Fixed-base Frequency Research Articles

Dynamic Load Angle Estimation Through an Angular Domain GDFT Filter for Optimal Energetic BLDC Control

Nowadays, Brushless dc (BLDC) motors are increasingly used to drive speed-controlled applications (e.g., drones, air compressors, etc.) thanks to their high power density, good torque inertia ratio, and their simple square wave commutation principle. However, with growing attention toward energy usage, a more efficient sinusoidal current wave is favored over the classical square wave profile. Nevertheless, changing the waveform to absent the silence phase implicates that simple control principles (e.g., hall-sensors or back electromotive force tracing) are no longer functional, and a more advanced sensorless solution is required. Earlier, an innovative sensorless load angle based controller was suggested with the potential to overcome all restrictions concerning state-of-the-art sensorless control. One of the proposed estimator’s fundamental building blocks is a sliding discrete Fourier filter, requiring both a signal with a fixed base frequency and a full signal period of samples before updating completely. Both requirements severely limit the application field. This article presents an enhanced load angle estimator that can estimate the load angle 66% faster on average and without quality deterioration, regardless of the rotor speed. Both speed and accuracy of the estimated load angle are validated based on BLDC measurements, confirming the potential and revealing possible further estimation lag decreases if a limited estimation quality regression is allowed.

Performance degradation of tuned-mass-dampers arising from ignoring soil-structure interaction effects

Soil-Structure Interaction effects on the performance of Tuned-Mass-Damper are studied by a fully three-dimensional model consisting of a structure instrumented with TMD on top, and with foundation embedded in layered half-space. The influence of a variety of parameters on TMD performance, such as the structure aspect ratios and height, the foundation embedment and the soil-layer thickness, are investigated by comparing structure responses of TMD-instrumented system with un-instrumented system. The performance degradation of TMD due to ignoring SSI, is studied by comparing the efficiency of a well-tuned damper, with one which is off-tuned to the fixed-base frequency of the structure. It is shown in case studies of four buildings in California that a well-tuned damper performs better than an off-tuned one by up to 25%, although an off-tuned one may also reduce the structure responses by up to 30%.

Anti-plane response caused by interactions between a dike and the surrounding soil

This paper proposes a novel strategy for the investigation of displacement amplitude (|uy|) near and along symmetric dikes comprising a trapezoidal structure with a circular-arc foundation when subjected to shear horizontal (SH) waves. Materials in the half-space dealt with two types of dike: (1) soft dikes, and (2) hard dikes. Modified transfinite interpolation (MTFI) was used to obtain the coordinates of nodes and determine the sequence of node numbering in the inner finite region, which included a dike and a semi-circular-arc annulus. MTFI was shown to overcome the difficulties involved in the meshing of irregularity. The proposed hybrid method, comprising finite element method and a Lamb series, was applied in conjunction with MTFI in order to study the effects of dike material, the incident angle of SH waves (θ), and a dimensionless frequency (η) on |uy|. We briefly describe a closed-form solution to the problem of rigid semi-cylindrical foundations proposed in a previous study and then conducted a comparison of theoretical solutions and numerical results obtained using the proposed hybrid method.In the case of soft dikes, the natural fixed-base frequency of the foundation was close to the quasi-resonance frequency (QRF), which resulted in a maximum value of |uy| (|uy|max) at the top of the trapezoidal structure for various η. However, in the case of hard dikes, the |uy|max at the top of trapezoidal structure and in the dike foundation appeared at various QRF due to the fact that the movement of a hard dike is close to a rigid body motion. Energy absorption in a soft dike was shown to be superior to that of a hard dike, based on the fact that the shape of the deformed soft dike was more complex than that of the hard dike, and a number of displacement peaks observed inside the soft dike may be indications of damage within the dike that must be taken into account. Interestingly, the proposed hybrid method with MTFI provides a better understanding of the soil-structure interaction, compared with results obtained in previous studies.

The “Spectrum Dip”: Dynamic Interaction of System Components

In the early 1960s, many full sized surface combatants, submarines and structural models were tested with underwater explosions in order to evaluate the shock load to the ship and internal equipment structures. Initially, shock spectra were calculated from base motion measurements of internal equipment and components. Attempts were made to envelop these spectra to develop shock design spectra inputs. At that time, earthquake engineers were using this enveloping method to develop design procedures from ground motion measurements to protect structures from earthquakes. However, for the measurements on ships, this procedure resulted in calculated loads that would have caused catastrophic failure of the equipment; yet the equipment had not failed on the ship tests. As a result, the data were re-analyzed over a period of over a year. It was concluded that the dynamic interaction of each component or structure reduced the measured spectral motion at the fixed-base frequencies of the structure by about an order of magnitude. In many cases, there was a dip in the shock spectra at the fixed-base frequencies: the “spectrum dip” phenomenon. This re-analysis led to shock spectra design curves for navy ships. This paper presents a review of an experimental study and analytical demonstration to explain the effect of dynamic interaction on the shock or response spectrum. In addition, a practical example of interaction of four single mass dynamic systems mounted on a realistic deck and subjected to a high impact shock input was studied by the authors and some of the results of that study are included.

Quantification of fundamental frequency drop for unreinforced masonry buildings from dynamic tests

The knowledge of fundamental frequency and damping ratio of structures is of uppermost importance in earthquake engineering, especially to estimate the seismic demand. However, elastic and plastic frequency drops and damping variations make their estimation complex. This study quantifies and models the relative frequency drop affecting low-rise modern masonry buildings and discusses the damping variations based on two experimental data sets: Pseudo-dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL. The relative structural frequency drop is shown to depend mainly on shaking amplitude, whereas the damping ratio variations could not be explained by the shaking amplitude only. Therefore, the absolute frequency value depends mostly on the frequency at low amplitude level, the amplitude of shaking and the construction material. The decrease in shape does not vary significantly with increasing damage. Hence, this study makes a link between structural dynamic properties, either under ambient vibrations or under strong motions, for low-rise modern masonry buildings. A value of 2/3 of the ambient vibration frequency is found to be relevant for the earthquake engineering assessment for this building type. However, the effect of soil–structure interaction that is shown to also affect these parameters has to be taken into account. Therefore, an analytical methodology is proposed to derive first the fixed-base frequency before using these results. Copyright © 2010 John Wiley & Sons, Ltd.

Soil-Structure System Identification of Millikan Library North-South Response during Four Earthquakes (1970-2002): What Caused the Observed Wandering of the System Frequencies?

Abstract An application is presented of a recently proposed system identification method for buildings that takes into account the effects of soil-structure interaction and the coupling of the horizontal and rocking motions of the foundation. The method gives the uncoupled structural fixed-base frequency f 1 and rigid-body rocking frequency f R using data only from two horizontal sensors (at base and roof). The fixed-base frequency is estimated from the wave travel time through the structure, the apparent system frequency from Fourier analysis, and the rocking frequency from a relation between these three. The case study is Millikan Library in Pasadena, California. Results are shown for four earthquakes between 1970 and 2002. The method makes it possible to quantify the degree to which the observed changes (wandering) of its resonant frequencies have been due to changes in the structure alone. The results show that (1) both f 1 and f R are amplitude dependent, (2) significant permanent reduction of frequency occurred over the years, ∼22% for f 1 and 11% for the apparent frequency f 1,app , mostly caused by the San Fernando earthquake of 1971, while (3) the changes of f R have been amplitude dependent and recoverable. (4) During the San Fernando earthquake, both f 1 and f R dropped, respectively, by ∼24% and ∼18%, resulting in 21% drop of f 1,app . (5) After this earthquake, the changes in the observed resonant frequencies, which are those of the system, have been due to a much larger degree (4–5 times) to changes of f R than to changes of f 1 . (6) The small permanent changes in f 1 that appear to have occurred after the San Fernando earthquake cannot be deciphered with certainty because of the small number of earthquake records available for this analysis since 1971. Records from the period 1988 to 2002, when released, can be used in future to refine and verify these trends.

Variability of the fixed-base and soil-structure system frequencies of a building-The case of Borik-2 building

Borik-2 is an IMS (Institute for Testing of Materials, Belgrade, Serbia)-type prefabricated 14-story reinforced-concrete building located in Banja Luka, Republic of Srpska (Bosnia, former Yugoslavia), and is a rare example of an instrumented building in Europe shaken by a significant number of earthquakes. This paper presents an analysis of its response to 20 earthquakes recorded in this building, and a comparison with results from previous full-scale tests and analyses. Only one of the 20 earthquakes (8/13/1981, M=5.4) could possibly have caused damage, but no structural damage was reported. For each of these earthquakes, the building fundamental fixed-base frequency f1 was computed from wave propagation travel times estimated by impulse response functions, and the soil–structure system frequency fsys was estimated from the peaks of the Fourier spectra of the response. The analysis suggests consistency of the estimates of fsys from the earthquake response data, from the forced vibration tests before the earthquakes, and ambient vibration tests conducted near the end of the earthquake sequence. The results suggest nonlinear but essentially ‘elastic’ behavior of the building for the amplitudes of motion covered by the data, and essentially linear soil–structure interaction. During the largest event, f1 and fsys decreased, respectively, by about 16 and 22% for EW motions, and by about 18 and 31% for NS motions, compared with the values before the earthquake from the small amplitude response. Comparison of f1 and fsys during the smaller events before and after EQ 11 event shows that f1 did not change, but fsys reduced permanently, by about 10% for EW and 15% for NS. Copyright © 2008 John Wiley & Sons, Ltd.

Impulse response analysis of the Van Nuys 7-storey hotel during 11 earthquakes and earthquake damage detection

Wave travel times of vertically propagating waves are measured in the Van Nuys 7-storey hotel, located in the Los Angeles metropolitan area, from impulse response functions computed by deconvolution of the recorded earthquake response. East-West response data from 11 earthquakes over a period of 24 years are analysed. Changes in wave travel times are used to infer about local (between sensors) and global changes of structural stiffness, from one event to another, and with time during the earthquakes that damaged the building (San Fernando and Northridge). Also, wave travel times are used to estimate the fundamental fixed-base frequency of the building, f1, which is compared with independent estimates of the soil–structure system frequency fsys during the same earthquakes and during five ambient vibration tests. The analysis shows that monitoring only the changes of fsys can be misleading for structural health monitoring and can lead to erroneous alarms, while monitoring changes of f1 over suitably chosen time windows (before, during, and after excitation by strong earthquake motions) can be a powerful and robust tool for structural health monitoring. It is concluded that, under favourable conditions, this method can be used as a tool for global and local structural health monitoring. Copyright © 2007 John Wiley & Sons, Ltd.

Earthquake damage detection in the Imperial County Services Building III: Analysis of wave travel times via impulse response functions

The majority of structural health monitoring methods are based on detecting changes in the modal properties, which are global characteristics of the structure, and are not sensitive to local damage. Wave travel times between selected sections of a structure, on the other hand, are local characteristics, and are potentially more sensitive to local damage. In this paper, a structural health monitoring method based on changes in wave travel times is explored using strong motion data from the Imperial Valley Earthquake of 1979 recorded in the former Imperial County Services (ICS) Building, severely damaged by this earthquake. Wave travel times are measured from impulse response functions computed from the recorded horizontal seismic response in three time windows—before, during, and after the largest amplitude response, as determined from previous studies of this building, based on analysis of novelties in the recorded response. The results suggest initial spatial distribution of stiffness consistent with the design characteristics, and reduction of stiffness following the major damage consistent with the spatial distribution of the observed damage. The travel times were also used to estimate the fundamental fixed-base frequency of the structure f 1 (assuming the building deformed as a shear beam), and its changes during this earthquake. These estimates are consistent with previous estimates of the soil–structure system frequency, f sys, during the earthquakes ( f 1< f sys as expected from soil–structure interaction studies), and with other estimates of frequency ( f 1 from ETABS models, and f sys from ambient vibration tests, and “instantaneous” f 1 from high-frequency pulse propagation).

Effects of the depth of the embedment on the system response during building-soil interaction

The effects of the depth of the embedment on the system response, under plane-strain conditions, have been studied for buildings supported by rigid circular foundations embedded into a homogeneous, isotropic and elastic half-space. The building has been represented by an equivalent single degree-of-freedom oscillator with a rotational spring and viscous damping. A linear analysis and the substructure approach have been used to calculate the system response. The wave passage effects have also been included. Results are shown for incident plane SV-waves. The system damping ratio and the system frequency have been measured directly from the transfer-function of the relative building response. The system damping ratio has been measured by the width of the peak response, normalized by the system frequency. The results have show that, during soil-structure interaction, deeper foundation act ‘stiffer’, and reduce less the system frequency, relative to the fixed-base frequency. The relative response, for the two-dimensional model, is smaller when the depth of the foundation is smaller. Except for heavy and tall buildings, the system damping ratio is smaller when the foundation is deeper. The results of this study have been compared with the results for three-dimensional rectangular prismatic foundations and for hemispherical foundations.