Dynamics of a Cubic Nonlinear Vibration Absorber

We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.     

Synthesis of polyethylene‐octene elastomer/SiO2‐TiO2 nanocomposites via in situ polymerization: Properties and characterization of the hybrid

In this study, a silicic acid and tetra isopropyl ortho titanate ceramic precursor and a metallocene polyethylene‐octene elastomer (POE) or acrylic acid grafted metallocene polyethylene‐octene elastomer (POE‐g‐AA) were used in the preparation of hybrids (POE/SiO₂? TiO₂ and POE‐g‐AA/SiO₂? TiO₂) using an in situ sol‐gel process, with a view to identifying a hybrid with improved thermal and mechanical properties. Hybrids were characterized using Fourier transform infrared spectroscopy, ²⁹Si solid‐state nuclear magnetic resonance (NMR), X‐ray diffraction, differential scanning calorimetry, thermogravimetry analysis, dynamic mechanical thermal analysis, and Instron mechanical testing. Properties of the POE‐g‐AA/SiO₂? TiO₂ hybrid were superior to those of the POE/SiO₂? TiO₂ hybrid. This was because the carboxylic acid groups of acrylic acid acted as coordination sites for the silica‐titania phase to allow the formation of stronger chemical bonds. ²⁹Si solid‐state NMR showed that Si atoms coordinated around SiO₄ units were predominantly Q₃ and Q₄. The 10 wt % SiO₂? TiO₂ hybrids gave the maximum values of tensile strength and glass transition temperature in both POE/SiO₂? TiO₂ and POE‐g‐AA/SiO₂? TiO₂. It is proposed that above this wt %, excess SiO₂? TiO₂ particles caused separation between the organic and inorganic phases. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1690–1701, 2005     

The effects of melt annealing and counterpart's molecular weight on the thermal properties and phase morphology of poly(L‐lactide)‐based blends

The thermal properties and phase morphology of poly(L ‐lactide) (PLLA)‐based blends have been studied. Two poly(ethylene glycol)s (PEGs) with molecular weight (MW) of about 1,500 (1.5k) g/mol and 2,000,000 (2M) g/mol, respectively, were used as counterparts. The blends were annealed at a preselected temperature of 200 °C for either 2 min or 30 min before the characterizations. Both PEGs were determined to enhance the crystallizability of PLLA. After a 2‐min process of annealing, the PEG(1.5k)'s crystallization efficiency on PLLA has been noted to increase with the increase of its content. Conversely, PEG(2M)'s crystallization efficiency declined with the increase of its content. Extending the annealing time has evidently changed the PEGs' crystallization effect on PLLA. Moreover, the PEG(1.5k) has, to a greater extent, brought about the depression of PLLA's melting temperature by increasing its content, and this depression increased with the annealing time. The blends exhibited lower thermal stability than those of the parent components, particularly for the PEG(1.5k)‐included system with a higher PEG content. Regardless of the annealing time, the PEG(1.5k)‐included blends have shown homogeneous melt morphology under light microscope, whereas the PEG(2M)‐included blends have displayed phase‐separated melt morphology. In addition to the composition, PEG's MW and annealing time influence the crystalline morphology of the blends. The ringed PLLA spherulites have appeared mostly in the 2‐min annealed PEG(1.5k)‐included blends. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1497–1510, 2009     

Facile method to prepare monodispersed Ag/polystyrene composite microspheres and their properties

This article presents a facile method to prepare silver/polystyrene composite microspheres. In this approach, monodispersed polystyrene (PS) particles were synthesized with carboxyl acid groups on the surfaces of the PS particles via dispersion polymerization at first. With the addition of [Ag(NH₃)₂]⁺ to the PS dispersion, [Ag(NH₃)₂]⁺ was absorbed to the surfaces of the PS particles, and then by heating the system, [Ag(NH₃)₂]⁺ complex ions were reduced to silver to form the Ag/PS composite microspheres. In the synthesis of PS dispersion, PVP was used as dispersant to stabilize the PS particles, it also acted as reducing agent in the reduction of [Ag(NH₃)₂]⁺ complex ions to silver, so no additional reducing agent was needed. The resulting composite microspheres were characterized by TEM, SEM, XPS, and XRD. The catalytic properties and surface‐enhance Raman scattering (SERS) was studied as well. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4547–4554, 2009     

Eigenvalue spectra and geometric transformation of polyhedra

Starting from one fullerene, the three geometric transformations, cap, face dual and edge dual produce series of carbon clusters and deltahedra. The geometric relation between these polyhedra implies that their topological matrices and eigenvalue spectra must be relative. We have developed a matrix algebra method to research some polyhedra with high symmetry and one kind, two or three kinds of equivalent vertices such as C₆₀(I_h), resolve their exact eigenvalues, and proved this point.     

X-ray diffraction by thermotropic main-chain polymers with side groups. II. semiflexible polyesters

Semiflexible thermotropic aromatic polyesters with lateral groups were aligned magnetically and mechanically in monodomains after separation into high-molecular-weight (polymer) and low-molecular-weight (oligomer) fractions. Based on the x-ray intensity distributions recorded for a series of seven different substituents in the arylsulfonyl substituted group, a novel smectic structure was determined for H, F, Cl, OCH₃, and CH₃ in the para position while a normal nematic alignment prevailed when it contained Br or NO₂.