Fundamental and subharmonic resonances in a system with a ‘1-1’ internal resonance

The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given.     

The chaotic response of a fluttering panel: The influence of maneuvering

The influence of maneuvering on the chaotic response of a fluttering buckled plate on an aircraft has been studied. The governing equations, derived using Lagrangian mechanics, include geometric non-linearities associated with the occurrence of tensile stresses, as well as coupling between the angular velocity of the maneuver and the elastic degrees of freedom. Numerical simulation for periodic and chaotic responses are conducted in order to analyze the influence of the pull-up maneuver on the dynamic behavior of the panel. Long-time histories phase-plane plots, and power spectra of the responses are presented. As the maneuver (load factor) increases, the system exhibits complicated dynamic behavior including a direct and inverse cascade of subharmonic bifurcations, intermittency, and chaos. Beside these classical routes of transition from a periodic state to chaos, our calculations suggest amplitude modulation as a possible new mode of transition to chaos. Consequently this research contributes to the understanding of the mechanisms through which the transition between periodic and strange attractors occurs in, dissipative mechanical systems. In the case of a prescribed time dependent maneuver, a remarkable transition between the different types of limit cycles is presented.Nomenclature a plate length - a _r u _r /h - D plate bending stiffness - E modulus of elasticity - g acceleration due to gravity - h plate thickness - j₁,j₂,j₃ base vectors of the body frame of reference - K spring constant - M Mach number - n 1 + ₀/g - N ₁ applied in-plane force - p–p aerodynamic pressure - P pa ⁴/Dh - q ₀/2 - Q _r generalized Lagrangian forces - R rotation matrix - R ₄ N, a ²/D - t time - kinetic energy - u plate deflection - u displacement of the structure - u _r modal amplitude - v₀ velocity - x coordinates in the inertial frame of reference - z coordinates in the body frame of reference - Ka/(Ka+Eh) - - elastic energy - 2qa ³/D - a/_mh - Poisson's ratio - material coordinates - air density - _m plate density - - _r prescribed functions - _r sin(r z/a) - angular velocity - a/v₀ - skew-symmetric matrix form of the angular velocity     

聚羧酸系高性能超塑化剂的研究进展

聚羧酸系超塑化剂由含磺酸基团、羧酸基团、聚氧烷基烯基团等不饱和单体在引发剂作用下合成的梳型高分子类聚合物,具有掺量低、减水率高以及增强效果显著等优点,是高性能混凝土中不可缺少的组分。随着高分子合成化学和高分子设计理论不断取得新的进展,成为高性能超塑化剂领域的研究热点。本文综述了国内外聚羧酸系超塑化剂的最新研究概况,对聚羧酸系超塑化剂的合成及作用机理进行了探讨,介绍了聚羧酸系超塑化剂所面临的问题,并对未来研究与应用发展方向进行了预测。     

油胺/油酸稳定的CdSe量子点的绿色合成

以液体石蜡为高温反应溶剂,油酸和油胺为混合稳定剂,利用高温热解法一步合成了高质量的CdSe量子点。通过紫外-可见吸收光谱、荧光发射光谱、红外光谱和X射线衍射等手段对量子点的光学性质和结构进行了表征。结果表明,油胺/油酸混合表面活性剂稳定的量子点吸收光谱峰形更尖锐,荧光发射光谱半峰宽更窄。反应温度和反应时间均对量子点的生长过程和光学性质有明显影响,220℃下反应15 min,荧光量子产率可达26%。得到的CdSe量子点为立方晶型,表面同时包覆了油酸和油胺,具有良好的光稳定性。该方法无需使用三烷基膦,价廉环保,且合成的CdSe量子点性质稳定、性能优越,有利于其在分析检测领域中的应用。     

Applicability of corresponding-states group-contribution methods for the estimation of surface tension of multicomponent liquid mixtures at 298.15 K

Corresponding-states group-contribution methods (CSGC-ST1 and CSGC-ST2) have been applied to four binary liquid mixtures (propyl acetate + o-xylene, propyl acetate + m-xylene, propyl acetate + p-xylene and propyl acetate + ethyl benzene); two ternary (benzene + cyclohexane + toluene and n-hexane + cyclohexane + benzene) and two quaternary liquid mixtures (pentane + hexane + cyclohexane + benzene and pentane + hexane + benzene + toluene) at 298.15 K. In this work, the CSGC-ST2 method is modified and extended to multicomponent liquid mixtures. The excess magnitudes of surface tension were also calculated and graphs were plotted using Redlich–Kister method.     

Direct Synthesis of Titanium Complexes with Chelating cis‐9,10‐Dihydrophenanthrenediamide Ligands through Sequential C?C Bond‐Forming Reactions from o‐Metalated Arylimines

A series of new titanium(IV) complexes with o‐metalated arylimine and/or cis‐9,10‐dihydrophenanthrenediamide ligands, [o‐C₆H₄(CH?NR)TiCl₃] (R=2,6‐iPr₂C₆H₃ ( 3 a ), 2,6‐Me₂C₆H₃ ( 3 b ), tBu ( 3 c )), [cis‐9,10‐PhenH₂(NR)₂TiCl₂] (PhenH₂=9,10‐dihydrophenanthrene; R=2,6‐iPr₂C₆H₃ ( 4 a ), 2,6‐Me₂C₆H₃ ( 4 b ), tBu ( 4 c )), [{cis‐9,10‐PhenH₂(NR)₂}{o‐C₆H₄(HC?NR)}TiCl] (R=2,6‐iPr₂C₆H₃ ( 5 a ), 2,6‐Me₂C₆H₃ ( 5 b ), tBu ( 5 c )), have been synthesised from the reactions of TiCl₄ with o‐C₆H₄(CH?NR)Li (R=2,6‐iPr₂C₆H₃, 2,6‐Me₂C₆H₃, tBu). Complexes 4 and 5 were formed unexpectedly from the reactions of TiCl₄ with two or three equivalents of the corresponding o‐C₆H₄(CH?NR)Li followed by sequential intramolecular C? C bond‐forming reductive elimination and oxidative coupling reactions. Attempts to isolate the intermediates, [{o‐C₆H₄(CH?NR)}₂TiCl₂] ( 2 ), were unsuccessful. All complexes were characterised by ¹H and ¹³C NMR spectroscopy, and the molecular structures of 3 a , 4 a – c , 5 a , and 5 c were determined by X‐ray crystallography.     

Ring Opening of Pymisyl‐Protected Aziridines with Organocuprates

The pyrimidine‐2‐sulfonyl (pymisyl) group is introduced as a new protecting group that can be used to activate aziridines towards ring opening. It is readily introduced and removed under mild conditions. Regioselective ring opening of pymisyl‐protected 2‐methyl‐aziridine with organocuprates gives the corresponding sulfonamides in high yields, and the pymisyl group can subsequently be removed upon treatment with a thiolate. The versatility of this new nitrogen protecting group is illustrated with a new synthesis of Selegiline, a monoamine oxidase‐B inhibitor marketed for the treatment of Parkinson’s disease.     

Synthesis of unnatural pentahydroxylated pyrrolizidines: 5-epi- and 5,7a-di-epi-hyacinthacine C1

Stereocontrolled synthesis of 5-epi- and 5,7a-di-epi-hyacinthacine C₁ (7 and 8), two potential glycosidase inhibitors are described using α,β-unsaturated ketone 9 as homochiral starting material. The key step in the synthesis is the highly diastereoselective dihydroxylation reaction of 9, that allows the obtention of a single bis-hydroxylated ketone (10). Further derivatization into two epimeric mesylate esters followed by internal cyclization form the pyrrolizidinic compounds 7 and 8. This type of compounds can be useful in glycobiology due to their ability to inhibit carbohydrate-processing enzymes.