Displacement Spectra Research Articles

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.

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.

A damage-oriented ground motion intensity for degrading super high-rise buildings

To explicitly identify the influence of different seismic damages on the correlation between ground motion intensity measure (IM) and demand measure (DM), with a specific concern of super high-rise buildings, a novel damage-integrated spectral acceleration-based combination-type IM is developed for degrading systems. With the integration of seismic damage measure, inelastic displacement spectrum, and design acceleration spectrum, the prototype of the IM is theoretically derived for single-degree-of-freedom systems with a Q-type hysteretic model. The high-mode effect is reflected by an optimal number of lower modes combined with corresponding modal damage. To estimate the optimal number of modes while maximizing the case-independency of DM predictions, the dynamic properties of concerned damaged and undamaged structures are estimated with the collaboration of the modified flexure-shear model (FSM-MS), and further utilized to establish the regression expression with a large number of near-field and far-field ground motions. The performance of the proposed IM is systematically demonstrated via a case study on two super high-rise buildings, along with other selected IMs.

Nearshore wave buoy data from southeastern Australia for coastal research and management

Wind wave observations in shallow coastal waters are essential for calibrating, validating, and improving numerical wave models to predict sediment transport, shoreline change, and coastal hazards such as beach erosion and oceanic inundation. Although ocean buoys and satellites provide near-global coverage of deep-water wave conditions, shallow-water wave observations remain sparse and often inaccessible. Nearshore wave conditions may vary considerably alongshore due to coastline orientation and shape, bathymetry and islands. We present a growing dataset of in-situ wave buoy observations from shallow waters (<35 m) in southeast Australia that comprises over 7,000 days of measurements at 20 locations. The moored buoys measured wave conditions continuously for several months to multiple years, capturing ambient and storm conditions in diverse settings, including coastal hazard risk sites. The dataset includes tabulated time series of spectral and time-domain parameters describing wave height, period and direction at half-hourly temporal resolution. Buoy displacement and wave spectra data are also available for advanced applications. Summary plots and tables describing wave conditions measured at each location are provided.

Induced seismic activity and source parameter characteristics in the Datong coal mine, China

To clarify the activity patterns and source characteristics of coal mining–induced microseismicity, this study analyzed the spatial distribution characteristics of microseismic events in the Datong coal mining area based on records from the regional digital seismic network. We conducted a detailed characterization of the depth distribution characteristics of microseismic events using the double-difference localization method. Additionally, the source parameters, including corner frequency ( fc), source rupture radius ( r), seismic moment ( M0), source radiated energy ( Es), and stress drop (Δσ), were calculated for 136 mine-induced earthquakes with magnitudes ranging from ML1.3 to ML3.2. The results show that ML ≥ 2.0 mining-induced seismic events occur mainly within numerous microfractures in the Datong mining area. The depth of the seismic sources in the mining area is concentrated at 200∼500 m, with significant north–south differences and a close correlation with the mining depth. The displacement spectra of microseismic sources show agreement with the Brune source model [Formula: see text] attenuation pattern. As M0 gradually increases, r, Δσ, and Es show an increasing trend, while fc gradually decreases, exhibiting characteristics similar to those of tectonic earthquakes. Compared to tectonic earthquakes, coal mining-induced earthquakes have lower corner frequencies and stress drop levels mainly because mining activities alter the originally stable geological structure and stress state, leading to weakened rock strength, decreased elastic modulus, and shallower source depths. These factors contribute to the reduction in corner frequencies. As mining operations continue, microfracturing occurs in the coal and surrounding rock mass, intensifying the dynamic instability of the rock mass that was already under high stress conditions. This situation triggers larger-magnitude, mining-induced seismic events under lower stress conditions.

Evaluation of damping reduction factors for displacement and acceleration spectra using code-compatible near-fault and far-fault ground motions depending on site conditions

Evaluation of damping reduction factors for displacement and acceleration spectra using code-compatible near-fault and far-fault ground motions depending on site conditions