Critical resonance

Problem What is the critical weighting i/>dip of the alternative dipolar amide resonance structure in (5.102) that would reverse the preference for pseudo-c/s over pseudo-trans geometry at Cal What are the corresponding bond lengths Rco and Rcn at this critical resonance weighting ... 

If aluminium be substituted for steel, and the area of cross section be doubled, there is still a reduction in weight and a vibration frequency four times greater which displaces the critical resonance range a certain number of octaves, thus making harmful coincidences more improbable. 

The surface work fiincdon is fonnally defined as the minimum energy needed m order to remove an electron from a solid. It is often described as being the difference in energy between the Fenni level and the vacuum level of a solid. The work ftmction is a sensitive measure of the surface electronic structure, and can be measured in a number of ways, as described in section B 1.26.4. Many processes, such as catalytic surface reactions or resonant charge transfer between ions and surfaces, are critically dependent on the work ftmction. 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

Randall used C-NMR to study the methylene spectrum of polystyrene. In 1,2,4-trichlorobenzene at 120°C, nine resonances were observed. These were assumed to arise from a combination of tetrads and hexads. Using m and r notation, extend Table 7.8 to include all 20 possible hexads. Criticize or defend the following proposition Assuming that none of the resonances are obscured by overlap, there is only one way that nine methylene resonances can be produced, namely, by one of the tetrads to be split into hexads while the remaining tetrads remain unsplit. 

Eigenvalue problems. These are extensions of equilibrium problems in which critical values of certain parameters are to be determined in addition to the corresponding steady-state configurations. The determination of eigenvalues may also arise in propagation problems. Typical chemical engineering problems include those in heat transfer and resonance in which certain boundaiy conditions are prescribed. 

As noted from general experience, except for specific large inductive loads such as of furnace or rectifiers, the fundamental content of the load current is high compared to the individual harmonic contents. In all such cases, it is not necessary to provide a filter-circuit for each harmonic unless the current is required to be as close to a sinusoidal waveform as possible, to cater to certain critical loads or instruments and devices or protective schemes operating in the system, where a small amount of harmonics may lead to malfunctioning of such loads and devices. Otherwise only the p.f. needs be improved to the desired level. Also to eliminate a parallel resonance with the... 

Rigorous design reviews must include the often highly complex resonance behavior of impellers and blading to ensure vibration-free or vibration-tolerant design of these critical turboexpander components. In other words, the manufacturer must perform comprehensive theoretical and experimental studies of the blade oscillations in the rotating system. 

Expander-compressor shafts are preferably designed to operate below the first lateral critical speed and torsional resonance. A flame-plated band of aluminum alloy or similarly suitable material is generally applied to the shaft in the area sensed by the vibration probes to preclude erroneous electrical runout readings. This technique has been used on hundreds of expanders, steam turbines, and other turbomachines with complete success. Unless integral with the shaft, expander wheels (disks) are often attached to the shaft on a special tapered profile, with dowel-type keys and keyways. The latter design attempts to avoid the stress concentrations occasionally associated with splines and conventional keyways. It also reduces the cost of manufacture. When used, wheels are sometimes secured to the tapered ends of the shaft by a common center stretch rod which is pre-stressed during assembly. This results in a constant preload on each wheel to ensure proper contact between wheels and shaft at the anticipated extremes of temperature and speed. 

Appears on gears like rotor critical speed. Vibration Torsional resonance Usually occurs only during startup... 

Vibration peaks at specific speed. Harmonic resonance Same as critical or resonance... 

Journal bearing eccentricity Bearing damage Rotor-bearing system critical Coupling critical Structural resonances Thrust bearing damage... 

Flexible rotor balancing must be performed with the rotor whirl configuration approximating the mode in question. The operating speed(s) is in the vicinity of a major flexible mode resonance (damped critical speed). As these two speeds approach one another, a tighter... 

Once the component values have been calculated, the physical construction of the transformer and the PCB layout become critical for the effectiveness of the filter stage. Magnetic coupling due to stray inductive pick-up of high-frequency noise by the traces and components can circumvent the filter all together. Added to this is the fact that the common-mode filter choke looks more and more capacitive above its self-resonance frequency. The net result is the designer needs to be concerned about the high-frequency behavior of the filter typically above 20 to 40 MHz. 

The torsional resonant response of a system is an interaction of all the components in the train. Calculation of torsional natural frequencies is based on the entire system and these frequencies are valid only for that given arrangement. If any component of the train is replaced by an item with torsional characteristics different from the original, the system tor sional response must be recalculated and new torsional natural frequencies determined. Occasionally, an original equipment manufacturer is requested to calculate the torsional and lateral critical speeds of the supplied item. Unfortunately, the purchaser is unaware that this request is of limited value since the torsional response of a single item in a train is meaningless. Likewise, a torsional shop test will yield meaningless results if the train is not assembled and tested with every item destined for the field. 

Should analysis indicate that a coupling is in a sensitive position, then a small amount of custom design in a relatively standard coupling can accommodate the de-tuning of the critical in question. One note of caution while changes in stiffness or inertia may de-tune a given resonance, their effect on the other criticals must also be determined, since any change in the system will result in a new set of resonant frequencies. 

Another aspect of deflection is the foundation s natural frequency. The foundation must be tuned in such a way that any resonances are not in coincidence with any of the compressor train natural frequencies. Rela tive to equipment considerations, it would be desirable to have all foundation natural frequencies well above any equipment critical speeds... 

The general chemical reasonableness of the results in Table 7-7 is gratifying, but this does not constitute a demonstration that the separation of substituent effects into inductive effects and resonance effects is quantitatively possible, for these effects may interact so as to be nonadditive. Ritchie and Sager express reservations about the approach in general, and other authors " have criticized results based on Eqs. (7-33) and (7-34). 

---