Displacement Spectra Research Articles

Source spectral studies using Lg wave in western Tibet

We investigate the spectral characteristics of Lg wave using 346 waveforms recorded at 24 seismic stations located across Karakoram Fault (KKF) in western Tibet. The tectonic structure of western Tibet is very complex and formed of several blocks, which are separated by distinct suture zones. It is predominated by KKF which is one of the major strike-slip faults in western Tibet. To understand the spatial variation in crustal properties, we subdivide the study region into two parts across the KKF. The analysis of the decay of the spectral amplitudes of Lg waves with epicentral distances allows for the evaluation of the crustal quality factor QLg, which is a direct measurement of attenuation. We have observed a frequency-dependent QLg with strong attenuation in the crust though no variation is observed across the KKF. This is consistent with the reported body wave attenuation study for this region. The corner frequency (fc) is observed to decrease linearly with distance in both sides of the KKF with an effective shift of 2.5 to 1 Hz at 400 km and 1 to 0.7 Hz near 1000 km respectively. The moment magnitude of each earthquake is computed using displacement spectrum and subsequently compared with the reported magnitude.

Study on normalization of residual displacements for single-degree-of-freedom systems

Residual displacement spectrum is one of the most important means to predict the permanent deformation of structures after the earthquake, and various normalizations of residual displacements have generally been used for construction of the spectrum. However, the issue regarding the merits and drawbacks of each normalization has not yet been investigated thoroughly. A comparison between two normalizations that relate the residual displacements to the elastic and inelastic displacements is made in terms of the effect of ground motion and structural characteristics by means of the results of nonlinear time history analysis. The statistical results reveal that the residual-to-peak-inelastic displacement ratios have the advantages of small dispersion, samples without any outliers, and relatively symmetric distribution, which benefits from the strong correlation between residual and peak inelastic displacements. Moreover, the residual-to-peak-inelastic displacement ratios are almost independent of site conditions, significant duration, and natural periods. Consequently, the peak inelastic displacements are superior to the elastic ones as an intermediate step for residual displacements estimation, provided that the peak inelastic displacements are estimated with a low uncertainty. For providing alternatives to estimate residual displacement demands, the constant-strength residual displacement spectra are developed for both normalizations.

Seismic evaluation of reinforced concrete bridges using capacity‐based inelastic displacement spectra

AbstractA simplified seismic evaluation method using capacity‐based inelastic displacement spectra is proposed for reinforced concrete (RC) bridges. The proposed method can not only estimate the maximum displacements of bridges, but can also discriminate the damage indices between the bridge columns, where the Park and Ang's damage index () is considered a promising performance indicator due to its good relationship with the strength capacity state and actual visual damage condition of the bridge column regardless of the imposed loading history. To realize the accuracy and reliability of the proposed method, a hypothetical case study bridge was constructed and analyzed using various structural analysis programs and seismic evaluation methods. It was found that the proposed method can receive satisfactory estimates of the maximum displacement and for both far‐field and near‐fault ground motions when compared to the nonlinear time history analysis results of the bridge. In contrast, the AASHTO's and Caltrans’ methods cannot reflect the response amplification effects caused by the frequency‐content characteristics of near‐fault ground motions and would therefore significantly underestimate the inelastic responses of bridges. When applying the proposed method to bridges having unequal‐height columns and subjected to longitudinal seismic actions, it was found that for the short column of the bridge, the AASHTO's regularity criteria (maximum bent/pier stiffness ratio of 4 for the three‐span case study bridge) would lead to a of approximately 3.5 times that of the tall column, resulting in significant damage localization and, hence, decreasing the overall lateral deformation capacity of the bridge.

Dynamic Characteristics of Transport Structures

There exists a great need to increase the bearing capacity of soils when building high embankments on a weak foundation in seismically hazardous areas. The article considers two methods for testing soils under dynamic conditions: 1) cyclic triaxial compression, which is used to determine the dynamic strength of water-saturated soils by cyclic triaxial tests with controlled load, as well as shear modulus and damping coefficient; 2) low-amplitude dynamic vibrations (resonance column) to determine the shear wave velocity, shear modulus and soil damping coefficient in a small range of shear deformations, which can be widely used in engineering seismology. In laboratory tests using the cyclic triaxial compression method, data are obtained with a high degree of accuracy for high strain levels, the results of which can be used in the integral Fourier transform. Spetras are used in engineering seismology and as a basic tool for assessing the spectral composition of recorded ground motion or structure response, as well as for assessing ground motion from fundamental seismological parameters in regions where ground motion records are not available. After carrying out these tests and analyzing the amplitude Fourier spectra of accelerations, velocities and displacements, the calculation results will be obtained.

Design of low frequency fiber optic Fabry–Perot seismometer based on transfer function analysis

We develop a low frequency fiber Fabry–Perot (F-P) seismometer based on transfer function analysis. The seismometer structure and demodulation system accuracy are limitations of low frequency seismic monitoring. The transfer function of the F-P seismometer is analyzed, and the mass displacement spectrum (MDS) is introduced. MDS provides guidance for mechanical structure design and optical interferometer analysis to achieve low noise. The F-P seismometer prototype is built. The experiment shows that the prototype has an average noise of 6.74 ng/√ Hz below 50 Hz, and its noise is less than that of the global new high noise model within 0.16–50 Hz, whose potential is considerable.

Residual drift spectra for RC bridge columns subjected to near-fault earthquakes

Permanent displacement of a bridge column can be directly measured during the inspection after near-fault earthquakes. However, the engineer needs to estimate the expected residual drift at the design stage to determine if the bridge seismic performance is satisfactory. The most direct method to estimate the residual displacement is nonlinear response history analysis, which is time consuming and cumbersome. Alternatively, an attractive but indirect method is generating estimated residual displacement spectra that depend on displacement ductility demand, column period, site conditions, and earthquake characteristics. Given the period and the expected displacement ductility demand for the column, the residual drift response spectra curves can be utilized to estimate the residual drift demand. Residual drift spectra that are applicable to RC bridge columns in different parts of the United States were developed based on nonlinear response history analyses using a comprehensive collection of recorded and synthetic near-fault ground motions and were linked to one-second spectral acceleration (S1) of the AASHTO maps. It was also found that the residual drift ratio is below one percent when S1 is less than 0.6 g.

Age-associated increase in postural variability relate to greater low-frequency center of pressure oscillations

BackgroundPostural control is impaired in older adults, as evidenced from greater variability of the center of pressure (COP) during postural tasks. Although COP variability associates with low-frequency COP oscillations (<1 Hz) in young adults, it remains unknown if the age-associated increase in COP variability relates to greater low-frequency COP oscillations. Research questionDo low-frequency oscillations contribute to greater postural sway (center of pressure (COP) variability) in older adults when attempting to voluntarily maintain posture in a forward leaning position compared to young adults? MethodsSeven young (25.7 ± 4.8) and seven older (71.0 ± 7.0) adults performed a postural lean forward task and attempted to match a COP target in the anterior-posterior direction as steady as possible. We quantified the COP variability as the standard deviation (SD) of COP displacements in the anterior-posterior and medial-lateral directions and quantified the frequency modulation of COP as the power in COP displacement spectra from 0-1 Hz. ResultsWe found that older adults had significantly greater anterior-posterior SD of COP (p = 0.027) and power below 0.5 Hz (p = 0.048) than young adults, but power from 0.5-1 Hz was similar (p = 0.083). In contrast, the medial-lateral SD of COP (p = 0.5) and power from 0-1 Hz (p = 0.228) was similar for the two age groups. For both the anterior-posterior and medial-lateral direction, the SD of COP was related to low frequency oscillations below 0.5 Hz. SignificanceFor the first time, we show that the age-associated increase in postural variability relates to greater COP oscillations below 0.5 Hz.

Error Characteristic Analysis of Fluid Momentum Law Test Apparatus

The flat-plate momentum test bench is a widely used experimental device in the verification of the momentum law of fluid mechanics, and its error characteristics are of positive significance for theoretical research and engineering innovation and expansion. The SPH-FEM coupling algorithm and spectrum analysis method are used to calculate and analyze the displacement response and spectrum characteristics of the characteristic points of the sensor under different jet loads. Based on them, the cause, classification, law, scope, influence and control method of the measurement error of the system are discussed and analyzed with the application of the error theory and the lateral effect theory of strain gauges; combined with physical experiments, the relevant analysis methods and conclusions are verified. The results show that the measurement error of the system includes linear error and periodic error. Structural deformation in the direction of jet impact is the main source of linear error; linear error increases with the increase of jet loads. Meanwhile, periodic vibration in non-jet direction is the main cause of periodic error, and the periodic error decreases with the increase of jet loads.

Still-camera multiview Spectral Optical Flow Imaging for 3D operating-deflection-shape identification

To measure high-frequency 3D vibrations, multi-camera, high-speed imaging hardware is normally required. An alternative using still-frame cameras was recently introduced with the Spectral Optical Flow Imaging (SOFI) method. In this research, the SOFI method is extended to multiview measurements of spatial operating deflection shapes. This is achieved by utilizing harmonically controlled illumination to perform an analogue Fourier transform on image-intensity data in multiple camera views. The obtained multiview displacement spectra are combined with geometrical data to perform frequency-domain triangulation and reconstruct spatial deflection shapes. By introducing additional camera views into the image-based measurement, its field of view is extended and the signal-to-noise ratio of the final result is increased. For linear, time-invariant mechanical structures under stationary excitation, full-field 3D measurements of high-frequency vibrations can be performed using a single still-frame monochrome camera. The proposed method identifies displacements in the frequency domain directly on the camera sensor, resulting in orders-of-magnitude smaller data sizes and post-processing times compared with conventional multiview image-based methods.

Computational investigation of off-sized bearing rollers on dynamics for hypoid gear-shaft-bearing coupled system

This paper presents a hybrid dynamic model for hypoid gear-shaft-bearing coupled system considering off-sized bearing rollers. The model includes bearing roller diameter error in calculating the contact deformation between the bearing roller and the race. The time-varying transmission error and mesh stiffness were also considered as system excitation, and flexible shafts were discretized by the finite element method. Dynamic differential equations are solved with numerical integration method. The effects of error magnitude, number and position distribution of off-sized rollers on the vibration of hypoid gear system were investigated. Results show that the off-sized rollers have significant influence on the gear radial displacement and bearing stiffness, and limited influence on the gear axial displacement, dynamic transmission error and dynamic mesh force. Due to off-sized rollers, the gear radial displacement spectra contain bearing cage rotational frequency. As the error magnitude increases, the peak-peak value of bearing stiffness increases, also the gear radial vibration becomes more severe. In addition, the increase in the number of off-sized rollers would also increase the gear radial vibration and the peak-peak value of bearing stiffness, while increasing the position angle of off-sized rollers has opposite effect.

Response of a plate in turbulent channel flow: Analysis of fluid–solid coupling

The paper performs simulation of a rectangular plate excited by turbulent channel flow at friction Reynolds numbers of 180 and 400. The fluid–structure interaction is assumed to be one-way coupled, i.e, the fluid affects the solid and not vice versa. We solve the incompressible Navier–Stokes equations using finite volume direct numerical simulation in the fluid domain. In the solid domain, we solve the dynamic linear elasticity equations using a time-domain finite element method. The obtained plate averaged displacement spectra collapse in the low frequency region in outer scaling. However, the high frequency spectral levels do not collapse in inner units. This spectral behavior is reasoned using theoretical arguments. The resonant vibration is stronger at the third natural frequency than at the first natural frequency. We explain this behavior by comparing the fluid and solid length scales. We further study the sources of plate excitation using a novel formulation. This formulation expresses the average displacement spectrum of the plate as an integrated contribution from the fluid sources within the channel. Analysis of the sources reveals that at the plate natural frequencies, the contribution of the fluid sources to the plate excitation peaks in the buffer layer. The corresponding wall-normal width is found to be ≈0.75δ. The integrated contribution of the overlap and outer regions together to the plate response is comparable to that from the buffer region for Reτ=180 and exceeds the buffer region contribution for Reτ=400. We analyze the decorrelated features of the sources using spectral Proper Orthogonal Decomposition (POD) of the net displacement source. We enforce the orthogonality of the modes in an inner product with a symmetric positive definite kernel. The dominant spectral POD mode contributes to the entire plate excitation. The contribution of the remaining modes from the different wall-normal regions undergo destructive interference resulting in zero net contribution. The envelope of the dominant mode further shows that the intensity of the sources peaks in the buffer region and the wall-normal width of the sources extend well into the outer region of the channel.

Characterization with scaling techniques on response energy of a single degree of freedom system subject to blast loading

In terms of work done by blast loading, an energy method to characterize response energy of a simplified mass-spring single-degree-of-freedom (SDOF) system is proposed. The study on the SDOF system includes perfectly elastic, elastic perfectly-plastic, and rigid perfectly-plastic cases. With scaling techniques, a characteristic scale of response energy is defined by the response kinetic energy of a free rigid body subject to blast loading, and response spectra of a dimensionless maximum energy ratio (ER) are investigated for the SDOF system. A simple and conservative criterion of maximum ER = 1 is proposed for damage assessment. Analyzing the derived closed-form ER for the perfectly elastic SDOF system subject to triangular blast loading yields the response spectra of maximum ER. The derived results with the energy method are validated by available data and two methods of P-I diagrams and the response spectra of the maximum displacements. The distinct advantage of the energy method can ensure the one-to-one relationship between variables in developing the response spectra and P-I diagrams. For the elastic perfectly-plastic case, the observation of maximum ER = 1 is validated with well-accepted data, although closed-form solutions are no longer available. For the rigid perfectly-plastic case, the observation of maximum ER = 1 can be derived analytically. In addition, with a similar concept to primary envelope boundaries of the response spectra of the maximum displacements and P-I diagrams, the secondary envelope boundary is introduced for damage assessment.

Calculation and Characteristic Analysis on Different Types of Shock Response Spectrum

Shock Response Spectrum (SRS) has been proved to be an effective standard tool for analyzing and quantifying shock environment in engineering, which is also the simplest tool for comparing shock severity and potential damage to structures. The calculation formulas of absolute acceleration spectrum, relative displacement spectrum, relative velocity spectrum and pseudo velocity spectrum are given respectively. The responses of different spectrum under typical semi-sinusoidal shock excitation are compared and analyzed, and some enlightening conclusions are obtained.

The Road Spectrum of Combine Harvester Based on Virtual Iteration

The combine harvester has a complex work environment, and the reliability of the rack is critical to the functionality of the machine. In order to shorten the test time, reduce the cost of research and development, and make the road spectrum can be reproduced on the test-bed, this paper takes the combine harvester as the research object, the acceleration spectrum was measured on asphalt road, hard road in field and wheat field, and the multi-body dynamic equation was established according to the actual parameters of the vehicle. The transfer function between the tire displacement signal and the target signal is established, and the tire displacement spectrum is calculated. The road spectrum is taken as the input load of the four-column test-bed, and the actual load condition is reproduced on the test-bed, which provides the input condition for the fatigue analysis of the combine harvester rack in the later stage, and greatly enhances the efficiency of durability design.

Modelling track and ground vibrations for a slab ballastless track as an infinitely long periodic structure subject to a moving harmonic load

This paper presents a model for predicting ground vibration generated from a slab ballastless track, subject to a moving harmonic load. The track consists of four layers: two rails, track slabs, bed plates and a track base resting on the ground. Different from existing models for slab tracks, the one developed in this paper takes into account both the discrete supports to the rail and the discontinuity of the slabs and bed plates, and treats the track/ground system as an infinitely long periodic structure. The rail and the base are represented as, respectively, an infinitely long Timoshenko beam and an infinitely long Euler-Bernoulli beam. The slabs and bed plates are modelled as Euler-Bernoulli beams of finite length, of which the responses are formulated using the mode superposition method. By using square window functions, the differential equations of motion of each track slab and bed plate are defined for the entire track length. The ground is idealised to be a horizontally layered structure. The steady-state response of the track/ground system is sought and formulated in the frequency-wavenumber domain. By using the periodic condition of a periodic structure, it is shown that the steady-state response of the track/ground system can be determined by the modal coefficients of the slabs and plates in the 0th unit cell (the 0th bay). Formulae are derived for these modal coefficients. Results including receptances of the rail, displacement spectra of the ground and critical speeds of an axle load are produced for two sets of track/ground parameters and compared with those when the slab and bed plates are assumed to be continuous beams, demonstrating when the later treatment works. The role of veering in dispersion curves of a periodic track in critical speed is identified. Formulations in this paper can be directly applied to the Chinese CRTS II and III tracks on a layered ground. They provide a basis for developing a complete ground vibration prediction model that incorporates a moving train, an infinitely long periodic track and a homogeneous or horizontally layered ground. They can also be used to assess if a periodic track/ground system can be simplified to be invariant in the track direction.

Multi-scale indentation creep behavior in Fe-based amorphous/nanocrystalline coating at room temperature

This work reports first ever investigation on multi-scale room temperature creep behavior of Fe-based amorphous/ nanocrystalline coatings, synthesized via plasma spraying at varying plasma power. Micro- and nano-indentation testing at different loading scales was carried out to reveal the combined effect of microstructural heterogeneities viz. porosity and constituent phases, as well as the individual contribution of amorphous and crystalline phases on the creep behavior of the coatings. Microindentation creep tests revealed higher creep resistance for the coating deposited at elevated power, ascribed to lower porosity and higher degree of crystallinity. Nanoindentation creep tests showed that mixed (amorphous and intermetallic) phase possessed lower creep displacement and retardation spectra compared to fully amorphous one, indicating better creep resistance. The present work provides valuable insight into the effect of microstructural features on the creep deformation behavior of amorphous-nanocrystalline coatings.

Nonlinear Seismic Response Characteristics of CAP1400 Nuclear Island Structure on Soft Rock Sites

CAP1400 nuclear island structure is an advanced and novel nuclear power plant structure. In order to explore the seismic response characteristics of CAP1400 nuclear island structure on soft rock sites, a three-dimensional refined nonlinear seismic response analysis model was established for a soft rock foundation-nuclear island structure system using ABAQUS software. The influences of the input ground motion intensity and the frequency spectrum characteristics on the acceleration, relative displacement, and floor response spectrum, as well as the critical shear wave velocity of nonbedrock sites for CAP1400 nuclear island structure, were proposed. The results suggested that the increasing amplitude of the peak acceleration and relative displacement of nuclear island structure decreased as the soft rock site entered a nonlinear state, and the high-frequency components of the input ground motion became more abundant. Specifically, the earthquake response was the largest at the cooling water tank on the top of the shield building, which was the focus of the seismic research on nuclear island structure. Due to the influence of the ground motion frequency spectrum characteristics and the nonbedrock site effect, the peak acceleration, peak relative displacement, and acceleration response spectrum of the nuclear island structure showed different changing trends for the near-field and far-field ground motions. Based on the influence of the site shear wave velocity on the seismic response of nuclear island structure, it was recommended that the critical shear wave velocity of nonbedrock sites for CAP1400 nuclear island structure should be 1250 m/s, and the nuclear island structure-foundation dynamic interaction could be ignored at this time. The research conclusions could provide some technical support and theoretical basis for the construction and seismic performance research of CAP1400 and other nuclear power plants.

Effects of turbulence integral scale on the buffeting response of a long-span suspension bridge

In this paper, the effects of the turbulence integral scale on the buffeting response of a long-span suspension bridge are studied via the proposed three-dimensional (3D) two-wavenumber buffeting analysis method. The root mean squares (RMS) of the buffeting lift and displacement of the streamlined bridge girder are analyzed in cases with different ratios of the turbulence integral scale to the half-width of the bridge girder (γ) and mean wind speeds. To achieve a deeper understanding of the effects of the turbulence integral scale, the spectra of wind fluctuations, buffeting forces and vertical buffeting displacements for typical ratios of γ and mean wind speeds are compared. The results demonstrate that the equivalent buffeting lift per unit span and vertical buffeting displacement show different variation trends as γ increases. The effect of the turbulence integral scale on the buffeting lift forces is independent of the mean wind speed, and becomes more significant for the vertical buffeting displacements at high mean wind speeds in cases with small values of γ. The effectiveness and accuracy of the numerical analysis is verified by full-bridge aeroelastic wind tunnel tests in large integral scale turbulent fields. The present study shows that it is essential to consider the effects of the turbulence integral scale on the buffeting responses of long-span bridges. To achieve reliable results, accurate estimations and appropriate simulations of γ are of high importance in both numerical analysis and wind tunnel tests for the buffeting predictions of long-span bridges.

Lagrangian-space Gaussian ansatz for the matter redshift-space power spectrum and correlation function

We study the predictions for the matter redshift-space power spectrum and correlation function of a Lagrangian-space Gaussian ansatz introduced in a previous work. This model is a natural extension of the Zeldovich approximation, where the displacement and velocity power spectra are determined by the equations of motion, instead of being set equal to the linear power spectrum. It does not contain any free parameter. As for the real-space statistics, we find that this Lagrangian-space approach is much more efficient for the correlation functions than for the power spectra. The damping of the BAO oscillations is well recovered but there is a large smooth drift from the simulations in the power spectra. The multipoles of the correlation functions are well recovered on BAO scales, with an accuracy of $2\%$ for $\xi^s_0$ down to $10 h^{-1}$ Mpc, and of $3\%$ for $\xi^s_2$ down to $26 h^{-1}$ Mpc, at $z \geq 0.35$.

New Equations for Determination of Shaping Window in Stochastic Method of Simulating Ground Motion

ABSTRACT in this study, new prediction equations are proposed to determine the variables of gamma envelope-shape Function. Envelope-shape functions are employed for the simulation of ground motion using a stochastic method in order to form the white noise. A variety of Envelope-shape functions have been already proposed, among which gamma equations are more used in computational programs for the simulation of ground motion, e.g. SMSIM or EXSIM. In addition to the detection of influential variables of gamma envelope-shape function, their relationship with important seismic criteria such as moment magnitude, closest distance to rupture plane, site conditions and mechanism of faulting are determined and suitable models are presented in this study. Limited research has been already undertaken to specify the variables of envelope-shape equations and their relationships with the main seismic criteria. Hence the results of this study can almost demonstrate this relationship with seismic criteria. The new equations are developed using Iran strong ground motion database, which includes 2228 records of 749 earthquakes that covering up to 2018. The proposed equations can be used to determine exponential window function for earthquakes with moment magnitude from 4.5 to 7.6 and rupture distance up to 200 km. The proposed model is compared with some existing models and the results suggest that the equations can lead to better and more reasonable results in the ground motion simulation process, particularly for the estimation of response spectrum of velocity and displacement.