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Field Testing of Pedestrian Bridges
Published in Eva O.L. Lantsoght, Load Testing of Bridges, 2019
Darius Bačinskas, Ronaldas Jakubovskis, Arturas Kilikevičius
The damping ratio of the structure may be also estimated using a method of logarithmic decrement, which is perhaps the most popular time-response method used to measure damping. The logarithmic decrement represents the rate at which the amplitude of a free damped vibration decreases. It is defined as the natural logarithm of the ratio of any two successive amplitudes, as schematically shown in Figure 12.23. The damping ratio is expressed as: ς=12πplnunun+p where un is the amplitude of vibration at time tn, un+p is the amplitude of vibration at time tn+p, and p is the time period between the measured peaks.
Vibration damping by internal friction
Published in Zbigniew Osiński, Damping of Vibrations, 2018
Two fiber glass/epoxy composite elements with lamination angles α = 0° and α = 7.12° were analyzed. Damping properties were determined by observing the vibration amplitude of the body connected to the floor by a linear spring. The logarithmic decrement was used as the measure of damping. Simulations were performed for different excitation frequencies. Mechanical properties of the floor were assumed to be independent of the frequency. The floor consisted of three layers. The upper one was made of duraluminum (PA6) with a thickness of 0.00178 m. The middle layer incorporated a dissipative material with a thickness of 0.05 m. The lower layer was made of steel with a thickness of 0.05 m. The length and width of the floor were 1 m. The floor was clamped at both sides (Fig. 4.39). The following material and geometric data were taken: where E is Young’s and G Kirchhoff’s modulus, ν is Poisson’s ratio, ρ the mass density and Q−1 the loss factor. The body mass was 50 kg and the spring constant k = 107 N/m2. The obtained results revealed that the “floating floor” exhibits better damping properties than a glass fiber/epoxy composite plate. The average logarithmic decrements were 0.00178 and 0.0032 for the floor and the plate components, respectively.
Non-linear damping identification in tuned liquid column dampers
Published in Alphose Zingoni, Insights and Innovations in Structural Engineering, Mechanics and Computation, 2016
K. Dziedziech, W.J. Staszewski, T. Uhl, A. Ghosh, B. Basu
where x(t) is the amplitude at time t and x (t + T) is the amplitude of the peak 1 period away. The damping ratio is then found from the logarithmic decrement () ζ(t)=11+(2πδ(t))2
Hydrodynamic response of three- and four-column semi-submersibles supporting a wind turbine in regular and random waves
Published in Ships and Offshore Structures, 2021
Free decay test of both floaters with the wind turbine in a parked condition was conducted in calm water condition. Figure 5 shows a typical heave and pitch-free decay time history for 4-C semi-submersible. Free decay tests were carried out for three initial heave displacements of 3, 5 and 7 cm (2.25, 3.75 and 5.25 m in prototype) and three initial heeling angles of 4°, 8° and 12° to assess the effect of initial displacement/rotation on the damping. Logarithmic decrement method was used to estimate the damping ratios from measurements. If x1 and x2 are two successive peaks in the decay curve, the logarithmic decrement, δ = ln (x1/x2). This yield damping ratio () as,The natural frequency (ωn) and natural time period (Tn) can then be found:where ωd is the damped natural frequency.
Video camera–based vibration measurement for the detection of the apparent properties of monofilaments
Published in The Journal of The Textile Institute, 2021
Mina Emadi, Pedram Payvandy, Mohammad Ali Tavanaie, Mohammad Mahdi Jalili
As shown in the diagrams of video processing, the vibration behavior of monofilaments is a damped sinusoid, and the system exhibits a motion whose amplitude keeps diminishing. The decrease in the amplitude from one cycle to the next depends on the amount of the damping ratio. The ratio of any two successive amplitudes is constant and serves as a function of the damping only. The successive peak amplitudes bear a certain relationship involving the damping ratio, leading to the concept of logarithmic decrement. The average damping coefficients for five specimens of each sample obtained from Equation (14) are given in Table 4, and the trend diagram of their changes is presented in Figure 9. As it was observed, the existence of one node does not cause a significant change in the damping coefficient values; however, with an increase in the number of knots in samples with two or more knots, these values are increased to some extent. Also, knot displacement does not change the values of the damping coefficients, but a sample in which the knot distribution is symmetric (e.g. the 2 knots at 2 sides sample) has a low value compared to a sample where the nodes are accumulated on one side of the string (as in the sample with 4 knots at 1 side). Moreover, an increasing in the number of strings greatly increases the damping coefficient. This coefficient decreases due to the presence of twists although it is found to rise as the number of twists is increased. The accuracy of the obtained results has been verified through comparing them with the diagrams obtained from video processing (Figures 5 and 6). It seems that, by obtaining the content of a signal through the Fourier series transform and the logarithmic decrement method, one can compare the physical properties of monofilaments such as the existence of nodes and twists and the number of strings.
Diagnosis of femoral implant loosening after total hip replacement by analysis of natural frequency
Published in Mechanics of Advanced Materials and Structures, 2022
Sara Hosseini, Rafael Claramunt, Marta Ibáñez, Antonio Ros
The logarithmic decrement is defined as the natural logarithm of the ratio of the amplitudes of any two successive peaks. where is the peak amplitude at time t and shows the peak amplitude of the n periods away. For two adjacent peaks (n = 1), we have: