The energetics of cis-trans proline isomerization in small peptide models have been investigated using the hybrid density functional theory method B3LYP with a 6-31+G* basis set. The molecules studied are models for the phospho-Ser/Thr-Pro substrate for Pin-1, a peptidyl-prolyl isomerase (PPIase) involved in cell division. Pin-1 requires phosphorylation of a Ser or Thr residue adjacent to a Pro residue in the substrate and catalyzes cis-trans isomerization about the proline amide bond. The dihedral angle that would correspond to the reaction coordinate for isomerization of the omega peptide bond was investigated for several small models. Relaxed potential energy scans for this dihedral angle in N-methylacetamide, 1, N,N-dimethylacetamide, 2, acetylpyrrolidine, 3 and acetylproline, 4, were carried out in 20 degrees steps using the B3LYP/6-31+G* level of theory. In addition, similar scans were carried out for 1-4 protonated on the acetylamide carbonyl oxygen. Optimized structures for 1-4 protonated on the amide nitrogen were also obtained at B3LYP/6-31+G*. Relative proton affinities were determined for each site at various angles along the reaction coordinate for isomerization. The relative proton affinities were anchored to experimental gas phase proton affinities, which were taken from the literature for 1 and 2, or determined in an electrospray ionization-quadrupole ion trap instrument using the extended kinetic method for 3 and 4. Proton affinities of 925 +/- 10 and 911 +/- 12 kJ/mol were determined for 3 and 4, respectively. These studies suggest that the nitrogen atom in these amides becomes the most basic site in the molecule at a dihedral angle of ca. 130 degrees . In addition, the nitrogen atoms in 2-4 are predicted to attain basicities in the range 920-950 kJ/mol, making them basic enough to be the preferred site for hydrogen bonding in the Pin-1 active site, in support of the proposed mechanism for PPIases.

The impact of geometry variations on integrally bladed disk eigenvalues is investigated. A large population of industrial Bladed Disks (Blisks) are scanned via a structured light optical scanner to provide as-measured geometries in the form of point-cloud data. The point cloud data is transformed using Principal Component Analysis that results in a Pareto of Principal Components (PCs). The PCs are used as inputs to predict the variation in a Blisk’s eigenvalues due to geometry variations from nominal when all blades have the same deviations. A large subset of the PCs are retained to represent the geometry variation, which proves challenging in probabilistic analyses because of the curse of dimensionality. To overcome this, the dimensionality of the problem is reduced by computing an active subspace that describes critical directions in the PC input space. Active variables in this subspace are then fit with a surrogate model of a Blisk’s eigenvalues. This surrogate can be sampled efficiently with the large subset of PCs retained in the active subspace formulation to yield a predicted distribution in eigenvalues. The ability of building an active subspace mapping PC coefficients to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.

The vibration bending fatigue life uncertainty of additively manufactured titanium (Ti) 6Al-4V specimens is studied. In this investigation, an analysis of microscopic discrepancies between ten fatigued specimens paired by stress amplitude is correlated with the bending fatigue life scatter. Through scanning electron microscope (SEM) analysis of fracture surfaces and grain structures, anomalies and distinctions such as voids and grain geometries are identified in each specimen. These data along with previously published results are used to support assessments regarding bending fatigue uncertainty. The understanding gained from this study is important for the future development of a predictive vibration bending fatigue life model.

The impact of geometry variations on integrally bladed disk eigenvalues is investigated. A large population of industrial bladed disks (blisks) are scanned via a structured light optical scanner to provide as-measured geometries in the form of point-cloud data. The point cloud data are transformed using principal component (PC) analysis that results in a Pareto of PCs. The PCs are used as inputs to predict the variation in a blisk's eigenvalues due to geometry variations from nominal when all blades have the same deviations. A large subset of the PCs is retained to represent the geometry variation, which proves challenging in probabilistic analyses because of the curse of dimensionality. To overcome this, the dimensionality of the problem is reduced by computing an active subspace that describes critical directions in the PC input space. Active variables in this subspace are then fit with a surrogate model of a blisk's eigenvalues. This surrogate can be sampled efficiently with the large subset of PCs retained in the active subspace formulation to yield a predicted distribution in eigenvalues. The ability of building an active subspace mapping PC coefficient to eigenvalues is demonstrated. Results indicate that exploitation of the active subspace is capable of capturing eigenvalue variation.

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