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.     

Preparation of 4-hydroxy-3-substituted, 2H-1-benzopyran-2-ones and 2H-1-benzothiopyran-2-ones from carboxylic esters and methyl salicylates or methyl thiosalicylate

C(α)-Carboxylic acid esters were treated with excess lithium diisopropylamide, condensed with methyl salicylates or methyl thiosalicylate, followed by acid cyclization to either 4-hydroxy-3-substituted, 2H-1-benzopyran-2-ones (coumarins), or 2H-1-benzothiopyran-2-ones (thiocoumarins).     

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.