Guidelines for Optimizing the Error in Area Ratio Damping Estimation Method

2021 ◽  
Author(s):  
Balija Santoshkumar ◽  
Firas A. Khasawneh
Keyword(s):  
Damping Ratio ◽  
Estimation Method ◽  
Optimal Number ◽  
Free Response ◽  
Single Degree Of Freedom ◽  
Recent Approach ◽  
Number Of Cycles ◽  
Damped Systems ◽  
Two Peaks ◽  
Damping Estimation

Abstract The logarithmic decrement (log-dec) is one of the most popular methods for viscous damping estimation in linear, single degree of freedom systems. It estimates the damping ratio by examining the decay in the amplitude between two peaks some number of cycles apart. The accuracy in the estimation is sensitive to the chosen number of cycles, where the latter can be optimized such that the uncertainty in the estimation is minimized. However, the log-dec method is not suitable for systems with high damping ratios (approximately > 0.3). Another recent approach for damping estimation is based on considering a ratio of the amplitudes of the positive and negative areas in the free response of the oscillator. Although prior works on the areas method only tested lightly damped systems, we show here that — in contrast to log-dec — this approach can estimate the damping ratio over the whole range of underdamped linear oscillators. However, in contrast to log-dec, there are no available guidelines on how many areas to include in the damping estimation. In this work, we derive uncertainty analysis expressions for the areas method and we utilize them to obtain the optimal number of areas to use. Our results show that for a very low damping ratio (< 0.01), choosing more than two areas in the estimation increases the uncertainty. In contrast, for moderate to high damping (between 0.05 and 1), we need to consider all the available areas in the estimation. One caveat in the range of high damping (between 0.3 and 1) is that while it is desirable to include all the available areas, uncertainty increases when considering up to 3 areas. Therefore, if only 4 areas are available in this range, then to reduce the uncertainty in the estimate only the first two areas must be considered. The results are verified using a large number of numerical simulations including different levels of noise.

scholarly journals Numerical and analytical study of seismic response of structural systems with new formulation using energy and impact methods

2021 ◽  
Vol 286 ◽  
pp. 04014
Author(s):  
Mehdi Babaei ◽  
Somayeh Mollaei ◽  
Amin Moslemi Petrudi ◽  
Maysam Jalilkhani ◽  
Ionut Cristian Scurtu
Keyword(s):  
Damping Ratio ◽  
Main Idea ◽  
Structural Systems ◽  
Single Degree Of Freedom ◽  
Numerical Example ◽  
Solution Methods ◽  
Conservation Principles ◽  
New Formulation ◽  
Damped Systems ◽  
Duhamel’S Integral

This paper presents two simple and robust technique for response estimating of single-degree-of-freedom (SDOF) structural systems. The impulse method, because it is formulated based on the fundamentals of dynamics; especially, the linear impulse concept, and also the energy method, because the main idea of this method is inspired by energy conservation principles. These methods can strongly cope with linear damped systems for which damping ratio ζ is greater than 0.01. Assessment of SDOF dynamic systems under any arbitrary excitations is easily possible through the proposed methods. There is no error propagation through the solving process. The numerical example reveals the simplicity and robustness of the new technique compared to Duhamel’s integral and similar techniques. Finally, a numerical example is investigated to demonstrate the efficiency of the algorithms. The most famous record of El Centro ground motion is applied to the systems. The obtained results show that the new algorithm works exactly enough to compete with a conventional method such as the Duhamel integration method and the Newmark-β method. A comparison between the results of this method with the solution methods used by other researchers is shown to be a good match.

scholarly journals Estimation of Additional Equivalent Damping Ratio of the Damped Structure Based on Energy Dissipation

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Xiuyan Hu ◽  
Qingjun Chen ◽  
Dagen Weng ◽  
Ruifu Zhang ◽  
Xiaosong Ren
Keyword(s):  
Energy Dissipation ◽  
Damping Ratio ◽  
Theoretical Concept ◽  
Estimation Methods ◽  
External Excitation ◽  
Single Degree Of Freedom ◽  
Equivalent Damping ◽  
Seismic Motion ◽  
Practical Engineering ◽  
Energy Dissipation Capacity

In the design of damped structures, the additional equivalent damping ratio (EDR) is an important factor in the evaluation of the energy dissipation effect. However, previous additional EDR estimation methods are complicated and not easy to be applied in practical engineering. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the additional EDR. First, an energy governing equation is established to calculate the structural energy dissipation. By means of dynamic analysis, the ratio of the energy consumed by dampers to that consumed by structural inherent damping is obtained under external excitation. Because the energy dissipation capacity of the installed dampers is reflected by the additional EDR, the abovementioned ratio can be used to estimate the additional EDR of the damped structure. Energy dissipation varies with time, which indicates that the ratio is related to the duration of ground motion. Hence, the energy dissipation during the most intensive period in the entire seismic motion duration is used to calculate the additional EDR. Accordingly, the procedure of the proposed method is presented. The feasibility of this method is verified by using a single-degree-of-freedom system. Then, a benchmark structure with dampers is adopted to illustrate the usefulness of this method in practical engineering applications. In conclusion, the proposed method is not only explicit in the theoretical concept and convenient in application but also reflects the time-varying characteristic of additional EDR, which possesses the value in practical engineering.

scholarly journals Time-Varying Wind Load Identification Based on Minimum-Variance Unbiased Estimation

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Huili Xue ◽  
Kun Lin ◽  
Yin Luo ◽  
Hongjun Liu
Keyword(s):  
Damping Ratio ◽  
Estimation Method ◽  
Minimum Variance ◽  
Wind Load ◽  
Ar Model ◽  
Unbiased Estimation ◽  
Recursive Identification ◽  
Time Varying ◽  
Building Structures ◽  
Shear Building

A minimum-variance unbiased estimation method is developed to identify the time-varying wind load from measured responses. The formula derivation of recursive identification equations is obtained in state space. The new approach can simultaneously estimate the entire wind load and the unknown structural responses only with limited measurement of structural acceleration response. The fluctuating wind speed process is investigated by the autoregressive (AR) model method in time series analysis. The accuracy and feasibility of the inverse approach are numerically investigated by identifying the wind load on a twenty-story shear building structure. The influences of the number and location of accelerometers are examined and discussed. In order to study the stability of the proposed method, the effects of the errors in crucial factors such as natural frequency and damping ratio are discussed through detailed parametric analysis. It can be found from the identification results that the proposed method can identify the wind load from limited measurement of acceleration responses with good accuracy and stability, indicating that it is an effective approach for estimating wind load on building structures.

scholarly journals A Normalized Hysteretic Energy Spectrum for Energy-Based Seismic Design

2020 ◽  
Vol 198 ◽  
pp. 04004
Author(s):  
Cuiling Ma ◽  
Changbing Chen ◽  
Xiaotang Lv ◽  
Jian Bian ◽  
Yuan Feng ◽  
...  
Keyword(s):  
Seismic Design ◽  
Soil Type ◽  
Damping Ratio ◽  
Site Classification ◽  
Single Degree Of Freedom ◽  
Hysteretic Energy ◽  
Type Site ◽  
Set Up ◽  
Ground Motion Records ◽  
Ductility Ratio

To disclose the impacts of hysteretic energy (HE) demand on energy-based seismic design, this paper introduces the dimensionless parameter βEH to express the cumulative HE indirectly and establishes the βEH spectrum for energy-based seismic design. After analyzing numerous seismic responses of a single degree-of-freedom (SDOF) system, the author set up a simplified βEH spectral formula based on the genetic algorithm. Then, 750 ground motion records were selected according to Chinese site classification, and used to examine the effects of soil type and damping ratio on the βEH spectra. The results show that the soil type, site group and damping ratio have significant effects on the βEH spectra; the ductility ratio has an impact on the spectral value but not the spectral shape.

Prediction of Optimal Number of Cycles in Docetaxel Regimen for Patients with mCRPC

2018 ◽  
pp. 345-355
Author(s):  
Hideyasu Matsuyama ◽  
Tomoyuki Shimabukuro ◽  
Isao Hara ◽  
Kazuhiro Suzuki ◽  
Hirotsugu Uemura ◽  
...  
Keyword(s):  
Optimal Number ◽  
Number Of Cycles

A prospective randomized phase II trial evaluating maintenance GM-CSF in an intermittent chemotherapy (chemo) regimen for metastatic castration-resistant prostate cancer (mCRPC): A DoD prostate cancer clinical trials consortium trial.

2012 ◽  
Vol 30 (5_suppl) ◽  
pp. 35-35
Author(s):  
Eric Jay Small ◽  
Vivian K. Weinberg ◽  
Charles J. Ryan ◽  
Celestia S. Higano ◽  
Amy Mimi Lin ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Optimal Number ◽  
Castration Resistant Prostate Cancer ◽  
Time To Progression ◽  
Gm Csf ◽  
Castration Resistant ◽  
Randomized Phase Ii ◽  
Intermittent Chemotherapy ◽  
Number Of Cycles ◽  
The Impact

35 Background: The optimal number of cycles of docetaxel for patients (pts) with mCRPC is not known, and in practice, treatment breaks are common. The current study was designed to test the safety and efficacy of utilizing 6 cycles of standard docetaxel with chemo free intervals in patients who achieve and maintain a response to docetaxel. Methods: Pts with mCRPC, no prior chemo, and KPS > 60% were eligible. Pts were treated with “induction” docetaxel 75 mg/m2 q 3 weeks, and prednisone 5 mg po bid. PSAWG1 criteria were used to define response and progression. After 6 cycles, responding pts stopped chemo and were randomized to observation (Obs) or to GM-CSF, 250 mcg/m2 daily for 14 days out of every 28-day cycle. Pts were followed with monthly PSA and imaging every 2 cycles until progression, at which point docetaxel was reinitiated for another 6 cycles, followed by the same “off chemo” regimen. The primary endpoint was the time to progression while on chemo (time to chemo resistance). Results: 114 pts have been enrolled: 3 are undergoing induction, and 111 are therefore evaluable. Of these pts, 82 completed induction, (10 did not due to PD, 9 due to adverse events (AE), 10 due to pt or MD choice). Of 111 evaluable pts, 48 (43%) had a response to chemo and were eligible for randomization. 22 were randomized to Obs and 26 to GM-CSF. Of 48 randomized pts, 25 restarted chemo, all for PSA PD. (23 pts did not re-start chemo because of AE, other therapy being started, or pt choice; 1 pt is still on GM-CSF.) 6/25 (24%) pts experienced a response to the 2nd series of chemo, and 1/6 (17%) to the 3rd. The time to chemo re-initiation (n=25) was 3.1 mos in Obs pts and 4.2 mos in GM-CSF pts. Conclusions: 43% of patients met criteria for undergoing intermittent chemo. The response proportion to the 1st, 2nd, and 3rd series of docetaxel was 43%, 24% and 17%, respectively. GM-CSF may modestly delay the time to chemo re-initiation, but the sample size is small and insufficient to assess the impact of GM-CSF on time to chemo resistance.

scholarly journals Effects of Damping Uncertainties on Damping Reduction Factors

2016 ◽  
Vol 61 (2) ◽  
pp. 341 ◽  
Author(s):  
Baizid Benahmed ◽  
Malek Hammoutene ◽  
Donatello Cardone
Keyword(s):  
Monte Carlo ◽  
Energy Dissipation ◽  
Dynamic Response ◽  
Design Process ◽  
Coefficient Of Variation ◽  
Damping Ratio ◽  
Response Spectra ◽  
Energy Dissipation Capacity ◽  
Damping Estimation ◽  
Reduction Factors

It is apparent that the dynamic response of a building dependson its energy dissipation capacity, hence damping ratio. Thedamping value experienced by a building during an earthquakediffers significantly from the value specified in the design step.This introduces uncertainties in the design process of the building.It would be desirable to consider not only the effects ofuncertainties in loading but also the uncertainties in the structuralparameters. In this paper, the effects of uncertainties in the estimation ofdamping ratio ξ, on the use of Damping Reduction Factors (DRF) for the evaluation of high damping response spectra,are examined. Damping uncertainties are described by a lognormalprobability distribution, and the Monte Carlo techniqueis used to generate the random values of damping. Theaverage of the distribution is the deterministic value of damping (taken equal to 5%, 7.5%, 10%, 20%, 30% and 40%) whilethree different values of coefficient of variation are considered (i.e. 10%, 20% and 40%, respectively). All the DRF formulations found in the literature are not able totake into consideration damping uncertainties, leading to significantdiscrepancies in the high damping response spectra. Based on the results of this study, a new DRF formulation, ableto account for uncertainties in damping estimation, is tentatively proposed.

An Experimental and Analytical Investigation Into Friction-Induced Vibrations and Parameters Affecting Its Occurrence

2010 ◽  
Author(s):  
A. Bahzad ◽  
M. O. A. Mokhtar ◽  
A. M. A. El-Butch ◽  
A. F. Fahim
Keyword(s):  
Damping Ratio ◽  
Excitation Frequency ◽  
Analytical Investigation ◽  
Load Factor ◽  
Stick Slip ◽  
Single Degree Of Freedom ◽  
Ratio Speed ◽  
Friction Models ◽  
Stick Slip Motion ◽  
Slip Motion

The condition for the occurrence of friction-induced vibrations is examined numerically and experimentally based on a single degree of freedom system with different friction models that relates the friction force with the relative interface speed. In this study the dimensionless parameters which control the occurrence of stick-slip motion are investigated, it is found that some of these parameters results in the occurrence of stick-slip motion while others are acting to avoid it. The equations governing the occurrence of friction-induced vibrations are derived in dimensionless form and solved numerically in order to have both high accuracy and reducing the number of the system parameters. The attained numerical results are validated by the comparison with the experimental results. Results also showed that damping ratio, speed, load factor, the used friction models and excitation frequency greatly affecting the occurrence of stick-slip motion.

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