam theory with nonlocal strain gradient theory in order to elucidate the impact of size effects on nanobeams. This research also demonstrates the reliability verification, which clearly validates the accuracy of the calculation formula used in this work. This study examines the impact of material parameters, viscoelastic foundation, temperature, and moisture on the displacement spectrum at the middle and entire length of the beam. The study also explores how the flexoelectric effect decreases the displacement in the nanobeam. Subsequently, we provide scientifically derived findings that have significant relevance for building practical nanobeam specifications.

Performance-Based Design Method of Hinged Wall with Buckling-Restrained Braces at Base Using the Elastic Displacement Spectrum

A performance-based seismic design method using the elastic displacement design spectrum based on equal displacement approximation is proposed for the Hinged Wall with BRBs at Base (HWBB) structural system. HWBB is simplified as an Equivalent Single Degree of Freedom (ESDOF) system. Design flowcharts are given. The proposed design approach aims to limit the lateral displacements to an allowable target displacement. Design examples are presented and target displacements are compared with numerical results. The results indicate that the plastic response of the HWBB structural system is accurately predicted by the elastic displacement spectrum, which verified that the performance-based design method of HWBB is accurate.

Asymmetric instability of flow-induced vibration for elastically mounted cube at moderate Reynolds numbers

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm and the selective frequency damping method and total dynamic mode decomposition (TDMD) are applied here to explore this problem. Due to the unsteady non-axisymmetric wakefield formed for flow passing a stationary cube, the FIV response was found to exhibit separate structural stability and oscillations (including lock-in and galloping behaviour) in the two different streamwise orthogonal planes while the body is released. The initial kinetic energy accompanying the release of the cube could destabilize the above-mentioned structural stability. The observed FIV asymmetric instability is verified by the root trajectory of the structural mode obtained via data-driven stability analysis. The stability of the structural modes dominates regardless of whether the structural response oscillates significantly in various (reduced) velocity ranges. Further TDMD analysis on the wake structure, accompanied by the time–frequency spectrum of time-history structural displacements, suggested that the present FIV unit with galloping behaviour is dominated by the combination of the shifted base-flow mode, structure modes and several harmonics of the wake mode.

Effect of Blade Material of Steam Turbine Rotor on Aeroelastic Characteristics

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Centrifuge tests for earthquake response of shallow soil with locally raised bedrock

ABSTRACT Centrifuge tests were performed to study the dynamic properties of shallow soil with locally raised bedrock (i.e. variable soil depth). The test parameter was the slope of bedrock: 0° (S0), 35° (S35), and 45° (S45). In each test, accelerations were measured along the soil depth, and the results of acceleration, displacement, Fourier transform, and response spectrum were compared. Based on the results, the transfer function (TF), the ratio of response spectrum (RRS), and the site period were estimated. The ground motion and site period of specimens with raised bedrock were smaller than those of the specimen without raised bedrock (i.e. with deeper soil). Further, parametric studies using 2-dimensional finite element (FE) analysis were performed to investigate the effect of design parameters on the response of shallow soil with variable soil depths. For design parameters, the length of raised bedrock and the length of foundation slab were considered. Parametric study results indicated that when the shallow soil region is wide, the results are similar to those of a 1-dimensional soil column. However, when the shallow soil region is narrow, the 2-dimensional response is smaller than the 1-dimensional soil column response. This was also observed in the actual site model.

Shear crack kinematics in reinforced engineered cementitious composite (ECC) beams

The fiber’s bridging effect across the shear cracks is considered to play an important role of resisting shear in engineered cementitious composite (ECC), and fiber reinforced material in general. To quantify the shear crack kinematics (i.e., shear crack opening and sliding displacements) in reinforced ECC (R/ECC) beams, a crack measuring algorithm based on the full-field displacement spectrum is developed by using the Digital Image Correlation (DIC) technology. In addition, a novel distributed strain-measuring methodology was used to detect the strain distribution along the transverse and longitudinal reinforcement. Reinforced beams made of traditional concrete (R/C) and mortar (R/M) were used as reference. Through aforementioned monitoring schemes, the role of matrix (Vc) and stirrups (Vs) in shear resistance mechanism could be independently understood and evaluated. The R/ECC beams exhibited much higher Vc than the reference reinforced concrete (R/C) beams (by 68%∼104%). Nevertheless, the shear crack measuring results revealed that the higher shear strength in R/ECC did not always result from the fiber’s bridging effect across the critical shear crack (CSC) but of high shear-resisting contribution from ECC in shear-compression zone. For a better understanding of the shear failure mechanisms, phenomenological models of shear crack kinematics in R/C and R/ECC beams are proposed.

Aeroelastic analysis using confocal sensors: experimental study and numerical validation with application to a future particle detector

This study investigates the structural displacements induced by aerodynamic loads in a future particle detector at the Large Hadron Collider (LHC): the Inner Tracking System 3 (ITS3) of the ALICE experiment. The development of an ultralight structure and use of air cooling lead to an unprecedentedly low material budget, resulting in improved accuracy compared to the current detector (ITS2). The airflow applied to the low-mass structure of the ITS3 is expected to cause vibrations, which requires an aeroelastic analysis that is performed using experimental and numerical methods. A novel experimental approach is proposed using confocal chromatic sensors to measure the structural displacements of an ITS3 prototype with submicron accuracy. A simplified mathematical model is developed for the fluid-structure interaction. The results obtained in the experimental setup show that the numerical model predicts the primary peaks in the spectrum of structural displacements induced by airflow. The validated model is used to analyze both the real anticipated configuration of the future ITS3 setup and potential modifications arising from changes in detector cooling and installation requirements.

The Derivation of Vertical Damping Reduction Factors for the Design and Analysis of Structures Using Acceleration, Velocity, and Displacement Spectra

Damping reduction factors (DRFs) play a vital role in the seismic design of structures. DRFs have been widely studied due to their primary importance to the lateral resistance of structures subjected to earthquakes. On the other hand, devastating earthquakes have occurred all over the world, and recently, the Kahramanmaraş earthquakes in Turkey revealed the import of the vertical component of earthquakes and their impact on structures and infrastructures. Considering the importance of this parameter, this paper aims to develop new damping reduction factor (DRF) equations for the acceleration (DRFa), velocity (DRFv), and displacement spectra (DRFd) of the vertical components of earthquakes. For this purpose, 775 real ground motion records were selected from the Pacific Earthquake Engineering Research (PEER) strong motion database, and the vertical elastic response spectra of selected records were computed according to linear dynamic analysis. Taking the 5%-damped vertical response spectra as the target, the vertical spectral damping reduction factors (DRFa, DRFv, and DRFd) were computed for 1%, 3%, 10%, 15%, 20%, 30%, and 40% damping ratios. The effect of the earthquake magnitude, distance, and soil types on the DRFs was investigated. The results indicated that magnitude, distance, and soil type had no particular effect on the trend in the DRFs. Based on the evaluations, extensive statistical analyses were carried out, and new prediction equations were developed according to the nonlinear regression method. The developed equations were then compared to those found in the literature and seismic design codes. The comparisons proved that the proposed DRFa, DRFd, and DRFv models are strongly compatible with real DRFs and show strong robustness compared to existing models.

Separation of source, attenuation and site parameters of 2 moderate earthquakes in France: an elastic radiative transfer approach

Summary An accurate magnitude estimation is necessary to properly evaluate seismic hazard, especially in low to moderate seismicity areas such as Metropolitan France. However, magnitudes of small earthquakes are subject to large uncertainties caused by major high-frequency propagation effects which are generally not properly considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. The key feature of our approach is the treatment of attenuation -both scattering and absorption- in a simple but realistic velocity model of the Earth’s lithosphere, including a velocity discontinuity at the Moho. To reach this goal, we developed a 2-step inversion procedure, allowing first to extract attenuation parameters for each source-station path from the whole observed energy envelope using the Levenberg-Marquardt and grid-search algorithms, then to determine site amplification and the source displacement spectrum from which the moment magnitude Mw is extracted. In the first step, we use the forward modeling procedure of Heller et al. (2022) in order to simulate energy envelopes by taking into account the full treatment of wave polarization, the focal mechanism of the source and the scattering anisotropy. The inversion procedure is then applied to the 2019 ML 5.2 Le Teil and 2014 ML 4.5 Lourdes earthquakes which both occurred in southern France. Data from 6 stations are selected for each event. The inversion results confirm a significant variability in the attenuation parameters (scattering and absorption) at regional scale and a strong frequency dependence. Scattering appears to be stronger towards the French Alps and Western Pyrenees. Absorption is stronger as frequency increases. Although not very resolvable, the mechanism of scattering appears to be forward or very forward. By inverting the source spectrum, we determine moment magnitudes Mw of 5.02 ± 0.17 for the Le Teil earthquake and 4.17 ± 0.15 for the Lourdes earthquake.

Barely visible impact damage detection in CFRP composite using vibrothermography with narrowband sweep excitation

The extensive use of carbon fiber-reinforced plastic (CFRP) composite materials in various industries has posed new challenges for conducting effective structural health monitoring and nondestructive evaluation techniques. Based on local defect resonance (LDR), the vibrothermography with narrowband sweep excitation is proposed to detect BVIDs in the CFRP composite. The response spectrum of displacement at the impact crater was collected by a laser Doppler vibrometer, which was used to determine the frequency range of narrowband sweep excitation. The frequency range was further validated by the analysis of local defect resonance for thermal responses, and the sweep duration was also optimized. Subsequently, the proposed vibrothermography was employed to detect BVIDs with varying severity. The impact damage could be efficiently activated and a significant temperature rise was generated in the defective areas, which enhances the temperature contrast of the thermal images and facilitates the quantification of defects.

Seismic Magnitude Estimation Using Low-Frequency Strain Amplitudes Recorded by DAS Arrays at Far-Field Distances

ABSTRACT Downhole distributed acoustic sensing (DAS) data are now routinely acquired on fiber-optic cables deployed in wells for seismic imaging and microseismic monitoring. We develop a semiempirical workflow for estimating scalar seismic moment and moment magnitude of earthquakes using strain data recorded by downhole DAS arrays. At far-field distances, the time integral of axial strain is proportional to the displacement scaled by apparent slowness. Therefore, seismic moment can be directly estimated from the amplitude of the low-frequency plateau of the strain spectra divided by frequency, similar to the methodology commonly employed for far-field displacement spectra. The effect of polarization on strain amplitudes for different types of body waves is accounted for. Benefitting from the large spatial coverage provided by DAS arrays, moment estimates from multiple channels are averaged and an average radiation coefficient is assumed over the focal sphere. We validate the methods using data of microseismic events simultaneously recorded by a surface geophone array and by DAS on fiber deployed in two horizontal wells during a hydraulic fracturing experiment. For 106 microseismic events in the magnitude range ∼ −0.65 to ∼ +0.55, we find the DAS-derived magnitudes to be consistent with the magnitudes derived from the geophone array using traditional methods, with ∼95% of the magnitude estimates differing by less than ∼0.26 units. The workflow can be potentially extended to DAS arrays in vertical wells and to S waves recorded on dark fiber DAS arrays at the surface. This methodology does not require any calibration beyond knowledge of local seismic properties, and the use of the lowest possible frequencies reduces the influence of subsurface heterogeneities and the finite spatiotemporal extent of earthquake ruptures. The capacity to estimate robust seismic magnitudes from downhole DAS arrays allows improved evaluation and management of fracture growth and more effective mitigation of induced seismicity.

Controllable nonlinear effects in a hybrid magnonical semiconductor microcavity

We investigate the bistability properties of the magnomechanical system driven by an amplitude-modulated pump laser. The bistable behavior exhibits a characteristic magnon switching pattern. This behavior is studied for different values of system parameters. A distinct indication of energy transfer between the mechanical and magnon modes becomes evident while examining the mechanical displacement spectrum within the system. Further, by appropriately adjusting the system parameters, it is observed that the system in its steady state exhibits entanglement dynamics. These findings imply that this system holds potential applications in highly responsive magnon switches, magnon sensors, and quantum communication platforms.

Seismic response analysis of single‐degree‐of‐freedom structure coupled with tuned self‐centering wall

AbstractThis paper investigates the possibility of using self‐centering walls (SCWs) as tuned mass dampers (TMDs) to control the seismic response of structures. The basic characteristics of this system are investigated using a two‐degree‐of‐freedom (2‐DOF) model, representing the main structure as a single‐degree‐of‐freedom (SDOF) oscillator interconnected with an SCW through viscous and elastic devices. The nonlinear equations of motion for the proposed coupled system are derived and then utilized to determine the displacement amplification response. The coupling parameters are optimized to minimize the dynamic response of the oscillator using a numerical method. A simulation study is conducted to investigate the response of the proposed system by considering six recorded earthquakes. Several parameters are studied, including the mass ratio, the influence of prestressing, and the slenderness angle of the wall. The displacement spectra are generated using the optimized parameters and compared to those of the uncoupled system and the traditional coupled system, which features a rigid connection between the structure and the wall. The results reveal that the proposed system effectively suppresses both maximum and root mean square responses of structures, outperforming the traditional coupled system in most cases. Improved performance for the proposed system can be achieved by increasing the wall's mass ratio and decreasing the slenderness angle. Moreover, prestressing has an adverse impact on the system's displacement response. Finally, the influence of wall flexibility is examined using a finite element model, revealing a minimal effect on the system's response.

Accelerated degradation test method and performance prediction with service mileage of the yaw damper in railway vehicles

The performance of the yaw damper for rail vehicles degrades significantly degradation after long-term operation, which directly affects the dynamic behaviour of the vehicle operation. To quickly achieve the performance degradation of the yaw damper and predict the operating mileage under actual service conditions, the operating displacement spectrum of the yaw damper under actual operating conditions is analysed and decomposed using the short-time Fourier transform. Based on the equivalent principle of energy loss during vibration attenuation, an accelerated test method is proposed for the performance degradation of yaw dampers. By conducting the accelerated degradation test of the yaw damper on the test bench, the continuous degradation relationship between the performance parameters of the damper and the loading times is obtained. By combining the operating displacement spectrum and the accelerated degradation test data, the performance degradation trajectory model of the yaw damper is established, taking into account the equivalent energy loss between the service mileage and the loading times. The mapping relationship among loading times, service mileage and performance degradation is constructed. Finally, parameter performance tests are conducted on yaw dampers under different service mileage to verify the accuracy of the performance degradation trajectory model. The results show that the proposed acceleration test method and degradation trajectory model can quickly realise the performance degradation of the damper and accurately predict the performance parameters for different service mileage under actual operating conditions.

The normalized inelastic displacement spectra for seismic response estimation of a SDOF system with a generalized flag-shaped hysteretic model

The normalized inelastic displacement spectra for seismic response estimation of a SDOF system with a generalized flag-shaped hysteretic model

Evaluating Seismic Performance in Reinforced Concrete Buildings with Complex Shear Walls: A Focus on a Residential Case in Chile

This study employs a non-linear static analysis, known as pushover analysis, to explore the flexural-compressive behavior of complex shear walls within a reinforced concrete (R.C.) structure, adhering to contemporary design standards in Chile. The primary objective is to assess the initiation of damage as the building approaches the limit states outlined in Achisina’s seminal “Performance Based Seismic Design” framework. To achieve this, a sophisticated fiber model, accounting for the confined behavior of concrete derived from the structural elements’ detailing, has been uniformly integrated across the building’s entire height. Furthermore, the analysis incorporates a rigid diaphragm to simulate the R.C. slab’s response accurately. The study implements the N2 method, adjusting for seismic demands in an acceleration-displacement format, which leverages the displacement spectrum defined by Supreme Decree 61, a legislative response to the 8.8 Mw Maule earthquake in 2010. The findings reveal that the analyzed structure meets the immediate occupancy performance level with drifts nearing 5‰ in the symmetrical Y direction. This outcome aligns with prior assessments of Chilean R.C. wall buildings. However, in the asymmetric X direction, the structure exhibits a higher degree of structural damage, aligning with a life safety performance level. This differentiation underscores the critical need for nuanced understanding and modeling of structural behavior under seismic loads, contributing to the ongoing refinement of seismic design practices and standards.