Computation of the time‐domain response of a polarizable ground

Geophysics ◽  
1982 ◽  
Vol 47 (11) ◽  
pp. 1574-1576 ◽  
Author(s):  
D. Guptasarma

Computation of the theoretical time‐domain response of a polarizable ground on the basis of a frequency‐domain model of relaxation, e.g., a Cole‐Cole or any other model that involves a fractional power of the complex frequency variable, runs into difficulties either because the Laplace transform can only be written as a very slowly converging summation or because it cannot be written in closed computable form. A clear way around this is to use a digital linear filter. A filter is presented in this paper that has been designed specifically to work well with complex impedance functions that tend asymptotically to real values at both extremes of the frequency variable, the magnitude descending monotonically from the low‐frequency asymptote to the high frequency asymptote. This filter produces the step response from the real part of the impedance‐versus‐frequency function with reasonable accuracy for all impedance functions that one may like to represent by models of electrical relaxation for a polarizable ground, but it does not work for functions containing sharp resonances or discontinuities.

Author(s):  
Tahzib Safwat ◽  
Ryan Tosto ◽  
Michael D. Grissom ◽  
Christopher D. Rahn

Piezoelectric materials are commonly found in many devices, but their usage is limited by the low strain and high stiffness of the material. This prevents their use in “soft” applications, such as compliant actuators for haptic feedback devices and wearable technology. The actuation dynamics of a ferro-electric relaxor terpolymer, a type of soft and high strain electroactive polymer (EAP), are examined. This paper studies the unimorph actuator via a linearized time-domain model and experiments to validate the model include step response and frequency response of tip displacement.


2021 ◽  
Vol 8 (1) ◽  
pp. E9-E16
Author(s):  
P.C. Eze ◽  
C.A. Ugoh ◽  
D.S. Inaibo

Direct current (DC) servomotor-based parabolic antenna is automatically positioned using control technique to track satellite by maintaining the desired line of sight for quality transmission and reception of electromagnetic wave signals in telecommunication and broadcast applications. With several techniques proposed in the literature for parabolic antenna position control, there is still a need to improve the tracking error and robustness of the control system in the presence of disturbance. This paper has presented positioning control of DC servomotor-based antenna using proportional-integral-derivative (PID) tuned compensator (TC). The compensator was designed using the control and estimation tool manager (CETM) of MATLAB based on the PID tuning design method using robust response time tuning technique with interactive (adjustable performance and robustness) design mode at a bandwidth of 40.3 rad/s. The compensator was added to the position control loop of the DC servomotor–based satellite antenna system. Simulations were carried out in a MATLAB environment for four separate cases by applying unit forced input to examine the various step responses. In the first and second cases, simulations were conducted without the compensator (PID TC) in the control loop assuming zero input disturbance and unit input disturbance. The results obtained in terms of time-domain response parameters showed that with the introduction of unit disturbance, the rise time improved by 36 % (0.525–0.336 s) while the peak time, peak percentage overshoot, and settling time deteriorate by 16.3 % (1.29–1.50 s), 43.5 % (34.7–49.8 %), and 7.6 % (4.35–4.68 s), respectively. With the introduction of the PIDTC for the third case, there was an improvement in the system’s overall transient response performance parameters. Thus to provide further information on the improved performance offered by the compensator, the analysis was done in percentage improvement. Considering the compensated system assuming zero disturbance, the time-domain response performance parameters of the system improved by 94.1, 94.7, 73.1, and 97.1 % in terms of rising time (525–30.8 ms), peak time (1,290–67.9 ms), peak percentage overshoot (34.7–9.35 %), and settling time (4.35–0.124 s), respectively. In the fourth case, the compensator’s ability to provide robust performance in the presence of disturbance was examined by comparing the step response performance parameters of the uncompensated system with unit input disturbance to the step response performance parameters of the compensated system tagged: with PID TC + unit disturbance. The result shows that PID TC provided improved time-domain transient response performance of the disturbance handling of the system by 91.0, 95.4, 80.0, and 93.1 % in terms of rising time (336–30.5 ms), peak time (1500–69.1 ms), peak percentage overshoot (34.7–10.0), and settling time (4.68–0.325 s), respectively. The designed compensator provided improved robust and tracking performance while meeting the specified time-domain performance parameters in the presence of disturbance.


1995 ◽  
Vol 117 (4) ◽  
pp. 311-317 ◽  
Author(s):  
P. So̸rensen ◽  
G. C. Larsen ◽  
C. J. Christensen

The present paper describes a frequency domain model of the structure of an operating horizontal axis wind turbine with three or more blades. The frequency domain model is implemented along with an analogous time domain model in a PC code. This PC code is used to verify the frequency domain model comparing loads on the structure calculated with the frequency domain model both to loads calculated with the time domain model and to measured loads.


2021 ◽  
pp. 875529302098199
Author(s):  
Danilo S Kusanovic ◽  
Elnaz Seylabi ◽  
Domniki Asimaki

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.


1973 ◽  
Vol 95 (4) ◽  
pp. 498-504 ◽  
Author(s):  
J. T. Karam ◽  
R. G. Leonard

A simple, theoretically based time domain model for the propagation of small, arbitrary signals in a finite, circular, fluid transmission line is developed. A recent simple theoretical solution for the step response at a downstream point in a semi-infinite fluid line is combined with a two-port representation of a finite line. The major feature of this finite line model is two “filters” which represent a convolution of their arbitrary inputs with the unit impulse response at the equivalent location in a semi-infinite line. Experimental tests are reported which further verify the simple semi-infinite line solution and verify the response of several example systems containing finite lines. The models developed herein show good agreement with experiment. The major anomaly noted was an amplitude dependence in the experimental response for signals larger than one percent of the bulk modulus of the fluid. Since the theory represents a linearized, small perturbation model, such disagreement might have been anticipated and is viewed as a limitation, rather than invalidation, of the model. Finally, quantitative comparisons are made between the proposed model and those in current use.


2020 ◽  
Vol 9 (1) ◽  
pp. 124-144
Author(s):  
Caglar Uyulan ◽  
Ersen Arslan

AbstractTrain safety and operational efficiency can be improved by investigating the dynamics of the train under varying conditions. Longitudinal train dynamics (LTD) simulations performed for such purposes, usually by utilising a nonlinear time-domain model. This paper covers two modes of LTD results corresponding to the time domain and frequency domain analysis. Time-domain solutions are essential to evaluate the full response used for parameter optimisation and controller design studies while frequency domain solutions can provide significant but straightforward clues regarding system dynamics. An advanced draft gear model, which works under a four-stage process is constructed considering all structural components, geometric relationships, friction modelling and dynamic characteristics such as hysteresis, stiffening, state transition, locked unloading, softening. Then, this model is parametrically reduced and implemented into an LTD simulation. The simulation in the time domain is conducted assuming a locomotive connected with a nine wagon via “ode3” fixed-step solver. The transfer function among the first wagon acceleration (output) and the locomotive force (input) estimated through system identification methodology. Then, the identification results interpreted by investigating step-response characteristic and best response giving parameter set is selected. Next, the modal and spectral analysis performed to reveal the behaviour of the in-train forces and the effects of vibration. This paper discusses a reliable methodology for the longitudinal dynamic analysis of the multi-bodied train in time and frequency domain and clarifies in-train vibration behaviour under the existence of sophisticated draft gear.


2021 ◽  
Vol 236 ◽  
pp. 109508
Author(s):  
Sang Woo Kim ◽  
Svein Sævik ◽  
Jie Wu ◽  
Bernt Johan Leira

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