Time histories

Figure 5 provides an example of AE monitoring data from 22.01.1997 to 03,03.1997, in terms of time history of the main plant parameters (fig.Sa), as well as of the AE RMS values (fig. 5b). Normally, very little or no events were recorded, with the exception of the above period, in which an AE activity, very much concentrated in time and space, could be observed a sharp step in cumulative AE events takes place in a short, well defined time interval. A smaller sharp step in EA events had been observed a few days earlier, in the same position. 

Kerogen Decomposition. The thermal decomposition of oil shale, ie, pyrolysis or retorting, yields Hquid, gaseous, and soHd products. The amounts of oil, gas, and coke which ultimately are formed depend on the heating rate of the oil shale and the temperature—time history of the Hberated oil. There is Htde effect of shale richness on these relative product yields under fixed pyrolysis conditions, as is shown in Table 5 (10). 

Figure 14.12(b) represents an actual time history (accelerogram) of the earthquake that occun ed in Chamoli, India, on 29 March 1999. It had apeak ground acceleration of nearly 0,15 g and a predominant frequency of about 2 Hz. 

Figure 14.12(b) Time history ot earthquake at Chamoli, India, which occurred in March 1999... 

Any of the three RS is adequate to derive a time history of an earthquake to simulate test conditions in a laboratory. This, however, being a complex subject, assistance must be obtained from experts in the field for constructing an RS for laboratory testing, preparing... 

ZPA = Peak ground or floor acceleration as recorded by the (Zero period time history. The rest is a response record, acceleration)... 

An RRS is normally constructed for several levels of critical dampings as illustrated in Figure 14.13. The most appropriate of these is then chosen for the purpose of testing. Any of the above response spectra can be developed into a time history of the earthquake, similar to that in Figure 14,12(b),... 

Ground acceleration This is the time history of ground acceleration as a result of an earthquake, where multiple frequency excitation predominates (Figure 14.12(b). A ground response spectrum (GRS) can be derived from this history. 

Floor acceleration This is the time history of acceleration of a partictilar floor nr structure caused by a given ground acceleration (Figure 14.16). It may have an amplified narrow band spectrum due to structural filtration, where single frequency excitation and resonance may predominate, depending upon the dynamic characteristics of the structure. A floor response spectrum (FR.S). as shown in Figure 14.18, can be derived from this history. Consideration of GRS or FRS will depend upon the location of the object under test. 

Now that it is possible to establish test facilities in a laboratory to simulate the time history of an earthquake seismic tests are conducted by creating the ground movements in the test object. Other methods, such as by analysis or by combined analysis and testing, are also available. Refer to IEEE 344 and lEC 60980 for more details. For this purpose a shake table, able to simulate the required seismic conditions (RRS) is developed on which the test object is mounted and its performance observed under the required shock conditions. Since it is not easy to create such conditions in a laboratory, there are only a few of these facilities available. The better equipped laboratories are in Japan, the USA, the UK, Greece, Germany, India and China. In India the Earthquake Engineering Department (EQD) of the University of Roorkee (UoR) is equipped with these facilities. 

This is the duration sufficient to simulate seismic conditions. It depends upon the algorithm used to find time history from the reqtiired response spectrum (RRS). The minimum duration of a strong movement, as recommended by IEEE 344, is 15 seconds as illustrated in Figure 14.24(b). This will require a total duration of the order of 20 seconds, including the movement s times of rise and time of decay. A duration of 20.48 seconds, as noted in the figure, is typical of a test conducted at University of Rorkee. The following tests may be conducted ... 

Figure 14.24(b) Typical time history (RRS) of shake table movements during a laboratory test... 

Normally the user provides the nature of a probable earthquake in the form of RRS, i.e. acceleration characteristic curves, period versus spectral acceleration, such as those in Figure 14.18. The first objective is to generate a signal which should be able to produce a time history, on a shake table, whose response spectra match those of the RRS. 

The Seismic Safety Margins Research Program developed a computer code called SMACS (Seismic Methodology Analysis Chain with Statistics) for calculating the seismic responses of structures, systems, and components. This code links the seismic input as ensembles of acceleration time histories with the calculations of the soil-structure interactions, the responses of major structures, and the responses of subsystems. Since uses a multi-support approach to perform the time-history response calculations for piping subsystems, the correlations between component responses can be handled explicitly. SMACS is an example of the codes that are available for calculating seismic response for PSA purposes. 

Results have been presented on one experiment. It involved a 5.659-m vessel containing 1000 kg of butane with a fill ratio of 39%. The vessel s contents were heated to 99°C, which is near but still below the supetheat-limit temperature, producing an internal pressure of 14.6 bar gauge. Vessel failure was then initiated. Measured pressure-time histories indicated that a number of separate pressure pulses occurred. They are plotted in Figure 6.6 as the overpressure-time relationship measured at 25 m from the vessel. 

Figure 6.11. Pressure-time history of a biast wave from a pressure vessei burst (Esparza and Baker 1977a).

The output from each case produces a wealth of information, including distribution of pressure, combustion products, rates of combustion, velocity components, etc. The results of each case will be summarized by presenting the pressure time histories at the eight locations that were presented in Figure 2 together with the flame speed along some selected directions. Some contour plots will also be presented. 

The eight pressure-time histories are shown in Figures 3 and 4, whereas the flame speed along the y-direction from the ignition point is shown in Figure 5. The largest pressure is found at location p8 in Figure 4, and it amounts to approx. 0.2... 

Figure 3. Pressure-time histories at four iocations (p1 -p4) in the process piant. Case 1.

The gauge records eimbient pressure Pq. At arrival time ta, the pressure rises quite abruptly (discontinuously, in an ideal wave) to a peak value Pj + Pq. The pressure then decays to ambient in total time tg + T+, drops to a partial vacuum of amplitude Pj, and eventually returns to Po in total time tg + T+ + T. The quantity P is usually termed the peak side-on overpressure, or merely the peak overpressure. The portion of the time history above initial ambient pressure is called the positive phase, of duration T+. That portion below Po, of amplitude Ps and duration T, is called the negative phase. 

Fig. 8.47 Strain-time history for ripple test (schematic)...

There is a fundamental relationship between d-dimensional PCA and d + 1)-dimensional Ising spin models. The simplest way to make the connection is to think of the successive temporal layers of the PCA as successive hyper-planes of the next higher-dimensional spatial lattice. Because the PCA rules (at least the set of PCA rules that we will be dealing with) are (1) Markovian (i.e. the probability of a state at time t + T depends only on a set of states at time t, and (2) local, one can always define a Hamiltonian on the higher-dimensioned spatial lattice such that the thermodynamic weight of a configuration 5j,( is equal to the probability of a corresponding space-time history Si t). ... 

Summing equation 7.59 over all possible space-time histories , 5t, we get that... 

If we now sum over all space-time histories and make the mean-field substitution of the densities p and p for S and S, respectively, we get the following simple mean-field iterative equation ... 

Notice that in this general case, correlation functions cannot be solved for directly instead, there is an entire hierarchy of lower-order correlations expressed as functions of higher-order correlations. For example if we take an average of equation 7.79 over all space-time histories, and assume that we have a steady-state so... 

It has been shown that the thermodynamic foundations of plasticity may be considered within the framework of the continuum mechanics of materials with memory. A nonlinear material with memory is defined by a system of constitutive equations in which some state functions such as the stress tension or the internal energy, the heat flux, etc., are determined as functionals of a function which represents the time history of the local configuration of a material particle. 

The conversion-time history is obtained by simxiltaneous solution of equations (ij) and (19) ... 

Equations (33) and (34) demonstrate that the motion quantities 5 (displacement) and v (velocity) are encoded in phase and frequency modulation of the detector output signal, purely referenced to the laser wavelength A. Tobeableto recover the time histories s(t) and v t) from the modulated detector signal, adequate phase and frequency demodulation techniques, or both, are utilized in the signal decoder blocks of a laser vibrometer. 

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