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Rebecca L Brown 《Journal of sound and vibration》2003,262(3):591-611
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. 相似文献
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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. 相似文献
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In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733. 相似文献
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Stephen G. Davies Ian A. Hunter Rebecca L. Nicholson Paul.M. Roberts Edward D. Savory Andrew D. Smith 《Tetrahedron》2004,60(35):7553-7577
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. 相似文献
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Maged H. M. Sharaf Paul L. Schiff Albert N. Tackie Charles H. Phoebe Robert L. Johnson Doug Minick Ronald C. Crouch Gary E. Martin C. Webster Andrews 《Journal of heterocyclic chemistry》1996,33(3):789-797
The isolation and structure determination of cryptomisrine, a novel indolo[3,2-b]quinoline dimeric alkaloid obtained from extracts of the roots of the Ghanaian medicinal plant Cryptolepis sanguinolenta is reported. The structure determination was made via a consideration of the spectral data, including uv, ir, nmr, and mass spectra. In particular, one-dimensional proton/carbon nmr, one-dimensional nOe difference nmr, and a series of homonuclear (COSY) and inverse-detected heteronuclear two-dimensional (HMQC, HMBC) experiments were utilized, as well as high resolution FABMS. Cryptomisrine is most unusual in that its two monomeric parts apparently exist in such a C2 symmetric environment that only one set of proton and carbon nmr resonances are observed. Cryptomisrine is the first example of a dimeric indolo-[3,2-b]quinoline alkaloid to have been isolated from nature. 相似文献
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Laser-ablated thorium atoms have been reacted with CO molecules during condensation in excess neon. Absorptions at 617.7 and 812.2 cm(-1) are assigned to Th-C and Th-O stretching vibrations of the CThO molecule. Absorptions at 2048.6, 1353.6, and 822.5 cm(-1) are assigned to the OThCCO molecule, which is formed by CO addition to CThO and photochemical rearrangement of Th(CO)(2). The OThCCO molecule undergoes further photoinduced rearrangement to OTh(eta(3)-CCO), which is characterized by C-C, C-O, and Th-O stretching vibrations at 1810.8, 1139.2, and 831.6 cm(-1). The Th(CO)(n) (n = 1-6) complexes are formed on deposition or on annealing. Evidence is also presented for the CThO(-) and Th(CO)(2)(-) anions, which are formed by electron capture of neutral molecules. Relativistic density functional theory (DFT) calculations of the geometry structures, vibrational frequencies, and infrared intensities strongly support the experimental assignments. It is found that CThO is an unprecedented actinide-containing carbene molecule with a triplet ground state and an unusual bent structure ( angleCThO = 109 degrees ). The OThCCO molecule has a bent structure while its rearranged product OTh(eta(3)-CCO) is found to have a unique exocyclic structure with side-bonded CCO group. We also find that both Th(CO)(2) and Th(CO)(2)(-) are, surprisingly, highly bent, with the angleC-Th-C bond angle being close to 50 degrees; the unusual geometries are the result of extremely strong Th-to-CO back-bonding, which causes significant three-centered bonding among the Th atom and the two C atoms. 相似文献