Free vibration of a rotating non-uniform beam with arbitrary pretwist, an elastically restrained root and a tip mass

The governing differential equations for the coupled bending-bending vibration of a rotating beam with a tip mass, arbitrary pretwist, an elastically restrained root, and rotating at a constant angular velocity, are derived by using Hamilton's principle. The frequency equation of the system is derived and expressed in terms of the transition matrix of the transformed vector characteristic governing equation. The influence of the tip mass, the rotary inertia of the tip mass, the rotating speed, the geometric parameter of the cross-section of the beam, the setting angle, and the pretwist parameters on the natural frequencies are investigated. The difference between the effects of the setting angle on the natural frequencies of pretwisted and unpretwisted beams is revealed.     

Methane plasma polymerization by low‐temperature cascade arc discharge for enhanced adhesion of primer to thermoplastic olefins

Improvement of primer adhesion to thermoplastic olefins (TPOs) by methane plasma polymerization with a low‐temperature cascade arc discharge was investigated. Methane plasma with a low‐temperature cascade arc plasma torch can be used for improving the primer adhesion to TPOs. Tape‐adhesion tests (ASTM 3359‐92a method) demonstrated this improvement, with a rating of 0 for untreated TPOs and 5 for methane plasma‐polymerized TPOs at certain plasma conditions even for aging at 60 °C and 80% relative humidity for 5 days. The adhesion to primer for the soft, flexible TPOs (ETA‐3041c and ETA‐3101) was easily enhanced. The adhesion to primer for the hard and brittle TPOs (ETA‐3183) needs to optimize the plasma conditions to pass the dry‐ and wet‐adhesion test with methane plasmas. To relate the surface characteristics of methane plasma‐polymerized TPOs to adhesion performance with primer, the wettability and polarity of TPOs were evaluated by the contact‐angle measurements of primer and deionized water to TPOs. TPO surface morphology was evaluated with scanning electron microscopy. The surface composition was characterized with electron spectroscopy for chemical analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2004–2021, 2003     

Preparation and properties of silylated PTFE/SiO2 organic–inorganic hybrids via sol–gel process

A study on poly(tetrafluoroethylene) (PTFE) reinforced with tetraethoxysilanes (TEOS) derived SiO₂ is described. It included the manufacturing process of SiO₂‐reinforced PTFE and the effects of silylation agent on the properties of the hybrid material, such as porosity, hydrophobic, thermal resistance, dielectric and mechanical properties, and microstructure. PTFE/SiO₂ hybrids of 50 wt % SiO₂ loading were prepared via a sol–gel process and were shaped by a two‐roll milling machine. Trimethylchlorosilane and hexamethydisilazane were used as the silylation agents. Our results showed that the water absorption and dielectric loss of PTFE/SiO₂ hybrid had significantly improved with silylation agent. The silylation process replaced Si? OH with Si? CH₃ on the surface of the TEOS‐derived silica colloidal particle. The existence of trimethylsilyl [? Si(CH₃)₃] on the surface of the modified PTFE/SiO₂ hybrid was confirmed via infrared and solid‐state ²⁹Si magic‐angle spinning nuclear magnetic resonance spectra. Nitrogen‐sorption techniques were used to characterize the modified and unmodified PTFE/SiO₂ hybrids. The microstructure of SiO₂ in the matrix was also evaluated with scanning electron microscopy and transmission electron microscopy. Our results showed that the silylated sol–gel‐derived PTFE/SiO₂ hybrids had exhibited high porosity (53.7%) with nanosize pores (10–40 nm) and nanosize colloidal particles (20–50 nm). This manifests itself as have the ultralow dielectric properties (D_k = 1.9 and D_f = 0.0021), low coefficient of thermal expansion (66.5 ppm/°C), high tensile modulus (141 MPa), excellent thermal resistance (T_d = 612 °C), and an increased hydrophobia (θ = 114°); moreover, the hydrophobic property of the PTFE/SiO₂ hybrid was thermally stable up to 400 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1789–1807, 2004     

Surface modification on thermoplastic olefins by low‐temperature cascade arc discharge‐air plasmas for enhanced adhesion with primer

Improvement of primer adhesion to thermoplastic olefins (TPOs) by surface modification with a low‐temperature cascade arc discharge‐air plasmas was investigated. Air plasma with a low‐temperature cascade arc plasma torch can be used for improving the primer adhesion to TPOs. Tape‐adhesion tests (ASTM 3359‐92a method) demonstrated this improvement with a rating of “0” for untreated TPOs and “5” for air plasma‐modified TPOs at certain plasma conditions even for aging at 60 °C and 80% relative humidity for 5 days. The adhesion to primer for the soft and flexible kind of TPOs (ETA‐3041c and ETA‐3101) was easily enhanced. The adhesion to primer for the hard and brittle TPOs (ETA‐3183) needs to optimize the plasma conditions to pass the wet‐adhesion test using air plasmas. To relate the surface characteristics of air plasma‐modified TPOs to adhesion performance with primer, the wettability and polarity of TPOs were evaluated by the contact‐angle measurements of primer and deionized water to TPOs. TPO surface morphology was evaluated using scanning electron microscopy. The surface composition was characterized with electron spectroscopy for chemical analysis. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 623–637, 2002; DOI 10.1002/polb.10122     

Hirota polynomials for the KP and BKP hierarchies

Using symmetric function techniques, we derive closed-form expressions for the Hirota polynomials for thepth modified KP and BKP hierarchies in terms of Schur and SchurQ-polynomials, respectively. The Hirota polynomials for the BKP hierarchy can also be expressed as Pfaffians while those for thepth modified KP hierarchies can, under certain conditions, be expressed as determinants.     

FDTD Analysis of EW Wave Circulating by a Magnetized Ferrite Body in Free Space

An efficient numerical method has been devised for the study of wave circulating by a magnetised ferrite body of an arbitrary shape. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. Several shapes of interest have been studied, including spheres, circular cylinders. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide junction circulator.     

Analysis of the H-Plane T-Junction Millimeter Wave Waveguide Circulator with a Ferrite Sphere

This paper presents an approximate but efficient field treatment of the new easy-to-fabricate ferrite sphere based H-plane waveguide circulator for potentially low-cost millimeter wave communication systems. A new three-dimension modeling strategy using a self-inconsistent mixed coordinates based mode matching technique is developed, i.e. the solutions of the Helmholz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical and general Cartesian modes respectively. The point matching method is then used on the interface to numerically obtain the coefficients of different orders basis functions of the field. Therefore, the field distributions as well as the characteristics of the circulator are numerically calculated and the good agreement is observed between the numerical results and the measured data.     

Reaction of Cyclic Sulfates with Phosphines

In their reactions with phosphines, cyclic sulfates 9, 10, 11, and 12 afforded corresponding olefins by way of phosphonium sulfate salts whereas sugar cyclic sulfates 21 and 22 gave anhydrosugar 23.