Equilibrium point damage prognosis models for structural health monitoring

Most structural dynamic systems are of high order; however, they often exhibit phenomena that can be dealt with effectively using low order models. This paper presents a method for describing certain kinds of damage evolution in mechanical systems. The method relies on a simple principle that as damage evolves in a structural dynamic system, the damage indicator (i.e., diagnostic feature) behaves like a stable quasi-stationary equilibrium point in a subsidiary non-linear bifurcating system within the so-called damage center manifold. It is shown that just as linear normal modes govern the behavior of linear structures with idealized damping, so too do non-linear normal forms govern the evolution of damage within structures in many instances. The method is justified with citations from the literature on certain types of mechanical failure and then applied in an experimental case involving reversible damage in a bolted fastener. Off-line experiments on a rotorcraft fuselage show that the evolution of damage is sensitive to both temporal and spatial bifurcation parameters. A diagnostic sensing strategy whereby output-only transmissibility features are used to decrease the order of high order structural dynamic measurements is also described.     

Learning to Make Sense of Division of Fractions: One K–8 Preservice Teacher's Perspective

Current reform documents in mathematics education recommend that teachers help students develop both conceptual and procedural understandings. However, teachers often do not possess the in-depth mathematical reasoning necessary to accomplish this goal. The purpose of this article is to provide one way in which preservice teachers can come to better understand the mathematics they will teach.     

N-α-Benzyloxyacetyl derivatives of (S)-4-benzyl-5,5-dimethyloxazolidin-2-one for the asymmetric synthesis of differentially protected α,β-dihydroxyaldehydes

α-Dibenzylamino- and α-benzyloxy- derivatives of N-acetyl-(S)-4-benzyl-5,5-dimethyloxazolidin-2-one readily undergo highly stereoselective boron mediated syn-aldol reactions with a range of aromatic and aliphatic aldehydes, generating the syn-aldol products in good to excellent yields as single diastereoisomers after purification. In the α-dibenzylamino series, deprotection of the functionalised aldol fragments to the corresponding α-amino-β-hydroxy methyl ester or α-amino-β-hydroxyaldehyde proved problematic, with a range of N- and O-protecting groups giving mixtures of products arising from endocyclic and exocyclic cleavage pathways. However, in the α-benzyloxy series, O-silyl protection of the aldol products, and subsequent DIBAL reduction gives stereoselectively the corresponding N-1′-hydroxyalkyloxazolidin-2-ones, which undergo base promoted fragmentation to the desired highly functionalised and differentially protected α,β-dihydroxyaldehydes in good yields and without loss of stereochemical integrity.     

PEG- and peptide-grafted aliphatic polyesters by click chemistry

Novel aliphatic polyesters with pendent acetylene groups were prepared by controlled ring-opening polymerization and subsequently used for grafting poly(ethylene glycol) and oligopeptide moieties by the Cu(I)-catalyzed addition of azides and alkynes, a type of "click" chemistry. These aliphatic polyesters possess an acetylene graft density that can be tailored by ring-opening copolymerization of alpha-propargyl-delta-valerolactone (1) with epsilon-caprolactone. Since the mild conditions associated with the click reaction are shown to be compatible with the polyester backbone, this method is a generally useful means for grafting numerous types of functionality onto aliphatic polyesters. The amphiphilic graft polyesters prepared in this study are shown to be biocompatible by in vitro cytotoxicity evaluation, suggesting their suitability for a range of biomaterial applications.     

Bond dissociation energies and radical stabilization energies associated with model peptide-backbone radicals

Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) have been calculated for a series of models that represent a glycine-containing peptide-backbone. High-level methods that have been used include W1, CBS-QB3, U-CBS-QB3, and G3X(MP2)-RAD. Simpler methods used include MP2, B3-LYP, BMK, and MPWB1K in association with the 6-311+G(3df,2p) basis set. We find that the high-level methods produce BDEs and RSEs that are in good agreement with one another. Of the simpler methods, RBMK and RMPWB1K achieve good accuracy for BDEs and RSEs for all the species that were examined. For monosubstituted carbon-centered radicals, we find that the stabilizing effect (as measured by RSEs) of carbonyl substituents (CX=O) ranges from 24.7 to 36.9 kJ mol(-1), with the largest stabilization occurring for the CH=O group. Amino groups (NHY) also stabilize a monosubstituted alpha-carbon radical, with the calculated RSEs ranging from 44.5 to 49.5 kJ mol(-1), the largest stabilization occurring for the NH2 group. In combination, NHY and CX=O substituents on a disubstituted carbon-centered radical produce a large stabilizing effect ranging from 82.0 to 125.8 kJ mol(-1). This translates to a captodative (synergistic) stabilization of 12.8 to 39.4 kJ mol(-1). For monosubstituted nitrogen-centered radicals, we find that the stabilizing effect of methyl and related (CH2Z) substituents ranges from 25.9 to 31.7 kJ mol(-1), the largest stabilization occurring for the CH3 group. Carbonyl substituents (CX=O) destabilize a nitrogen-centered radical relative to the corresponding closed-shell molecule, with the calculated RSEs ranging from -30.8 to -22.3 kJ mol(-1), the largest destabilization occurring for the CH=O group. In combination, CH2Z and CX=O substituents at a nitrogen radical center produce a destabilizing effect ranging from -19.0 to -0.2 kJ mol(-1). This translates to an additional destabilization associated with disubstitution of -18.6 to -7.8 kJ mol(-1).     

New synthetic pathways into dithiazolyl radicals: Preparation and characterisation of 3′-methyl-benzo-1,3,2-dithiazolyl, M’BDTA

A general three-step synthesis to a range of benzo-fused-1,3,2-dithiazolylium salts bearing both electron-withdrawing (CN) and electron-donating (Me) groups is described. This methodology has also been extended to pyridyl derivatives and offers a potential route to a diversity of 1,3,2-dithiazolylium rings and their corresponding 1,3,2-dithiazolyl free radicals. The key steps in the reaction are treatment of a substituted 1,2,-dichlorobenzene with two equivalents of [^tBuS]Na, followed by chlorination to yield the corresponding bis(sulfenyl chloride). Subsequent ring closure with Me₃SiN₃ yields the target 1,3,2-dithiazolylium ring system in good yield. The preparation and crystal structures of 3′-methyl-benzo-1,3,2-dithiazolylium chloride and 3′-methyl-benzo-1,3,2-dithiazolyl are described and the electronic properties of the radical examined through EPR spectroscopy, DFT calculations and variable temperature magnetic susceptibility measurements.     

Characterization of the solvation environment provided by dilute aqueous solutions of novel siloxane polysoaps using the fluorescence probe pyrene

Solubilization environment afforded by several of the novel allyl glycidyl ether-modified methylhydrosiloxane polymers are investigated using a common polycyclic aromatic hydrocarbon fluorescence probe, pyrene. The backbone of the polymer has been modified by the addition of an alkyl chain of varying length (either C8, C12, or C18) and to differing degrees of substitution. The nomenclature adopted for the purposes of these studies is as follows: "AGENT" represents the backbone polymer with no alkyl substitution, and "OAGENT", "DAGENT", and "SAGENT" are substituted with n-octyl, n-dodecyl, and n-octadecyl, respectively. The percentage of alkyl substitution is designated as 10, 15, and 20%. The pyrene polarity scale (defined as the ratio of the intensity of peak I to peak III) was used to determine the relative dipolarity of the cybotactic region provided by approximately 1 w/w% aqueous polymer solutions compared to 10 mM sodium dodecylsulfate (SDS) micellar solution. Results indicate that 10-15% DAGENT afforded the most hydrophobic solubilization site, followed by 15% OAGENT and 15% SAGENT. In addition, as the degree of alkyl substitution of DAGENT increased from 10 to 20%, the cybotactic region appeared to become more hydrophobic. Furthermore, a deeper investigation into the relative size of the solubilization site revealed that all alkyl-substituted polymers promoted excimer formation at relatively low pyrene concentrations, indicating the possibility of localized concentration enhancement within the solvation pockets and/or compartmentalization of the solute molecules. The pyrene fluorescence excitation data strongly indicates ground-state heterogeneity that is most prominent in AGENT and decreases as the alkyl chain length is increased. This provides a relative sense of the size and shape of the solvation pockets afforded by each polymer solution. An overall analysis of the collected data indicated that these alkyl-substituted polymers may provide a more selective and efficient pseudostationary phase in electrokinetic chromatography with better solvation capacity for hydrophobic compounds compared to SDS.     

Stereoselective synthesis of the cyclic ether core of (+)-laurenyne

A concise enantioselective synthesis of the cyclic ether core of the marine natural product (+)-laurenyne has been accomplished using ring-closing metathesis for medium-ring construction.