Root mean square acceleration

Other roughness indices have also been introduced, such as moving average, power spectral density, half roughness index. Mays response meter, root-mean-square acceleration, root-mean-square vertical acceleration, Texas MO and Brazil Ql, to name a few (Sayers and Karamihas 1996). 

The root mean square acceleration is a parameter used in the past to measure the radiated energy. It is defined as the square root of the mean of the squared acceleration computed for a specific time interval of the record (i.e., AT = T2-T1) ... 

All vibration amplitude curves, which can represent displacement, velocity, or acceleration, have common elements that can be used to describe the function. These common elements are peak-to-peak, zero-to-peak, and root-mean-square, each of which are illustrated in Figure 43.11. 

Root-mean-square (RMS) is the statistical average value of the amplitude generated by a machine, one of its components, or a group of components. Referring to Figure 43.11, RMS is equal to 0.707 of the zero-to-peak value, A. Normally, RMS data are used in conjunction with relative vibration data acquired using an accelerometer or expressed in terms of acceleration. 

A tube with obstacles can model some industrial explosions. A simple analysis indicates that there are two contributing factors involved in flame acceleration along a tube with obstacles. They are the character of the motion of the gas in front of the flame and the turbulence induced by the interaction of the motion of the gas in front of the flame with the boundary condition in the tube with obstacles. To study in detail the mechanism of flame acceleration by means of obstacles, explosion tests and measurements of the parameters of mean flow velocity and root mean squared (RMS) turbulent velocity were performed. The characteristics of methane-air and comstarch-air flame acceleration were investigated in a closed tube 0.19 m in diameter and 1,86 -m long filled with obstacles. The nonuniformity in the mean flow velocity and the RMS turbulent velocity across the tube with and without obstacles were measured in a substitutional tube in which the air free flow velocity ranged from 9 m/s to 177 m/s. Experimental results demonstrated that in the environment with obstacles flame acceleration caused by the nonuniformity of flow velocity is more efficient than that caused by the RMS turbulent velocity. 

The impedance test for anodized aluminum (ASTM B 457) is used to study the seal performance of anodized aluminum. In this sense, the test is similar to the FACT test, except that this method uses a 1 V root mean square 1 kHz signal source from an impedance bridge to determine the sealed anodized aluminum impedance. The test area is again defined with a portable cell, and a platinum or stainless steel auxiliary electrode is typically used. The sample is immersed in 3.5% NaCl. The impedance is determined in ohms X 10. In contrast to the methods discussed previously, this test is essentially nondestructive and does not accelerate the corrosion process. 

Note that here / is a frequency not a function. The typical units of a PSD are acceleration [g /Hz] or [(m/s ) /Hz] versus frequency [Hz], It can also be given in strain /Hz or Mpa /Hz, depending on the gauge used for the time history measurement. As previously noted, Eq. (8.74), the amplimde (area) of each frequency is actually RMS /Hz, where RMS is the root-mean-square. The RMS value of a normalized signal is equal to the standard deviation, assuming a zero mean. A pure sinusoidal function has the following relationship... 

Resolution It is the minimum acceleration amplitude that it may measure. In early accelerometer digital recorders, it was limited by the digitizer (A/D converter) resolution. In modem instmments, the digitizer is usually 24 bit, and the resolution is related to the self-noise level of both the accelerometer and the digitizer. So it is usually given as self-noise level, or it may be obtained from the dynamic range. Good-quality accelerometers have noise levels under 1 pm/s rms (root mean square). 

As m increases, At becomes progressively smaller (compare the difference between the square roots of 1 and 2 (= 0.4) with the difference between 100 and 101 (= 0.05). Thus, the difference in arrival times of ions arriving at the detector become increasingly smaller and more difficult to differentiate as mass increases. This inherent problem is a severe restriction even without the second difficulty, which is that not all ions of any one given m/z value reach the same velocity after acceleration nor are they all formed at exactly the same point in the ion source. Therefore, even for any one m/z value, ions at each m/z reach the detector over an interval of time instead of all at one time. Clearly, where separation of flight times is very short, as with TOF instruments, the spread for individual ion m/z values means there will be overlap in arrival times between ions of closely similar m/z values. This effect (Figure 26.2) decreases available (theoretical) resolution, but it can be ameliorated by modifying the instrument to include a reflectron. 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

In this instrument ions produced in the source are accelerated to a given velocity. The unresolved beam is then injected into a field-free region and the ions drift towards the collector. The velocities will be inversely proportional to the square roots of the masses. This means that a pulse of ions will split up according to the ionic masses. The unresolved beam thus becomes resolved in time. Provided that the response time of the electronics is sufficiently fast a spectrum can be recorded. Obviously an average over many such pulses is necessary to provide a reliable signal. Once again the electronics lie at heart of this problem, which demands very fast amplifiers. Initially the time-of-flight mass spectrometer (TOF) was the province of physicists and later of chemists but, with the tremendous advance in electronics, instruments are now produced that are capable of routine operation by relatively untrained operators. 

---