Frequency Characteristics Analysis of Micro-Displacement Structure with Parallel Flexure Hinges

Flexure hinges based micro-displacement structure has been widely used for micro-precision machinery, and the natural frequency characteristics analysis is one of the most important elements in the structure design. In this paper, natural frequency characteristics analysis of a micro-displacement structure with parallel flexible hinges is presented. The effects of each structure parameter to the natural frequency of the micro-displacement structure are simulation by dynamics modeling. The parameters can be divided into three categories, namely, parallel flexure hinges parameter, micro-displacement structure parameter and material parameter. Two micro-displacement structures using common materials are machined for frequency test. The test results of two micro-displacement structure verified the modeling analysis, and the natural frequency characteristics analysis in this paper can be referenced in micro-displacement structure design.

Double-Grating Displacement Structure for Improving the Light Extraction Efficiency of LEDs

To improve the light extraction efficiency of light-emitting diodes (LEDs), grating patterns were etched on GaN and silver film surfaces. The grating-patterned surface etching enabled the establishment of an LED model with a double-grating displacement structure that is based on the surface plasmon resonance principle. A numerical simulation was conducted using the finite difference time domain method. The influence of different grating periods for GaN surface and silver film thickness on light extraction efficiency was analyzed. The light extraction efficiency of LEDs was highest when the grating period satisfied grating coupling conditions. The wavelength of the highest value was also close to the light wavelength of the medium. The plasmon resonance frequencies on both sides of the silver film were affected by silver film thickness. With increasing film thickness, plasmon resonance frequency tended toward the same value and light extraction efficiency reached its maximum. When the grating period for the GaN surface was 365 nm and the silver film thickness was 390 nm, light extraction efficiency reached a maximum of 55%.

A Note on the Inversion of Sylvester Matrices in Control Systems

We give a sufficient condition (the solvability of two standard equations) of Sylvester matrix by using the displacement structure of the Sylvester matrix, and, according to the sufficient condition, we derive a new fast algorithm for the inversion of a Sylvester matrix, which can be denoted as a sum of products of two triangular Toeplitz matrices. The stability of the inversion formula for a Sylvester matrix is also considered. The Sylvester matrix is numerically forward stable if it is nonsingular and well conditioned.