NH Stretching Frequencies of Intramolecularly Hydrogen-Bonded Systems: An Experimental and Theoretical Study

The vibrational NH stretching transitions in secondary amines with intramolecular NH···O hydrogen bonds were investigated by experimental and theoretical methods, considering a large number of compounds and covering a wide range of stretching wavenumbers. The assignment of the NH stretching transitions in the experimental IR spectra was, in several instances, supported by measurement of the corresponding ND wavenumbers and by correlation with the observed NH proton chemical shifts. The observed wavenumbers were correlated with theoretical wavenumbers predicted with B3LYP density functional theory, using the basis sets 6-311++G(d,p) and 6-31G(d) and considering the harmonic as well as the anharmonic VPT2 approximation. Excellent correlations were established between observed wavenumbers and calculated harmonic values. However, the correlations were non-linear, in contrast to the results of previous investigations of the corresponding OH···O systems. The anharmonic VPT2 wavenumbers were found to be linearly related to the corresponding harmonic values. The results provide correlation equations for the prediction of NH stretching bands on the basis of standard B3LYP/6-311++G(d,p) and B3LYP/6-31G(d) harmonic analyses, with standard deviations close to 38 cm−1. This is significant because the full anharmonic VPT2 analysis tends to be impractical for large molecules, requiring orders of magnitude more computing time than the harmonic analysis.

The Logic of Six-Based Minor for Harmonic Analyses of Popular Music

Harmonic analyses of popular music typically take the minor tonic to be Roman numeral “one.” By nature, this “one-based” approach requires a new numbering scheme when songs shift between relative key centers. Recent scholarship has argued, however, that popular music often involves ambiguity between relative tonalities, as exemplified in the “Axis” progression, if not sometimes a tonal fusion of two relative keys. I thus argue for the utility of a “six-based” approach to the minor tonic, where the minor tonic is taken to be scale-degree 6. This six-based approach, common among practitioners of popular music as seen in the Nashville number system, avoids the forced choice of a single tonic, and it thus offers a consistent way to track chord function and behavior across shifts between relative key centers. After considering these shifts in a diatonic context on the levels of both phrase and song form, I posit that popular music involves three possible tonalities, together which form a “triple-tonic complex” akin to Stephenson’s three harmonic palettes: a major system, a parallel-minor system, and a relative-minor system. I conclude by considering how chromatic chords common in a major key, such as II and ".fn_flat('')."VII, correspond to their counterparts in the relative minor, IV and ".fn_flat('')."II, thereby collapsing the landscape of diatonic modes into three modal complexes. Overall, the paper serves to reveal the logic of six-based minor—why it is useful, what issues it resolves, and what insights it can afford us about harmonic syntax in popular music.

Evaluation of Vibration Amplitude Stepping and Welding Performance of 20 kHz and 40 kHz Ultrasonic Power of Metal Welding

Today ultrasonic power technique is consider a mandatory technique which is always entered in many processes such as in metal and plastic welding to overcomes many issues, with aided of applying force (pressure) and supplied high frequency vibration, a solid-state weld can be generated by ultrasonic metal welding technique. That give a technique the ability to join not only a small components, whereas also to join thicker specimens, depend on a proper control of matching welding conditions. Therefore a welding performance can be study and compared after designed welding horn to resonance at frequencies of 20 kHz and 40 kHz. The analyses of the designed horn are completed through use a vibration mathematical expressions, modal and harmonic analyses to ensure the weldability due to applying ultrasonic power to the working area and also to compare the performance of joint at using two resonance frequencies of 20 kHz and 40 kHz. The dimensions of the horns were determined to match the selected resonance frequencies, which the lengths were calculated as 132 mm and 66 mm respectively. The analysis of the exciting modal indicates that the axial vibration modes of 19,584Hz and 39,794Hz are obtained in 10th mode, while the two frequency values are recorded 19,600 Hz and 39,800 Hz from the frequency response of the two horns. The weld strength between Al and Cu specimens with a thickness 0.5 mm were evaluated using tensile test, which the analyses were obtained under using different welding pressure and varied amplitudes. The results were recorded within exciting a horn with two different resonance frequencies, show the enhancement of weld strength and quality through control of stepping amplitude, the enhancement means obtain good strength of the weld, reduce sticking horn to specimen, and lower specimen marking.

Evaluation of Vibration Amplitude Stepping and Welding Performance of 20 kHz and 40 kHz Ultrasonic Power of Metal Welding

Today ultrasonic power technique is consider a mandatory technique which is always entered in many processes such as in metal and plastic welding to overcomes many issues, with aided of applying force (pressure) and supplied high frequency vibration, a solid-state weld can be generated by ultrasonic metal welding technique. That give a technique the ability to join not only a small components, whereas also to join thicker specimens, depend on a proper control of matching welding conditions. Therefore a welding performance can be study and compared after designed welding horn to resonance at frequencies of 20 kHz and 40 kHz. The analyses of the designed horn are completed through use a vibration mathematical expressions, modal and harmonic analyses to ensure the weldability due to applying ultrasonic power to the working area and also to compare the performance of joint at using two resonance frequencies of 20 kHz and 40 kHz. The dimensions of the horns were determined to match the selected resonance frequencies, which the lengths were calculated as 132 mm and 66 mm respectively. The analysis of the exciting modal indicates that the axial vibration modes of 19,584Hz and 39,794Hz are obtained in 10th mode, while the two frequency values are recorded 19,600 Hz and 39,800 Hz from the frequency response of the two horns. The weld strength between Al and Cu specimens with a thickness 0.5 mm were evaluated using tensile test, which the analyses were obtained under using different welding pressure and varied amplitudes. The results were recorded within exciting a horn with two different resonance frequencies, show the enhancement of weld strength and quality through control of stepping amplitude, the enhancement means obtain good strength of the weld, reduce sticking horn to specimen, and lower specimen marking

Design and Tests of a New Damper for a Gas Turbine Thin-Shell Duct

Gas turbine (GT) liners, transition ducts and exhaust diffusers are large thin-shell ducts bounded by two barrels, typically characterized by multiple natural frequencies inside the operating speed range of the engine rotor. In most applications, GT ducts are supported on one side only and they are free to expand inside the gas turbine so to avoid thermal distresses. The GT ducts are typically damped structures able to prevent high cycles fatigue failures. Damping is provided by sliding features as insulation or bolted joints. This paper describes the redesign of a transition duct (TD) after it was discovered that in some operating conditions, duct could crack for high cycle fatigue (HCF). The TD connects the flow path of the gas generator turbine with the flow path of the power turbine. The new TD has been made more robust, but it has also been equipped of dampers capable to operate at high temperature. Starting from the analyses of field data, a predictive FEA model has been developed and validated. After a deep investigation of the TD modes that could be excited by flow path and/or by rotor vibrations, it was decided to add two dampers, one for each barrel of the TD. Due to internal space limitations, a new type of damper has been designed for the external barrel. Both dampers have been sized using FEA. Harmonic analyses rather than forced response transient analyses have been performed so to verify the effectiveness of the new design. In the simulations, dampers have been replaced by harmonic forces able to reproduce the friction force of the dampers. Validation of the method and damper calibration has been done by performing lab tests and full-size TD tests.

Design and Optimization of Slotted Block Horn Utilized in Ultrasonic Insertion Process Through Rsm-fea-ga Integration Technique

This paper investigates design and optimization of slotted block horn used in ultrasonic insertion process by integrating response surface methodology (RSM), finite element analysis (FEA) and genetic algorithm (GA). Performance and reliability of block horn depend on the uniformity of displacement amplitude developed at the output face of horn. Amplitude uniformity of horn can be improved by optimizing the design of block horn. Modal and harmonic analyses are carried out as per design matrix obtained from RSM, and then non-linear model for displacement amplitude is developed. Design optimization of block horn is performed by coupling the non-linear model with GA as fitness function. Thermal analysis is carried out to validate optimized dimensions of block horn theoretically by predicting the temperature at joint. Slotted block horn is fabricated with optimum geometry using Aluminium alloy (AA6351) and the design is validated experimentally by measuring the temperature at joint using thermocouple and Data Acquisition System (DAQ). Results of this study show that the temperature predicted from thermal analysis correlates well with temperature measured from experiments and the design of slotted block horn is validated.