Time-domain Response Analysis Research Articles

A semi-analytical time-domain model with explicit fluid force expressions for streamwise fluidelastic instability of a single and multiple flexible tube array

Fluidelastic instability (FEI) within steam generator tube arrays poses a significant safety concern for nuclear power plants. Traditionally assumed to manifest in the transverse direction, recent failures at the San Onofre Nuclear Generating Station have underscored the importance of understanding streamwise FEI (SFEI). These incidents have spurred analytical investigations into SFEI, but progress has been hindered by the lack of explicit fluid force formulations, particularly in semi-analytical SFEI models. This paper presents a novel semi-analytical time-domain SFEI model featuring an ideal geometry-based decay function and meticulously derived explicit fluid elastic force expressions. The proposed model supports both frequency-domain stability analysis and true time-domain response analysis, and it is applicable to configurations featuring either a single elastic tube in a rigid array or multiple flexible tubes in an array. Additionally, the tube motion phases are obtained by comparing time-domain responses and employing modified multi-tube frequency-domain SFEI analyses. The stability thresholds predicted for a parallel triangular array using our theoretical model closely align with reported experimental data, thereby validating its accuracy. Our work supplements and advances semi-analytical modeling, alleviating implementation challenges for analyzing SFEI phenomena.

Active suspension control using novel HB3C optimized LQR controller for vibration suppression and ride comfort enhancement

This article addresses the optimization of a Vehicle Active Suspension System (VASS) through the application of a Linear Quadratic Regulator (LQR) controller. The primary objective is to enhance ride comfort and ensure vehicle stability by addressing the divergent needs of vibration control. The research identifies key issues in existing optimization algorithms, namely, the exploration stage inefficiency in Big Bang Big Crunch Optimization (B3C) and the slow convergence rate in Coyote Optimization (CO). To overcome these challenges, a novel hybrid algorithm, Hybrid Coyote optimization based Big Bang Big Crunch (HB3C), is proposed. The research objective is to optimize the LQR weighting matrices using the HB3C algorithm, aiming for improved ride comfort and vehicle safety. The problem statement involves the inadequacies of existing algorithms in addressing the exploration and convergence issues. The motivation lies in enhancing the efficiency of VASS through optimal control, leading to better ride comfort and safety. The methodology involves integrating CO within a loop with B3C to compute the optimum reduction rate for the algorithm. Since, B3C algorithm’s success is highly dependent on selecting the ideal reduction rate. This hybrid approach is then applied to optimize the existing LQR weighting matrices. The results are evaluated in terms of time domain and frequency domain response analysis, with a focus on ride comfort based on ISO 2631-1 standards. The study demonstrates a maximum reduction of approximately 74% achieved by the optimized HB3C-LQR controllers.

A semi-analytical time-domain model with explicit fluid force expressions for fluidelastic vibration of a tube array in crossflow

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis.

Residual LSTM-based short duration forecasting of polarization current for effective assessment of transformers insulation

The empirical application of polarization and depolarization current (PDC) measurement of transformers facilitates the extraction of critical insulation-sensitive parameters. This technique, rooted in time-domain dielectric response analysis, forms the bedrock for parameterization and insulation modeling. However, the inherently time-consuming nature of polarization current measurements renders them susceptible to data corruption. This article explores deep-learning-based short-duration techniques for forecasting polarization current to address this limitation. By incorporating spatial shortcuts, the residual long short-term memory (LSTM) network facilitates the seamless propagation of spatial and temporal gradients. Furthermore, the relative forecasting assessment of the proposed residual LSTM model’s performance is made against traditional LSTM, attention LSTM, gated recurrent units (GRU), and convolutional neural network (CNN) models. Thus, optimal model selection strategies are evaluated based on their capability to capture extended dependencies and short-term information present in the data. In addition, the Monte Carlo dropout prediction is employed to estimate uncertainty in polarization current forecasts. The findings demonstrate that the proposed residual LSTM network model for polarization current forecasting yields the lowest error metrics and maintains prediction consistency over the testing duration. Thus, the proposed approach significantly reduces PDC measurement time, providing an effective means to develop proactive maintenance strategies for evaluating the insulation condition of transformers.

Time domain response analysis of multi-flow channel hydraulic mount

In order to analyze the effect of the combination of long and short inertia channels and orifice flow channels on the time domain response of hydraulic mounts. Firstly, six hydraulic mounts with different combinations of inertia channels and orifice flow channels are proposed. And then, the transfer functions of dynamic stiffness and upper chamber pressure for six structures of hydraulic mounts are derived using the lumped parameter method. Next, the time domain analytic formulas for the transfer force and upper chamber pressure for six structural hydraulic mounts under steady-state excitation and step excitation are obtained using the convolution method. Finally, the analytical formula is compared with the hydraulic mount’s model built by AMEsim; Meanwhile, the effects of inertia terms of inertia channels, damping, and damping of orifice flow channels on hydraulic mounts transfer forces are analyzed; Analyze the effect of transfer force variation and excitation amplitude on hydraulic mounts damping for different configurations of structures. Research shows that inertia channels and orifice flow channels directly affect the low-frequency dynamic characteristics of hydraulic mounts. At the same time, the effective damping height of the hydraulic mounts depends on the excitation amplitude.

Linear and Nonlinear Earthquake Analysis for Strength Evaluation of Masonry Monument of Neoria

An evaluation of the seismic behavior of a massive masonry monument with vaults, namely, the Neoria complex at the old port of Chania, is presented here. The usage of modal response analysis requires the combination of many eigenmodes in order to capture the required amount of vibration energy. Alternatively, a number of earthquakes can be used within a time domain response analysis in order to evaluate the response and, subsequently, the strength of the structure. Results of linear analysis are compared here, since this is what is required from current seismic codes. A nonlinear analysis with adequate material models will also be presented in order to demonstrate a comparison with linear analysis and a prediction of damage appearance under ultimate conditions. From the present investigation, it is shown that the results of the modal analysis and the linear time-step analysis are comparable. Therefore, some confidence is gained towards using the results for the design of strengthening and rehabilitation studies. Nonlinear models are very sensitive with respect to design earthquakes and material models. Therefore, at this stage, their results are used for the identification of areas where interventions must be performed very carefully.

Temperature Dependency of Ion Mobility in Synthetic Ester by Dielectric Response Analysis in Time and Frequency Domain

Synthetic ester is a promising alternative to mineral oil for emerging applications relying on high-power static conversion, such as solid-state transformers (SST). The highly compact components used in SSTs must fulfill MV-DC insulation requirements to guarantee the safe operation of the system, therefore, their design relies on the characterization of the dielectric stress caused by the electric field. The prediction of the electric field induced by DC voltages requires analyzing the conduction phenomena in the liquid, including the effect of charge transport due to ion drift. In this scenario, one of the critical parameters that determine the transport of charge and the resulting electric field distribution is the mobility of ions μ; the value of μ in synthetic ester is available only at room temperature, however, investigations on other dielectric liquids indicate a significant temperature dependency, which therefore needs to be characterized. In this paper, the temperature dependency of μ in synthetic ester liquid is determined by comparing alternative methodologies based on the analysis of the dielectric response in the time and frequency domain, and the viscosity of the fluid. The characteristics obtained by these methodologies are consistent; the temperature dependency of μ obeys the Arrhenius law and an increase of one order of magnitude starting from 1.1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–10</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /Vs is observed in the 303K–353K temperature range.

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

SummaryFractional‐order circuits, which contain fractance devices ( and ) described by fractional‐order differential equations, are widely used in interdisciplinary engineering research. The application of time‐domain response (TDR) measurement increases rapidly in analyzing the characteristics of fractance devices and fractional‐order circuits. However, the previous methods are mainly focused on deducing TDR expressions of a single fractance device or series fractional‐order circuits in some specific input signals, while overlook the TDR analysis of series‐parallel fractional‐order circuits (SPFOC) that are commonly applied in modeling electrochemical impedance or electrical bioimpedance. This paper proposes a novel method to derive TDR expressions of SPFOC in an arbitrary periodic signal. First, a discretization method to represent the SPFOC as the sum of first‐order circuits is proposed in Cole distribution function, which could approximate the transfer function of fractional‐order impedance/admittance. Second, the TDR expression of SPFOC in sinusoidal input signals is deduced in inverse Laplace transform, which can be applied as the components of a general TDR expression of SPFOC in an arbitrary periodic signal based on the Fourier series theory. Finally, both TDR simulations and experiments on Cole impedance model (a basic SPFOC) are conducted to verify the proposed method, which shows excellent agreement compared to theorical analysis. This paper presents a TDR solution to SPFOC that consist of a or element. In future, the theoretical and application extension of the proposed TDR analysis method is still necessary on analysis of more general fractional‐order circuits.

One dimensional time-domain non-linear site seismic response analysis program integrating two hysteresis models of soil

In the numerical simulation of site seismic responses, traditional equivalent linearization methods typically realized in the frequency domain cannot satisfactorily analyze the high-degree non-linearity of soil under strong input motions. Therefore, the “true” non-linear numerical methods performed in the time domain are often utilized in such cases. However, a crucial element of the time-domain non-linear method, which is the hysteresis model of soil that describes the rule controlling the loading–unloading behavior of soil, has no established guidelines for earthquake engineering. Different researchers presented different models, revealing the epistemic uncertainty related to the dynamic properties of soil. Thus, the time-domain non-linear method should consider this uncertainty in practice. Therefore, in this study, a one-dimensional (1D) time-domain non-linear site seismic response analysis program was developed. The developed program was coded using Fortran95 and integrates two kinds of soil hysteresis models (i.e., extended Masing model and dynamic skeleton curve model). In both models, the damping correction was introduced to calibrate the hysteresis loop area toward the damping ratio measured in the dynamic triaxial test or resonant column test. Moreover, the temporospatial finite difference algorithm was used to resolve the 1D non-linear wave equation, and its precision was demonstrated in comparison with the results of the frequency-domain program for the linear case. Finally, the non-linear seismic response of a specific site was calculated by the proposed program. The findings of the fitting were compared to those of the two popular time-domain non-linear programs DEEPSOIL (Hashash, V6.1) and CHARSOIL (Streeter et al., CHARSOIL, Characteristics Method Applied to Soils, 1974 March 25). Simultaneously, the Japanese KIK-net strong motion observation station data were applied to validate the reliability of this program.

A correction method for large deflections of cantilever beams with a modal approach

Abstract. Modal-based reduced-order models are preferred for modeling structures due to their computational efficiency in engineering problems. One of the important limitations of the classic modal approaches is that they are geometrically linear. This study proposes a fast correction method to account for geometric nonlinearities which stem from large deflections in cantilever beams. The method relies on pre-computed correction terms and thus adds negligibly small extra computational efforts during the time domain response analyses. The accuracy of the method is examined on a straight-beam model and International Energy Agency (IEA) 15 MW wind turbine blade model. The results show that the proposed method increases the accuracy of modal approaches significantly in secondary deflections due to nonlinearities such as axial and torsional motions for the two studied cases.

Time-domain signal analysis of dielectric response of nonlinear SDBD thruster in near space

The nonlinear time domain response signals of surface dielectric barrier discharge (SDBD) are the basis for studying the energy loss of SDBD thruster. This paper is based on the construction of a double layer lumped parameter circuit model in solid dielectric and discharge plasma regions; based on virtual instrument technology, a test device for AC dielectric characteristics of a nonlinear SDBD thruster was built to obtain the time domain signals of AC voltage and response current. According to the characteristic spectral curve of the voltage and the response current signal in the time domain, the response current is decomposed into resistive current (conduction current) and capacitive current (relaxation current) by an appropriate algorithm. The experimental results show that the response current in the discharge plasma region is mainly the capacitive current, and the peak capacitive current is about 2.9 times of the peak resistance current; Relaxation planned loss is the main form of energy loss in the discharge plasma region. Due to space charge limiting current effect and space charge saturation effect, the static and dynamic resistance of discharge plasma region have platform area and negative resistance characteristics respectively; Both static and dynamic capacitance have negative capacitor characteristics.

A comparative analysis of seismic response of shallow buried underground structure under incident P, SV and Rayleigh waves

In this study, A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P, SV and Rayleigh waves are established, based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input. After verifying the calculation accuracy, a comparative study on seismic response of a shallow-buried, double-deck, double-span subway station structure under incident P, SV and Rayleigh waves is conducted. The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves. The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves. At the bottom of the side wall, the top and bottom of the center pillar of the underground structure, the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close, and are significantly larger than the calculation result under the incidence of P wave. At the center of the side wall and the top floor of the structure, the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave. In addition, the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions, and the magnification effect in the vertical direction is more significant. Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves, sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.

Achieving ultra-broadband and ultra-low-frequency surface wave bandgaps in seismic metamaterials through topology optimization

Achieving broadband low-frequency surface wave bandgaps is technically challenging, which calls for a systematic design paradigm instead of intuitive approaches. In this study, we use topology optimization to design seismic metamaterials (SMMs) for achieving maximum surface wave bandgaps in the typical frequency range of seismic waves (1 ∼ 20 Hz) which might cause strongly destructive effects to surrounding buildings/structures. The proposed unified inverse-design scheme leads to a series of SMMs, which offer broadband low-frequency surface wave energy insulation. Typically, the lower-edge frequency of the bandgap can reach as low as 1.6 Hz, alongside a 10.3 Hz bandwidth (a relative bandwidth of around 150%). Overall, most optimized structures share similar topological features: slim connections and large masses, which can enhance the local resonance mode. Single pillared barrier is shown to exhibit three typical modes. As a result, multiple pillars (within one unit cell) are necessary for the higher-order bandgaps, and the number of pillars gradually increases with the targeted bandgap order. Frequency- and time-domain response analyses verify that the optimized SMMs can reduce the vibration amplitude over the ground surface within the designed bandgaps. At last, SMMs are customized to cope with realistic seismic signals by completely covering the dominant frequency region.

Simulation of stationary non-Gaussian stochastic vector processes using an eigenvalue-based iterative translation approximation method

The simulation of stationary non-Gaussian stochastic vector processes is of great importance in the time-domain response analysis of structures under non-Gaussian excitations. When incompatibility between the target cross power spectral density matrix and the marginal probabilistic density function of the stochastic vector process occurs in the sense of translation processes, an iterative simulation scheme must be required. Currently, the Cholesky decomposition-based iterative translation approximation method is widely utilized. However, the use of this method still encounters some difficulties. First, it requires performing Cholesky decompositions three times at each iteration and is therefore cumbersome. Second, a complicated random shuffling procedure is necessary, which renders the final iteration result non-unique. Third, it is very difficult for this method to handle cases with complex-valued spectral matrices. Lastly, it can generally be used to simulate stochastic vector processes with very limited components. To overcome these difficulties, an eigenvalue-based iterative translation approximation method is proposed in this study. This method can not only avoid the cumbersome Cholesky decomposition and complex random shuffling, but can also handle cases with complex-valued and large spectral matrices more easily. Four numerical examples with no incompatibility, significant incompatibility, complex-valued coherence and a large number of component processes are respectively employed to demonstrate the effectiveness of the proposed method. The results show that the proposed method has similar accuracy to the Cholesky decomposition-based iterative method in the first two examples. For the last two examples, the simulation accuracy is also satisfactory. The above results verify that the proposed method is superior to the Cholesky decomposition-based iterative translation approximation method overall.

Influence of De-Trapped Charge Polarity in Sensing Health of Power Transformer Insulation

Assessment of insulation condition by sensing and subsequent analysis of oil-impregnated paper response at periodic intervals is necessary for reliable operation of transformers. Sensing frequency domain insulation response requires the application of either a sinusoidal excitation voltage (over a wide range) or a custom excitation waveform. This not only requires a specially designed variable-frequency variable-amplitude excitation voltage source but also makes measurement practically problematic. Measurement of low-frequency data is time-consuming and the data tends to get affected by field noise. In comparison, a simpler and cheaper alternative is the analysis of time-domain insulation response. This involves the measurement of low amplitude polarization and depolarization current. A pico-ammeter or Electrometer is generally used for this purpose. The available interpretation scheme of time domain response sensed using Electrometer does not consider the de-trapping charge’s polarity. The result presented in the paper shows that such an assumption inadvertently leads to inaccurate diagnosis. This, in turn, generates doubt regarding the current sensing capability of the Electrometer involved. In the present work, a better interpretation scheme of the data sensed by the Electrometer is discussed. The significance and influence of de-trapped charge polarity on polarization and depolarization currents are investigated. The analysis is tested on data collected from real-life in-service power transformers.

Research on Vibration Reduction of Half-Vehicle Active Suspension Sys-tem Based on Time-delayed Feedback Control with Wheel Displacement

This paper proposes parameter controlling optimization of the time-delay feedback that is based on "equivalent harmonic excitation" in effective frequency band towards optimization of delay feedback control parameters for vehicle semi active suspension system. In this way, the optimal values of delay feedback control parameters based on different types of delay feedback control (displacement, velocity and acceleration) of wheels in the effective frequency band are obtained. Finally, through the stability analysis of vehicle semi-active suspension system based on different types of wheel delay feedback control and the numerical simulation analysis of time-domain response of suspension system performance evaluation index, the superiority of the time-delay feedback control strategy based on wheel displacement and the effectiveness and feasibility of the equivalent harmonic excitation optimization strategy are verified. Therefore, it provides a theoretical reference for the selection of time-delay feedback control strategy and the optimal design of time-delay feedback control parameters of vehicle active and semi-active suspension system.

Stochastic nonlinear ground response analysis considering existing boreholes locations by the geostatistical method

The field and laboratory evidence of nonlinear soil behaviour, even at small strains, emphasizes the importance of employing nonlinear methods in seismic ground response analysis. Additionally, determination of dynamic characteristics of soil layers always includes some degree of uncertainty. Most of previous stochastic studies of ground response analysis have focused only on variability of soil parameters, and the effect of soil sample location has been mostly ignored. This study attempts to couple nonlinear time-domain ground response analysis with variability of soil parameters considering existing boreholes’ location through a geostatistical method using a program written in MATLAB. To evaluate the efficiency of the proposed method, stochastic seismic ground responses at construction location were compared with those of the non-stationary random field method through real site data. The results demonstrate that applying the boreholes’ location significantly affects not only the ground responses but also their coefficient of variation (COV). Furthermore, the mean value of the seismic responses is affected more considerably by the values of soil parameters at the vicinity of the construction location. It is also inferred that considering boreholes’ location may reduce the COV of the seismic responses. Among the surface responses in the studied site, the values of peak ground displacement (PGD) and peak ground acceleration (PGA) reflect the highest and lowest dispersion due to variability of soil properties through both non-stationary random field and geostatistical methods.

Nonlinear dynamic response of open and breathing cracked functionally graded beam under single and multi-frequency excitation

The present work investigates a time domain nonlinear modeling and response analysis of cracked functionally graded Timoshenko beam. Response of the system influenced by various sources of nonlinearity is studied in detail. Properties of functionally graded material (FGM) are assumed to vary nonlinearly in thickness direction by an exponential gradation relation. Initially, an open crack model is considered and subsequently, methodology is extended for breathing cracks assuming periodic variation in the stiffness of beam on opening and closing of cracks. It is to be highlighted that hardly any work has been carried out to model and analyze breathing crack in continuous or discrete multi degree of freedom (MDOF) models for FGM beams. In addition, present methodology seems to be computationally easier and can effectively solve dynamic problems with coupled nonlinearity, one arises from time dependent stiffness (nonlinearity due to crack) and another due to geometric aspect (nonlinear strain-displacement), for isotropic as well as nonlinear material property variation of beam models, leading to wide ranges of applications. Nonlinear differential equations of motion are derived using Lagrange’s equation. These equations are solved using an implicit direct time integration method, known as Newmark-β method, in conjunction with an iterative technique. Accuracy of the solution is confirmed by comparing some of the results with that of available results. Subsequently, an exhaustive parametric study on effects of cracks, material properties, multi frequency excitation, influence of super harmonics on periodic as well as quasi periodic nonlinear dynamic response of thick and thin beams are performed.

Nonlinear and Equivalent Linear Site Response Analysis of Istanbul Soils

The effect of local soil characteristics on the propagation of earthquake waves has been commonly studied by researchers. However, the validity of the results obtained by these studies is limited only to the relevant soil conditions. The main purpose of this study is to examine the effect of soil conditions on the propagation of seismic waves in Istanbul. In this regard, soil information belonging to different districts of Istanbul has been compiled. The site response analysis was simulated using a time-domain nonlinear response analysis based on the effective stress method and frequency-domain equivalent linear analysis based on the total stress method. A widely used one-dimensional response analysis program DEEPSOIL was used to estimate the soil response of the sites. Modeled soil profiles were subjected to 1999 Kocaeli earthquake motion and the results of the analysis are presented as spectral acceleration, PGA, and lateral displacements. The results obtained from both of the analyses were evaluated comparatively in terms of the effect of soil properties on the propagation of the seismic waves. The effect of the analysis method based on different approaches on the results is examined. The highlighting results obtained on how the propagation of earthquake waves will be affected by soil conditions. The liquefaction potential of soil profiles was also evaluated using the data of the soil properties of the investigation area.

Optimization of frequency domain impedances for time-domain response analyses of building structures with rigid shallow foundations

The effects of dynamic soil–structure interaction (SSI) have been extensively studied in the last few decades, and proper analysis for the linear elastic case in frequency domain has been established successfully. However, SSI is rarely considered in the design of building structures, and instead, buildings are frequently analyzed using a rigid base assumption and quasi-static loading conditions that ignore SSI and its dynamic nature. Acknowledging these shortcomings, the National Institute of Standards and Technology (NIST) published in 2012 a set of recommendations on time-domain analyses of SSI for building structures compatible with standard finite element packages for consideration in engineering design. The so-called NIST GCR 12-917-21 report introduced a major simplification to enable frequency domain tools to be implemented in time domain analyses. That is, replacing the frequency-dependent soil impedance functions by a single-valued functions read at the flexible-base structure frequency; This work seeks to quantify the accuracy of this simplification considering fully coupled two-dimensional (2D) finite element models (FEM) as the reference. Using a Bayesian approach based on ensemble Kalman inversion (EnKI) and a range of numerical simulations of soil–foundation–building interaction, we estimate the optimal frequency that can be used to estimate soil impedance for time domain analyses; and we evaluate the improvement that the corresponding impedance offers relative to the full FEM results when compared to time domain analyses performed in accordance to the NIST recommendations outlined above.