Damped Response Research Articles

The use of ensembles trees machine learning method in estimating damping of granular materials

Granular Materials (GM) employed within the mechanism of particle dampers attenuate the vibration energy due to their interparticle and particle-wall interactions. Estimating their damping effect using the analytical equivalent single mass approach overlooked the particles' individual losses that are built into the total damping. Alternatively, the numerical techniques (e.g., Discrete Element) are time-inefficient and computationally demanding. Therefore, this study explores the implementation of Machine learning (ML) algorithms to estimate the damping effect of GM. The ML model in this study will rely on a Data-Driven Modeling approach (DDM) incorporating the ensemble tress nonlinear regressor method. The models' training and testing data were obtained from an experimental setup of an acrylic beam internally integrated with Stainless Steel (SS) and glass spheres undergoing low excitation amplitude (RMS <1N). The main aim was to map between seven input features (e.g. filling ratio) and one targeted output: the beam's damped frequency response. Three ensemble trees' algorithms were used to create the DDM; Decision Tree, Random Forest, and XGBoost. The hyperparameter combination based on the Gridsearch CV function increases the prediction accuracy of each model. The developed ML models provided high accuracy (86-93%) in predicting the damping effect of the granular materials spheres.

Deep-neural-network model for predicting ground motion parameters using earthquake horizontal-to-vertical spectral ratios

This study proposed a deep-neural-network (DNN) model for seismic ground motion prediction by utilizing a unified strong motion database by the National Research Institute for Earth Science and Disaster Resilience, and earthquake horizontal-to-vertical spectral ratio (EHVR) database in Japan. The model aims to enhance the accuracy of predictions by incorporating the EHVRs for complementing site effects, and utilizing existing ground motion prediction equations (GMPE) as the base model for source and propagation path effects. The hybrid approach enables the prediction of peak ground accelerations (PGAs), peak ground velocities (PGVs), and 5% damped absolute acceleration response spectra (SAs). After classifying the training and test sets from the database, the trained DNN models were applied on the test set to evaluate the performance of the predicted results. The accuracy assessment by the residuals, R-squared ( R2), and root mean square error (RMSE) between the predicted and observed values in the test set revealed the superior performance of the proposed model compared with the traditional GMPE with proxy-based site effects such as V S30s especially in predicting both the spectral amplitude and shape of SAs.

Revisiting the 1934 Mw 8.2 Bihar–Nepal earthquake—Simulation of broadband ground motions

SUMMARY The 1934 Mw 8.2 Bihar–Nepal earthquake was one of the devastating earthquakes, which made seismologists realize the importance of proper seismic hazard analysis and design aspects in India. The event occurred way before proper seismic networks were implemented and hence there are no recorded ground motions available for this event. This study, thus aims to generate possible ground motions for the 1934 Mw 8.2 Bihar–Nepal event. The complex geographical features, ambiguous source information and lack of ground motion data make the simulation and validation of ground motions very difficult. In this regard, the broad-band (BB) ground motions are simulated and validated for the most recent well-documented Himalayan event, that is, the 2015 Mw 7.9 Nepal earthquake in order to calibrate the model and simulation methodology. For this purpose, the computational model is presented for a region of 1000 km × 670 km (longitude 80–89 °E and latitude 23–30 °N) in the Indo-Gangetic Basin to simulate the low-frequency (LF) ground motions using spectral element method. These deterministically simulated LF ground motions are combined with stochastically simulated high-frequency (HF) ground motions based on an improved seismological model . The seismic moment and dimensions of the rupture plane are used to generate ten samples for the finite fault source model having different slip distribution along the rupture plane as a random field. The BB ground motions (0.01–25 Hz) are obtained by merging LF and HF ground motions in the time domain by matching them at a frequency of ∼0.3 Hz. Such BB results are simulated at a grid of stations and at locations where modified Mercalli intensity (MMI) values are available. The estimated MMI values and the observed MMI values are compared to emphasize the efficacy of the model. The maximum PGA estimated from the simulated ground motions in horizontal and vertical directions are observed to be 0.48 g and 0.4 g. Further, 5 per cent damped response spectra and spectral amplification are analysed concerning the sediment depth of the Indo-Gangetic Basin. The results from the study can serve as inputs for dynamic analysis and the design of earthquake-resistant structures across different locations in the Indo-Gangetic Basin.

Sensitivity analysis of frequency response functions with imaginary parts decoupling based on multicomplex-step perturbation

Imaginary perturbation is used in the complex step differentiation method to compute first-order derivatives, widely known as an effective approach for sensitivity analysis in structural dynamics. However, coupling of imaginary parts occurs in the damped frequency response functions when employing this method. To mitigate this coupling, a novel approach for sensitivity analysis based on multicomplex-step perturbation is proposed in this paper, for sensitivity analysis of Frequency Response Functions in structural dynamics. The structural parameters are perturbed in multicomplex domain, the dimensions of structural matrices are expanded using the Cauchy Riemann matrix representation, the equation of motion for sensitivity analysis in frequency domain is transformed to matrix operation in field of real numbers, imaginary term will not exist in the equation of motion for sensitivity analysis, the imaginary part of the frequency response function and the imaginary part of the perturbation are decoupled, the structural frequency response functions and the corresponding sensitivities are obtained from the dimension-expanded equation of motion. A truss structure and a solar wing are adopted to verify the accuracy of the proposed method. Results show that the sensitivity of FRFs can be effectively calculated using the proposed method. Compare to the finite difference method, the proposed method is not depended on the step-size selection procedure. The multi-order and mixed-order sensitivity matrices, especially Hessian matrix can also be obtained using the proposed method.

Correction Factors to Account for Seismic Directionality Effects: Case Study of the Costa Rican Strong Motion Database

This article presents the findings of a study on the directionality effect observed in strong motion records. We set out to establish ratios between several seismic intensity measures that depend on sensor orientation (e.g., GMar, Larger) and others that are orientation-independent (e.g., RotDpp, GMRotDpp, and GMRotIpp), with the intention of proposing multiplicative correction factors. The analysis included an evaluation of the impact of site conditions, ground motion intensity, earthquake magnitude, and hypocentral distance on these ratios. Following a concise overview of the directionality effects and the associated intensity measures, the Costa Rican Strong Motion Database, comprising a total of 4199 horizontal accelerograms (two components), was employed to determine the correction factors. The analysis was carried out for 5% damped response spectra within the 0.01–5 s period range. The study focuses on orientation-independent intensity measures that are derived by combining the maximum values from the recorded motions. In the comprehensive analysis of the complete database, a trend was observed between these intensity measures and the magnitude of the earthquake along with the hypocentral distance. Specifically, records from earthquakes with greater magnitudes exhibited a lower maximum spectral response to the geometric mean of the response spectra of the as-recorded (ar) components ratio (RotD100/GMar), similar to records from earthquakes with larger hypocentral distances. Based on these findings, a proposal was put forth to estimate RotD100 values using GMar values. This ratio can prove useful in transforming data from previous seismic hazard studies, including those applied in many seismic codes, and in defining the maximum anticipated seismic intensity for design purposes in a more straightforward manner.

A method for solving an electro-viscoelastic contact problem with damped response and friction

A method for solving an electro-viscoelastic contact problem with damped response and friction

Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer.

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics

In this paper, we study the well-posedness of a class of evolutionary variational–hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme showing that the problem has a unique mild solution. In addition, we established the continuity of the flow map with respect to the initial data. Under the general framework, we consider two new applications for modeling of frictional contact for viscoelastic materials. In the first application, we consider Coulomb’s friction with normal compliance, and in the second, normal damped response. The structure of the friction coefficient μ is new with motivation from geophysical applications in earth sciences with dependence on an external state variable α and the slip rate | u · τ | .

Current Sensor-Free Output-Feedback Voltage Control for DC/DC Converters via Critical Damping Injection Technique for Converter-Fed Servo System Applications

This study proposes an observer-based multi-loop output-feedback system that regulates the output DC-link voltage of DC/DC converters to the desired value to lower the system model dependence level. There are a few features: (a) the outer loop injecting the nonlinear active damping to ensure the critically damped output voltage response, (b) a model-independent output voltage derivative observer facilitates the inner loop and eliminates the need for complex matrix calculations for tuning the estimation performance, and (c) the use of a pole-zero cancellation acceleration error stabilizer for the inner loop helps maintain the targeted closed-loop performance. The experimental study adopts a 420 W brushless DC motor dynamo system as the load for the prototype 600 W bi-directional converter controlled using the proposed solution.

On a dynamic frictional contact problem with normal damped response and long-term memory

A dynamic frictional contact problem between a viscoelastic body and a foundation is studied. The contact is modeled with normal damped response and a friction law. The constitutive law with long memory is assumed to be nonlinear. The existence result is proved using nonlinear monotone operators, fixed point argument, and extension procedure. Moreover, the exponential stability of the energy solution is established using the multiplier method.

Exponential stabilization of a dynamic frictional contact problem for viscoelastic materials with normal damped response and infinite memory

Exponential stabilization of a dynamic frictional contact problem for viscoelastic materials with normal damped response and infinite memory

Coupled Dynamics of Droplet Impact on a Flexible, Hydrophilic Cantilever Beam.

We experimentally study the droplet impact on a flexible, hydrophilic cantilever beam. Droplets of water, water-glycerol (1:1 v/v), and glycerol were considered on a copper beam. Side visualization of the droplet impact on the cantilever was carried out by using a high-speed camera. We systematically vary cantilever stiffness to obtain a characteristic time scale of the beam dynamics, that is, shorter on the same order and longer than the characteristic time scale of droplet dynamics. Water droplet spreading reduces with an increase in the beam's flexibility, due to the "springboard effect". Results reveal that a threshold cantilever length exists beyond which the droplet vibration mode "locks-in" to the cantilever vibration mode. During lock-in, the bending energy of the beam increases with an increasing length or decreasing stiffness. The time-varying cantilever deflection exhibits an oscillatory, exponentially decaying response. However, in the case where both time scales are almost the same, we found a two-stage damping in the measurements: a fast, initial damping followed by a slower, damped response. We explain this damped response by the interplay of droplet and cantilever early dynamics. As expected, increasing the droplet viscosity dampens the magnitude of droplet spreading and displacement of the cantilever's tip due to a larger dissipation of kinetic energy in the bulk of the droplet. The decay is exponential in all cases, and the time taken to reduce the spreading and displacement is shorter with a larger viscosity. The damping coefficient is found to inversely scale with the cantilever length or mass. We corroborated the measurements with available analytical models, confirming the hypotheses used to explain the results. Overall, the present study provides fundamental insights into controlling the coupled dynamics of droplet and flexible substrates, with potential applications such as the design of efficient agricultural sprays and wings of microaerial vehicles.

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

Abstract This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments. This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.

Tropical Volcanic Eruptions and Low Frequency Indo‐Pacific Variability Drive Extreme Indian Ocean Dipole Events

AbstractVolcanic eruptions can have significant climate impacts and serve as useful natural experiments for better understanding the effects of abrupt, externally forced climate change. Here, we investigate the Indian Ocean Dipole's (IOD) response to the largest tropical volcanic eruptions of the last millennium. Post‐eruption composites show a strong negative IOD developing in the eruption year, and a positive IOD the following year. The IOD and El Niño‐Southern Oscillation (ENSO) show a long‐term damped oscillatory response that can take up to 8 years to return to pre‐eruptive baselines. Moreover, the Interdecadal Pacific Oscillation (IPO) phase at the time of eruption controls the IOD response to intense eruptions, with negative (positive) IPO phasing favoring more negative (positive) IOD values via modulation of the background state of the eastern Indian Ocean thermocline depth. These results have important implications for climate risk in low‐likelihood, high‐impact scenarios, particularly in vulnerable communities unprepared for IOD and ENSO extremes.

Modification of Ground-Motion Models to Estimate Orientation-Dependent Horizontal Response Spectra in Strike-Slip Earthquakes

ABSTRACT A model to estimate the 5% damped response spectra of horizontal components at specific orientations is presented. The model, which explicitly accounts for directionality, is based on prior research by the authors that identified that the orientation of maximum horizontal spectral response at a site in strike-slip earthquakes tends to occur at or close to the transverse orientation with respect to the epicenter. Using a database of 1962 ground motions recorded in shallow crustal earthquakes with strike-slip faulting, it is shown that there is a significantly larger probability of exceeding orientation-independent RotD50 intensities in the transverse orientation than in the radial orientation. Furthermore, the results indicate that, on average, spectral responses in the transverse orientation are significantly larger than those in the radial orientation and that these differences become more significant as the period of the oscillator increases. For example, spectral responses in the transverse orientation are, on average, 12% larger than those in the radial orientation for 1 s oscillators and 78% larger for 10 s oscillators. A period- and orientation-dependent model is developed and calibrated to estimate 5% damped response spectral ordinates at specific orientations by modifying orientation-independent RotD50 intensities. The proposed orientation-dependent model can explicitly account for directionality by modifying the means and standard deviations of any ground-motion model that estimates RotD50 response spectral ordinates for strike-slip earthquakes to obtain probability distributions of response spectral ordinates but now at specific horizontal orientations.

Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states.

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern abinitio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.

Nonlinear active control of thermally induced pyro-coupled vibrations in porous-agglomerated CNT core sandwich plate with magneto-piezo-elastic facings

In this article, the damped nonlinear transient response of a smart sandwich plate (SSP) comprising of agglomerated CNT-reinforced porous nanocomposite core with multifunctional magneto-piezo-elastic (MPE) facesheets, subjected to the thermal environment, is numerically investigated. The synergistic influence of agglomeration, porosity and pyro-coupling on vibration control is studied for the first time under the finite element framework. The attenuation of the vibrations is caused by active constrained layer damping (ACLD) treatment. The kinematics of the plate is based on the layer-wise shear deformation theory and von-Karman’s nonlinearity. The viscoelastic properties of the ACLD patch and CNT agglomeration of the core are mathematically modelled using Golla–Hughes–McTavish and Eshelby–Mori–Tanaka methods, respectively. A comprehensive examination of the inter-related effects of different agglomeration states, porosity distributions and thermal loading profiles has been performed. The new insights on controlling pyro-coupled induced vibrations of smart sandwich plates by supplying control voltage directly to the MPE facesheets without ACLD treatment have been discussed thoroughly. The numerical analysis confirms the significant effects of pyro-coupling associated with active vibration control response of SSP.

Core Excitations of Uranyl in Cs2UO2Cl4 from Relativistic Embedded Damped Response Time-Dependent Density Functional Theory Calculations.

X-ray spectroscopies, by their high selectivity and sensitivity to the chemical environment around the atoms probed, provide significant insights into the electronic structures of molecules and materials. Interpreting experimental results requires reliable theoretical models, accounting for environmental, relativistic, electron correlation, and orbital relaxation effects in a balanced manner. In this work, we present a protocol for the simulation of core excited spectra with damped response time-dependent density functional theory based on the Dirac-Coulomb Hamiltonian (4c-DR-TD-DFT), in which environmental effects are accounted for through the frozen density embedding (FDE) method. We showcase this approach for the uranium M4- and L3-edges and oxygen K-edge of the uranyl tetrachloride (UO2Cl42-) unit as found in a host Cs2UO2Cl4 crystal. We have found that the 4c-DR-TD-DFT simulations yield excitation spectra that very closely match the experiment for the uranium M4-edge and the oxygen K-edge, with good agreement for the broad experimental spectra for the L3-edge. By decomposing the complex polarizability in terms of its components, we have been able to correlate our results with angle-resolved spectra. We have observed that for all edges, but in particular the uranium M4-edge, an embedded model in which the chloride ligands are replaced by an embedding potential reproduces rather well the spectral profile obtained for UO2Cl42-. Our results underscore the importance of the equatorial ligands to simulating core spectra at both uranium and oxygen edges.

Simulating the strong ground motion of the 2022 MS6.8 Luding, Sichuan, China Earthquake

Stochastic finite-fault simulations are effective for simulating ground motions and are widely used in engineering to determine the impacts of ground motion and develop relevant predictive equations. In this study, the source, path, and site amplification coefficient of western Sichuan Province, China, and stochastic finite-fault simulations were used to simulate the acceleration time series, Fourier amplitude spectra, and 5% damped response spectra of 28 strong-motion stations with rupture distances within 300 km of the 2022 MS6.8 Luding earthquake. The simulation results of 14 stations at rupture distances of 45–185 km match the observation. However, the simulation results of 3 near- and 6 far-field stations at rupture distances of 12–36 km and 222–286 km, respectively, were obviously deviated from the observations. Simulation results of the near-field stations are larger than the observations at high frequencies (>6 Hz). The discrepancy likely comes from the nonlinear site effect of near-field stations, which reduced the site amplification at high frequencies. Simulation result of the far-field stations is smaller than the observation at frequencies above 1 Hz. As these stations are located close to the Longmenshan Fault Zone (LFZ), thus, we obtained a new quality factor (Q) from data of historical events and stations located around LFZ. Using the new Q value, the discrepancies of the high-frequency simulation results of the far-field stations were corrected. This result indicated that the laterally varying Q values can be used to address the impact of strong crustal lateral heterogeneity on simulation.

Next generation ground-motion prediction equations for Indo-Gangetic Plains, India

Seismic hazard analysis (SHA) of Indo-Gangetic Plains (IGP), India, and its proximity to the Himalayas requires reliable ground motion prediction equations (GMPEs). This study attempts to derive the GMPEs for IGP using strong-motion accelerometer data recorded from 2005 to 2015 on IGP. For regression, peak ground acceleration (PGA) and pseudo-spectral acceleration (PSA) of 5% damped linear pseudo-absolute acceleration response spectra at 27 periods ranging from 0.01–10 s were used. Two-stage nonlinear regression trains the functional form of nonlinear magnitude scaling, distance scaling, and site conditions. The model includes a regionally independent geometric attenuation finite fault distance metric, style of faulting, shallow site response, basin response, hanging wall effect, hypocentre depth, regionally dependent anelastic attenuation, site conditions, and magnitude-dependent aleatory variability. Developed GMPEs are validated for active crustal continental earthquakes for epicentral distances REPI ranging from 10–1500 km, magnitude ranging from 3.3–7.9, and focal depths 1–70 km. The GMPEs developed are compared with the Campbell and Bozorgnia 2008, 2013 and 2014, and North Indian GMPEs, which are agreed upon consistently. The model can predict the horizontal ground motion for SHA on IGP, considering possible maximum magnitude earthquakes from the seismic gaps of the Himalayas.