Resonant Period Research Articles

Wave overtopping due to harbour resonance

Harbour resonance and its contribution to wave overtopping are examined for a small irregular-shaped harbour in the eastern Mediterranean. Offshore wave measurements are used to determine the incident wave conditions during storm events. Resonant periods of the harbour basin are identified through in situ measurements at four different deployment locations during multiple storm events. Numerical simulations using a Boussinesq-type model and an idealised offshore spectrum yielded similar resonant frequencies to the field measurements and allowed us to visualise the corresponding resonant modes. Wave overtopping along the vertical docks of the harbour is inferred by combining numerical time series of free surface elevation with EurOtop formulae. Two approaches to estimate wave overtopping rates are examined and compared: a novel approach considering wave energy in the sea-swell frequency range and varying the freeboard through time series in the infragravity frequency range, and the conventional method that considers spectral parameters along the entire frequency range. The novel approach provides an estimate for the contribution of harbour resonance to wave overtopping considering that infragravity wave energy inside the basin is mainly resonance-driven.

Research about a fast identification method for intermittent single Sub-synchronous Resonance phenomenon in large scale doubly-fed wind farm

In this paper, a synchronous resonance (SSR) phenomenon caused by a large scale doubly-fed wind farm group after putting in series compensation device is analysed. By analysing the changing trends of the indicators during period of SSR phenomenon, 11 power quality indicators are chosen for calculated, then divided all the 11 indicators into 3 source data and 8 preliminary stage operational data by the observability of value. After divided the two kinds of data, a Pearson correlation coefficient between this two kind data was calculated to judge the relationship of them, and the characteristic indexes with stronger correlation during the resonance period were analysed. The maximum value of the above 8 characteristic indexes in the normal power generation process is used as the basic data for comparison, so as to realize the rapid and accurate judgement of the SSR moment. In the process of SSR judgement, the method has the characteristics of faster speed and simple determination, and it does not need to reform the existing power quality online monitoring device, and can realize real-time analysis and judgement of SSR phenomenon only by increasing extraction of the existing data function from the monitoring system. Finally, by testing data of two actual SSR events, the characteristic index determination method proposed in this paper is analysed and verified, and the feasibility of this method is proved.

Evaluation of Uncertainties in Site Response Analysis of Deep Soil Profiles in South Carolina Coastal Plain

ABSTRACTThe South Carolina Coastal Plain consists of deep soil sediments over basement bedrock. The depth of basement bedrock varies from being present at the surface to a depth of more than 1200 m at the southern tip of the state. A large variation exists in the thickness of the sediment, which impacts the seismic site response analyses of the Coastal Plain, particularly in areas where the availability of deep shear-wave velocity profiles is limited. This study evaluates the impact of variations in the shear-wave velocity profiles for two sites in the South Carolina Coastal Plain. The shear-wave velocity profiles were measured using different geophysical methods, including a combined multichannel analysis of surface waves and microtremor array measurement (MASW-MAM) method and P–S suspension logging. The equivalent-linear site response analyses were conducted by applying a synthetic earthquake motion at the depth of the B–C boundary (a depth of competent rock in which the shear-wave velocity is 760 m/s). The results are presented in terms of the amplification factor and its standard deviation. Results show that the average shear-wave velocity at the first 30 m (VS30), the shear-wave velocity contrast at the interface of the base layer and the B–C boundary, and the depth to the B–C boundary have a significant impact on the amplification factor and its variability, particularly for the amplification factor at periods higher than 0.1 s. The MASW-MAM method provided significantly lower VS30 values than the P–S suspension logging method at one of the two sites. Consequently, an additional peak in the amplification factor was observed for the site that had a low VS30, and the corresponding period was close to the resonant period of the loose, surface deposit.

Розрахунок оптимальних параметрів коректувальних елементів в індукційних системах прискорення

The formulations of a number of optimization problems for a linear induction acceleration system with respect to the adjustment parameters are considered. The dynamics of the transverse motion of electrons in the horizontal plane is investigated in the presence of given energy values for each resonator period: the particles at the initial moment of time are somewhat displaced relative to the accelerator axis (we neglect the displacements of the ends of the solenoids and the centers of the accelerating gaps relative to the accelerator axis). A connection is established between the initial and final coordinates and the components of the momentum. The presence of parasitic electric and magnetic fields arising as a result of the displacement of particles relative to the axis of the accelerator, which change the transverse components of the pulses, is taken into account. For the mathematical formulation of problems, in order to apply algorithms of practical stability, the original difference model of the induction system was converted to a linear form. By introducing into consideration the vector of parameters, the scatter of phase coordinates, and tolerances on the parameters, the problem of calculating the tolerances for given linear constraints on the scatter of phase coordinates for the corresponding inhomogeneous system is formulated. For the case of nonlinear dynamic constraints on the spread of the vector of phase coordinates, it is proposed to approximate a convex closed set by tangent hyperplanes. Numerical estimation of the range of tolerances for the parameters of correcting elements is reduced to the problems of practical stability of discrete parametric systems. In this case, the region of the initial conditions on the state vector, the tolerances on the parameters, are given structurally in the form of an ellipsoid, which makes it possible to numerically solve the original problem as an extremal one. From the standpoint of practical stability in the corresponding space of functions, the problem of assessing the range of tolerances for the parameters of correcting elements in the presence of specified restrictions on the spread of the quality criterion is considered. Attention is focused on an important class of problems of numerical modelling of a linear induction acceleration system − problems of practical stability. Numerical estimation of the region of initial displacements of the transverse coordinates of the linear induction acceleration system in the given structures in the presence of linear constraints on the vector of phase coordinates in dynamics is carried out. Key words: modeling, induction system of acceleration, solenoid, parameters, elements of correction, optimization, stability

Wavelet‐Based Characterization of Very‐Long‐Period Seismicity Reveals Temporal Evolution of Shallow Magma System Over the 2008–2018 Eruption of Kīlauea Volcano

AbstractVery‐long‐period (VLP) volcano seismicity often encodes subsurface magma movement, and thus provides insight into subsurface magma transport processes. We develop a fully automated signal processing workflow using wavelet transforms to detect and assess period, decay rate, and ground motions of resonant VLP signals. We then generate a VLP catalog over the 2008–2018 open‐vent summit eruption of Kīlauea Volcano containing thousands of events. Two types of magma resonance dominate our catalog: vertical sloshing of the open magma column in and out of the shallow magma reservoir, and lateral sloshing of magma in the lava lake. These events were triggered mainly from the surface and less commonly from depth. The VLP catalog is then combined with other geophysical datasets to characterize evolution of the shallow magma system. VLP ground motion patterns show both abrupt and gradual changes in shallow magma reservoir geometry. Variation in resonant periods and decay rates of both resonance types occurred on timescales from hours to years, indicating variation in magma density and viscosity that likely reflect unsteady shallow outgassing and convection. A lack of correlation between decay rates of the two dominant resonant modes suggests a decoupling between magma in the conduit and lava lake. Known intrusions and rift zone eruptions often represented change points for resonance characteristics and their relations with other datasets. This data synthesis over a 10‐year eruptive episode at Klauea Volcano demonstrates how VLP seismicity can sharpen insights into magma system evolution for use in monitoring and understanding eruptive processes.

Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography

Seiches and resonances are two closely related phenomena that can cause damage to coastal areas. Seiches that occur in a basin at a distinct period named the resonant period may generate resonance when a wave induced by external forces enters the basin and has the same period as the seiches. Studying this period has become essential if we want to understand the resonance better. Thus, in this paper, we derive the resonant period in various shapes of semi-closed basin using the shallow water equations. The equations are then solved analytically using the separation of variables method and numerically using the finite volume method on staggered grid to discover the resonant period for each basin. To validate the numerical scheme, we compare its results against the analytical resonant periods, resulting in a very small error for each basin, suggesting that the numerical model is quite reliable in the estimation of the analytical resonant period. Further, resonant wave profiles are also observed. It is revealed that, in the coupled rectangular basin, the maximum wave elevation is disproportionate to the ratio of the length of the basin, while, in the trapezoidal basin, the ratio of the depth of the basin has no significant impact on the maximum wave elevation.

Numerical investigation on the wave power extraction for a 3D dual-chamber oscillating water column system composed of two closely connected circular sub-units

The key to promote the development of wave energy device industry lies in economy, which ensures the benefit output is greater than the input cost. To extract wave power over a much broader range of wave frequencies, an offshore dual-chamber oscilating water colum (OWC) system composed of two closely connected 3D circular sub-units, aligned in the direction of wave propagation is proposed and investigated under the framework of CFD toolbox OpenFOAM. Wave conditions with a variety of periods are considered and the power take-off system for each individual chamber is modelled by a top orifice. Different methods used in estimating the wave energy capture width ratio are compared and the effects from the variation of the front and rear chamber breadth ratio, the shape angle of the supporting structure existing in the front chamber, on the wave power extraction are examined and discussed. The results show that the marginal non-uniformity in the vertical air flow velocity through the orifice makes the method based on the air pressure and air flow velocity more reasonable for estimating the capture width ratio. A system with the front and rear chamber breath ratio equal to 2/3 is more desirable as remarkable improvement can be identified from the total capture width ratio when it is operated near the resonant period condition of the front chamber. In addition, the optimal shape angle is identified when designed as a value of 180∘ as more wave power entering into the front chamber and less wave power reflected by the lip-wall can be guaranteed simultaneously.

A self-floating oscillating surge wave energy converter

This paper proposes a new conceptual configuration for oscillating surge wave energy converters. The concept is a self-floating device consisting of two vertical flaps with a common hinge and an averaged density equal to that of water. The two flaps will oscillate in opposite directions when driven by incident waves. Kinetic energy will be extracted from the relative speed between the two flaps by a power take-off embedded at the hinge. Numerical studies reveal that the self-floating device has a smaller resonant period and optimal power take-off damping compared with a bottom-hinged floating device of the same overall dimensions. As long as the power take-off damping is appropriately tuned, the opposite-rotation mechanism is valid in both regular and irregular waves, and no matter whether the hinge is fixed or connected with mooring lines. With the self-floating feature and opposite-rotation mechanism, the proposed concept can potentially benefit deep ocean applications by exerting a significantly less reaction loading on mooring lines and eliminating the need for a supporting frame to house the power take-off. The influence of various design parameters such as flap dimensions, submerged depth, incident wave direction, and water depth is also analyzed for a comprehensive evaluation of the proposed concept.

Improvement of the ultra-low-frequency active vertical vibration isolator with geometric anti-spring structure for absolute gravimetry.

For absolute gravimeters, which play important roles in geophysics and geological exploration, an ultra-low-frequency vertical vibration isolator is necessary to achieve the required measurement precision. A novel active vibration isolator that uses a geometric anti-spring (GAS) structure has been proposed by our team at Tsinghua University previously, but its performance is mainly limited by the large-scale drift in the detection signal of the system. In this paper, after a brief theoretical introduction to the overall system, recent improvements in this novel vibration isolator are presented. The main improvements to the isolator are the use of new blades in the GAS structure and the addition of an extra compensation circuit to eliminate the drift. The improved prototype has a resonance period of 29.2s and a continuous working time of several days, as compared with the resonance period of 19.2s and a working time lasting only several minutes of the previous prototype. Experiments show that the improved prototype performs well in the homemade T-1 laser-interferometry absolute gravimeter. The standard error of the mean (SEM) of a 50-drop measurement performed in Tsinghua University is reduced significantly from 404 μGal (1 μGal = 1 × 10-8ms-2) without the vibration isolator to 10.8 μGal with the improved prototype at its best level. Additionally, the SEM of a 50-set measurement (including 800 drops) lasting for 25 h achieves 5.9 μGal with the improved prototype.

Near-infrared plasma cavity metasurface with independently tunable double Fano resonances

We report a metasurface device based on nano metal-dielectric-metal plasmon cavity arrays. Investigation of the proposed device indicates the sharp absorption peak of double Fano resonance and multiple periods of time-domain oscillations caused by the three-dimensional double resonance. By adjusting the structure parameters, different absorption patterns can be regulated independently with high degree of freedom. The metasurface exhibits sensitive behavior to the environmental refractive index and possesses the sensitivity of 667 nm RIU−1 as a refractive index sensor in the mid-near infrared band, which can be further considered for glucose or temperature sensing.

Spatiotemporal variations in extreme precipitation on the middle and lower reaches of the Yangtze River Basin (1970–2018)

Extreme precipitation events are likely occur more frequently and lead to casualties and socio-economic losses as global warming intensifies. Therefore, exploring the characteristics of extreme precipitation events is essential. Based on meteorological station data from the middle and lower reaches of the Yangtze River Basin (MLYRB) from 1970 to 2018, we analyzed the spatiotemporal distributions of 11 extreme precipitation indices and considered the correlation between altitude and large-scale atmospheric circulation with extreme precipitation. To this end, we employed Sen's trend analysis, rescaled range analysis, the Mann-Kendall test, and continuous wavelet transform. The results indicate that on this spatial scale, extreme precipitation indices in the northwestern region of the MLYRB have mainly decreased, but they have increased along the eastern coastal region. From the perspective of the entire region, Hurst values of extreme precipitation indices are >0.5. Areas with consistent increases are mainly concentrated in the central region, while those with consistent decreases are mainly scattered in the northern and southern regions. Abrupt change in extreme precipitation indices mostly occurred in the 1980s and 1990s. The periodic oscillations of most indices tendtoward high time-frequency scales (2.3 years or less). Consecutive wet days increased with increasing altitude; other indices changed similarly with increasing altitude, first increasing then decreasing before increasing again. Additionally, we found significant resonance periods between the extreme precipitation indices and the atmospheric circulation index, however, there were obvious differences in time domains.

Numerical examination of wave power absorption by the Edinburgh Duck wave energy converter device

A two-dimensional computational fluid dynamics (CFD) numerical model is developed to study the power takeoff (PTO) efficiency of an Edinburgh duck wave energy converter (WEC) device by using the OpenFOAM source package. After the numerical validations and the convergent verifications, the characteristics of the duck WEC device for the power takeoff in various incident wave periods are examined. The present numerical investigation indicates that the maximum absorbed power of the duck WEC device is attained in its resonant period, while the maximum efficiency is achieved in a lower period. The influence of the damping coefficient on the PTO is also investigated. The optimal damping coefficient for acquiring more power and better efficiency is determined from a numerical examination.

Polar motion resonance in the prograde diurnal band

Summary Until now, the polar motion resonance (PMR) complex frequency has been determined in the seasonal and retrograde diurnal band of the polar motion. In this study, this resonance is studied in the prograde diurnal band, where polar motion is mainly composed of periodic terms caused by the diurnal oceanic tide. The resonance parameters (period and quality factor) are encompassed in the frequency transfer function between generating tidal potential and polar motion, and can be estimated accordingly. To this aim, we gather three published sets of prograde diurnal terms determined from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI), to which we append our own estimates based upon a processing of the VLBI delays over the period 1990–2020. Then, by fitting the PMR parameters so that the prograde diurnal terms match the corresponding components of the tide generating potential, we obtained a resonance period of about 401 d and an equivalent quality factor of −22, differing from those reigning in the seasonal band (PPMR ≈ 431 d; QPMR ≈ 56–255) and in the retrograde diurnal band (PPMR ≈ 380 d; QPMR ≈ −10). Our estimates confirm strikingly the theoretical prediction derived from the tidal ocean angular momentum derived from the FES 2014 ocean tide model.

Mapping long-period soil resonances in the Kathmandu basin using microtremors

This study reports the geostatistical analysis of a set of 40 single-station horizontal-to-vertical spectral ratio (HVSR) passive seismic survey data collected in the Kathmandu basin (Nepal). The Kathmandu basin is characterized by a heterogeneous sedimentary cover and by a complex geo-structural setting, inducing a high spatial variability of the bedrock depth. Due to the complex geological setting, the interpretation and analysis of soil resonance periods derived from the HVSR surveys is challenging, both from the perspective of bedrock depth estimation as well as of seismic-site effects characterization. To exploit the available information, the HVSR data are analyzed by means of a geostatistical approach. First, the spatial continuity structure of HVSR data is investigated and interpreted taking into consideration the geological setting and available stratigraphic and seismic information. Then, the exploitation of potential auxiliary variables, based on surface morphology and distance from outcropping bedrock, is evaluated. Finally, the mapping of HVSR resonance periods, together with the evaluation of interpolation uncertainty, is obtained by means of kriging with external drift interpolation. This work contributes to the characterization of local seismic response of the Kathmandu basin. The resulting map of soil resonance periods is compatible with the results of preceding studies and it is characterized by a high spatial variability, even in areas with a deep bedrock and long resonance periods.

Modal analysis of concrete arch dam–reservoir–massed foundation system in frequency domain

Modal analysis of concrete arch dam–reservoir–foundation rock systems is a challenging task. The complexities arise mainly due to computing mode shapes encountered when solving an eigenvalue problem with asymmetric generalized mass and stiffness matrices. Moreover, the problem becomes complicated when wave propagation is occurring due to the inclusion of water compressibility and foundation rock mass. In the present study, a computational tool is especially developed for this purpose. The theoretical background is explained initially. Subsequently, dynamic analysis of the Morrow Point arch dam–reservoir–foundation rock system is carried out with different values of reservoir bottom absorption coefficient. In addition, some of the modal characteristics of such systems, including resonant frequencies and natural periods, are discussed. The main objective is to perform these analyses by modal analysis. However, the direct method of analysis is also carried out in each case as a basis for comparison from the perspectives of accuracy and efficiency.

Analytical and numerical studies for seiches in a closed basin with various geometric shapes of longitudinal section

Seiches are long-period standing waves with a unique period called a natural resonant period, during which the phenomenon of resonance occurs. The occurrence of resonance in coastal areas can cause destruction to surrounding natural and man-made structures. By determining the resonant period of a given basin, we can pinpoint the conditions that allow waves to achieve resonance. In this study, a mathematical model is developed from the shallow water equations to examine seiches and resonances in various types of closed basin. The developed model is solved analytically using the separation of variables method to determine the seiches' fundamental resonant periods. Comparisons between the analytical solutions and experimental measurements for resonant periods are also provided. It is shown that the analytical resonant period confirms the experimental data for closed basin of various geometric profiles. Using a finite volume method on a staggered grid, the model is solved numerically to simulate the wave profile when resonance phenomenon occurs. Through those numerical simulations, we also obtain the fundamental resonant period for each basin which agrees with the derived analytical period.

Characteristics of dry-wet changes in Xinjiang based on SPEI index

The standardized precipitation evapotranspiration index (SPEI), calculated from 55 stations 37 over the period 1961-2015, was used to analyze the spatial and temporal variability of the dry 38 and wet climate in Xinjiang on a three and six-month time scale, so as to help to actively deal 39 with the negative effects of climate change and reduce disaster losses. The obtained results 40 show that precipitation and temperature in Xinjiang have an increasing trend, with rates of 41 8.90 mm and 0.39 ºC per decade, respectively. SPEI-3 and SPEI_6 show the same linear 42 change trend, with a change rate of 0.005 and 0.007 per decade, respectively. Severe droughts 43 occurred in 1997 and 2008, and particularly in 2008 SPEI_6, the number of meteorological 44 stations with moderate drought and extreme drought accounted for 60% of all stations. 45 Analysis of Empirical Orthogonal Function (EOF) indicates that SPEI-3 and SPEI_6 have 46 similar spatial distribution in the three EOF modes. EOF1 reflects that the overall dry and wet 0 10 20 30 40 50 1961 1971 1981 1991 2001 2011 Numbers stations Year (a) SPEI_3 Extreme drought Moderate drought Mild drought Normal Mild moist Moderate moist Extreme moist 0 10 20 30 40 50 1961 1971 1981 1991 2001 2011 Numbers stations Year (b) SPEI_6 Extreme drought Moderate drought Mild drought Normal Mild moist Moderate moist Extreme moist 47 changes in the study area were weakening, and there was a drying trend; EOF2 was a reverse 48 change in the northern and Southern Xinjiang; EOF3 shows that the East Tianshan had a 49 drying trend, while the western part of Southern Xinjiang tends to relieve the drought. The 50 spectra of wavelet coherence and cross wavelet transform showed that the SPEI values in 51 Xinjiang have resonance periods of different time scales with the Atlantic multi-year 52 intergenerational oscillation (AMO), El Nino Southern Oscillation (ENSO), North Atlantic 53 Oscillation (NAO), and Pacific interdecadal oscillation (PDO), but in different time-domain 54 correlation has certain differences. Among them, AMO is the main atmospheric circulation 55 factor that affects SPEI in the region.

Predicting seiche hazard for coastal harbours along the northern and western coasts of France

Long-period waves propagating inside harbours can lead to the generation of seiche that can affect and significantly disrupt port operations. This study is based on the analysis of a multi-years tide gauge database provided by the sea-level observation network (RONIM). It aims to propose simple models to compute seiche amplitudes at a series of French harbours. The study sites, located along the Atlantic coast, English Channel and North Sea, are representative of the diversity of French harbour configurations and are exposed to different wave regimes. First, the resonant periods of each site are determined by combining analysis of measured water levels and solutions of a linearised mild-slope equation model. Then, the role of incoming bound waves on the generation of seiches is investigated using the solutions of the WAVEWATCH III spectral wave model to compute low frequency spectra using the (Hasselmann in J Fluid Mech 12(04): 481–500, 1962) nonlinear theory. The study shows strong correlation between incoming bound waves and low frequency harbour oscillations for small ports and inside harbour waterway. For a series of sites, empirical formulations based on offshore bulk wave parameters (Bowers in Edge (ed) Proceedings of 23rd international conference on Coastal Engineering, Venice, Italy, 1992) are proposed to predict the long wave significant heights inside the harbour basins generated by short waves. Comparisons with observations show a fairly good agreement. This result suggests that seiche events can be reasonably predicted using such formulations forced by a spectral wave model as WAVEWATCH III. In addition, this study highlights the value of maintaining long-term water-level observation systems to develop operational forecasting system and improve harbour operation management.

Coupled motion characteristics of a large-scale tunnel element suspended by immersion rigs in the vicinity of seabed

During the near-seabed immersion stage, the submerged tunnel element suspended by immersion rigs and anchored to the seabed is at risk of possible bottom grounding and collision with the installed elements. Specifically, the wall effect would have an important role on the motion characteristics of the tunnel element when it approaches the seabed (The wall effect is the influencing behavior of one large planar surface approaching another large planar surface underwater). To investigate this effect, this research conducts 3D experiments using a 1:60 scale model of a combined tunnel element and immersion rig system. The six-DOF motions of the tunnel and immersion rig are measured simultaneously for various regular wave conditions. The collected measurements for different relative clearances are compared in both time and frequency domain. Nonlinear effects of the near-seabed interference are found to be particularly significant when the relative clearance ratio (clearance beneath tunnel / height of tunnel element) is smaller than 0.26, especially when the incident wave period is near the resonant roll period of the tunnel/rigs. To further explore the contributing factors of the seabed interference and to determine suitable operating conditions in practice, a fully coupled tunnel-rig numerical model is built based on the potential flow theory. Additional damping is also included in the coupled motion equations for the resonant roll scenarios and good agreement with experimental data is achieved for relative clearance ratio of δ/d ≥ 0.42. Overall, the experimental and numerical results demonstrate that besides the relative clearance, the near-wall effect of the seabed is also closely associated with the roll of the tunnel element and thereby has a strong dependence on the incident wave height, wave period and wave obliquity. The study is expected to be helpful for understanding the near-seabed effect on the responses of large-scale rectangular floater so that the installation and positioning can be performed accurately and effectively.

Velocity Profiler Optimization for High Precision Linear Servo Drives

When installing a servo linear electric drive on platforms with supports of passive vibration isolation during positioning, elastic vibrations occur with the natural frequency of the elastic platform. The features of the velocity profile of such an electric drive with the ability to limit the jerk are considered. A mathematical model and a structural diagram of an elastic system are presented. When simulating such a system, the dependences of overshoot on the relative period of vibrations were obtained. It is shown that the optimal jerk time - from the point of view of minimizing the overshoot - is its value equal to the period of the 1st resonance of the "elastic" platform. The calculation of the minimum value of the displacement, at which the efficiency of the choice of the optimal value of the jerk, is ensured. The proposed choice of the optimal jerk time is confirmed by the experimental study.