Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory

In this paper, exact closed-form solutions in explicit forms are presented for transverse vibration analysis of rectangular thick plates having two opposite edges hard simply supported (i.e., Lévy-type rectangular plates) based on the Reddy’s third-order shear deformation plate theory. Two other edges may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. Hamilton’s principle is used to derive the equations of motion and natural boundary conditions of the plate. Several comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate accuracy of the present new formulation. Comprehensive benchmark results for natural frequencies of rectangular plates with different combinations of boundary conditions are tabulated in dimensionless form for various values of aspect ratios and thickness to length ratios. A set of three-dimensional (3-D) vibration mode shapes along with their corresponding contour plots are plotted by using exact transverse displacements of Lévy-type rectangular Reddy plates. Due to the inherent features of the present exact closed-form solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.     

Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force

The pull-in instability and the vibration for a prestressed circular electrostatically actuated microplate are investigated in consideration of the Casimir force. Based on von Kármán’s nonlinear bending theory of thin plates, the governing equations for the whole analysis are decomposed into two two-point boundary value problems. For static deformation of the plate, the geometric nonlinearity is involved and the pull-in parameters are obtained by using the shooting method through taking the applied voltage or Casimir parameter as an unknown. This algorithm is also used to study the small amplitude free vibration about the predeformed bending configuration following an assumed harmonic time mode, and the variation of the prestress and Casimir parameters dependent fundamental natural frequency with the applied voltage is presented. Several case studies are compared with available published simulations to confirm the proposed method. The influences of various parameters, such as the initial gap-thickness ratio, Casimir effect, prestress on the pull-in instability behavior and the natural frequency are examined.     

一个新的非常规各向异性元的收敛性分析

构造了一个新的非常规各向异性Hermite型矩形单元并据此对二阶椭圆问题提出了一个混合元格式,同时给出了该格式的收敛性分析.     

Spectral-optical-electrical-thermal properties of deposited thin films of nano-sized calcium(II)-8-hydroxy-5,7-dinitroquinolate complex

Spectral–optical–electrical–thermal properties of deposited thin films of nano-sized calcium(II)-8-hydroxy-5,7-dinitroquinolate complex, Ca[((NO₂)₂-8HQ)₂], were explored, studied and evaluated in this work. Thin films of Ca[((NO₂)₂-8HQ)₂] were assembled by using a direct, simple and efficient layer-by-layer (LBL) chemical deposition technique. The optical properties of thin films were investigated by using spectrophotometric measurements of transmittance and reflectance at normal incidence in the wavelength range 200–2500 nm. The refractive index, n, and the absorption index, k, of Ca[((NO₂)₂-8HQ)₂] films were determined from the measured transmittance and reflectance. The real and imaginary dielectric constants were also determined. The analysis of the spectral behavior of the absorption coefficient in the intrinsic absorption region reveals a direct allowed transition with band gaps of 1.1 eV and 2.4 eV for the optical and transport energy gaps, respectively. The current–voltage characteristics of Ca[((NO₂)₂-8HQ)₂] showed a trap-charge limited conduction in determining the current at the intermediate and high bias regimes. Graphical representation of the current–voltage characteristics yields three distinct linear parts indicating the existence of three conduction mechanisms. Structural characterization and identification were confirmed by using Fourier transform infrared spectroscopy (FT-IR). Scanning electron microscopy (SEM) was also used to image the surface morphology of the deposited nano-sized metal complex and such study revealed a high homogeneity in surface spherical particle distribution with average particles size in the range 20–40 nm. Thermal gravimetric analysis (TGA) was also studied for [(NO₂)₂-8HQ] and Ca[((NO₂)₂-8HQ)₂] to evaluate and confirm the thermal stability characteristics incorporated into the synthesized nano-sized Ca[((NO₂)₂-8HQ)₂] complex.     

Facile fabrication of metallic nanostructures by tunable cracking and transfer printing

You crack me up: A topographically patterned PDMS stamp was coated with thin metal film and swelled under organic vapor to induce the tunable cracking of the brittle film into metallic nanostructures (see SEM images, scale bars 1?μm). UV/Vis spectra, OLED efficiency, and SERS spectra demonstrate the fine controllability of the metallic nanostructures, the well-ordered and highly regulable surface plasmons, and the facile fabrication process.     

Direct Patterning of Copper on Polyimide by Site‐Selective Surface Modification via a Screen‐Printing Process

We demonstrate a simple route to fabricating copper circuit patterns on the surface of polyimide film. The copper pattern can be obtained in three steps: 1) Formation of partially potassium hydroxide modified pattern via a screen‐printing process, 2) formation of macromolecular metal complex with copper, and 3) copper metallization by DMAB reduction. The morphologies of these copper patterns are determined by cross‐sectional transmission electronic microscopy (TEM), scanning electronic microscopy (SEM), and atomic force microscopy (AFM). Furthermore, the growing process of the metallic copper film is investigated. The direct patterning of copper patterns onto polyimide substrates is promising for use in electronics industry as a large‐area and low‐cost processing technique.     

Surface‐Plasmon‐Coupled Emission of Rhodamine 110 in a Silica Nanolayer

The first observation of strong directional surface‐plasmon‐coupled emission (SPCE) of Rhodamine 110 in silica nanofilms deposited on silver nanolayers is reported. The preparation of the material is described in detail. The intensity of SPCE exceeds 10 times that of free space fluorescence and total linear light polarization in the SPCE ring is observed. A new experimental setup and an original data collection method is presented. Our material completely preserves its fluorescence properties for at least eight months.     

Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate

Based on the von Karman plate theory of large deflection, we have derived a non-linear partial differential equation for the vibration of a thin orthotropic plate under the combined action of a transverse magnetic field and a transverse harmonic mechanical load. The influence of the magnetic field is due to the magnetic Lorentz force induced by the eddy current. By employing the Bubnov-Galerkin method, the non-linear partial differential equation is transformed into a third-order non-linear ordinary differential equation. The amplitude-frequency equations are further derived by means of the multiple-scale method. As numerical examples for an orthotropic plate made of silver, the influence of the magnetic field, orthotropic material property, plate thickness, and the mechanical load on the principal resonance behavior is investigated. The higher-order effect and stability of the solution are also discussed.