相位型波带板应用于大尺度X射线源成像的分析与模拟

针对大尺度物体的keV-X射线高分辨成像,分析了相位型菲涅耳波带板(FPZP)对物平面1mm区域内点源的成像,确定像的空间分布具有不变性,提出了一种FPZP对扩展光源成像的计算方法.使用这一方法,模拟了放大倍数为10的典型实验条件下最外环宽0.35 μm的FPZ对扩展单色光源的成像.结果表明,随着扩展光源尺度的增加,像的对比度降低.FPZP的负1级和0级衍射是导致像的背景增强和对比度降低的主要因素,并相应导致成像对物方的空间分辨能力下降.对于强度空间分布为正弦调制、对比度为1的1mm尺度方形光源,像的对比度低于0.4,物方分辨能力为0.75 μm.     

Projection-free proper orthogonal decomposition method for a cantilever plate in supersonic flow

This paper explores the use of the proper orthogonal decomposition (POD) method for supersonic nonlinear flutter of a cantilever plate or wing. The aeroelastic equations are constructed using von Karman plate theory and first-order piston theory. The two-dimensional POD modes (POMs) in xy plane are determined from the chaotic results given by the traditional Rayleigh–Ritz (RR) approach. For a specific structure, the POMs need to be calculated once and then can be used for various parameters of interest. The derivatives of the POMs are calculated numerically to avoid the complex projection from the POMs to the Rayleigh–Ritz modes (RRMs). Numerical examples demonstrate that the POD method using 4 POMs can obtain accurate limit cycle oscillation (LCO) results with substantial computational cost savings, compared with 12 RRMs by the Rayleigh–Ritz method. The POD method is employed for the analysis of the chaotic oscillations. It is also demonstrated that the POD modes are robust over a range of flight parameters.     

Vibrations of a square plate with parabolically varying thickness

Vibration results for a square plate with a parabolically varying thickness distribution and built-in edges are presented. Frequency and mode shape predictions obtained from a finite element analysis are compared with measurements made with real-time laser holography. In general, the agreement between the two is very good except for a few of the lower modes where the predicted frequencies are about 15% high. So far, a satisfactory explanation for this has not been found. The vibration mode shapes for the plate exhibit a striking blend of radial and square symmetries that results from the axisymmetric thickness distribution and the square symmetry of the boundary frame.     

Vibrations of an orthotropic elliptic plate of non-uniform thickness and temperature

An analysis is presented of the free vibrations of an orthotropic elliptic plate whose temperature and thickness spatial variations both are parabolic along a line through the plate centre. An approximate but quite convenient frequency equation is derived by using Galerkin's method with a two-term deflection function. The upper bounds of frequencies corresponding to the first two modes of vibrations of a clamped orthotropic elliptic plate for various values of aspect ratio, taper constant and temperature constant are obtained.     

Vortex characteristics of Fraunhofer diffractions of a plane wave by a spiral phase plate limited by pseudoring polygonal apertures

We introduce a multilevel spiral phase plate (SPP) limited by a pseudoring polygonal aperture (PRPA). Such an SPP has the advantages of easier fabrication and greater suppression of the sidelobes of the diffraction field over that generated with a polygonal aperture (PA). The Fraunhofer diffraction fields generated by an SPP with a PRPA or with a PA have the same topological charge features and a similar diffraction pattern. Numerical evaluations show that the maximum bright annular-intensity difference between the diffraction patterns for the SPP with a PRPA and that of a PA does not exceed 3% under optimal design parameters.     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

Vibrations of segmented cylindrical shells by a fourier series component mode method

The vibrations of a multi-segment cylindrical shell with a common mean radius are studied. The shell is uniform for any segment but the material and geometric properties may vary from segment to segment. The solution is based on the component mode method coupled with Fourier series and Lagrange multipliers. It is shown that a single segment shell with boundary conditions of free support without tangential constraint is sufficient for an arbitrary shell with arbitrary boundary conditions. Results are presented for simply supported shells and clamped-free shells for two segments with different length and thickness.     

Formation of hook-shaped and straight silica wires by a thermal vapor method

Hook-shaped and straight silica wires have been successfully synthesized on silicon wafer through a simple thermal vapor method with or without assistance of Al, respectively. The hook-shaped silica wires have amorphous structures with nearly 100 μm long and about 4 μm in average diameters, while the straight silica wires are hundreds of micrometers long and approximately 50–300 nm in diameters. The composition analysis revealed that larger Al/SiO_x islands can form on the silicon substrate with Al catalysts, whereas tiny silica clusters form without Al catalysts. They could act as the nucleation centers for the growth of silica wires with different shapes. The formation process of hook-shaped silica microwire results from a thermal gradient on the silicon substrate. The thermal gradient may be caused by the cold gas flowing during the process or other factors that lead to uneven temperature. On the contrary, straight growth of silica submicrowire is unacted on the thermal gradient factor due to the tiny silica clusters as nucleation centers. The present simple and low-cost process of producing hook-shaped and straight silica wires in bulk may lead to potential applications in catalysts, electrode materials, biosensing, etc.     

Vibrations of a periodic rail-sleeper system excited by an oscillating stationary transverse force

The rail-sleeper system is idealized as an infinite, periodic beam-mass system. Use is made of the periodicity principle for the semi-infinite halves on either side of the forcing point for evaluation of the wave propagation constants and the corresponding modal vectors. It is shown that the spread of acceleration away from the forcing point depends primarily upon one of the wave propagation constants. However, all the four modal vectors (two for the left-hand side and two for the right-hand side) determine the driving point impedance of the rail-sleeper system, which in combination with the driving point impedance of the wheel (which is adopted from the preceding companion paper) determines the forces generated by combined surface roughness and the resultant accelerations. The compound one-third octave acceleration levels generated by typical roughness spectra are generally of the same order as the observed levels.     

Reflection of compressional and Rayleigh waves on the edges of an elastic plate with quadratic nonlinearity

Previous ultrasonic studies have demonstrated that measurements of material nonlinearities can provide a means for detecting early signs of fatigue damage using both compressional (P) and Rayleigh (R) surface waves. However, these experimental studies have typically been limited to the direct wave arrival between the source and receiver in simple geometries where no reflection occurs. In particular, the degree of material nonlinearity is often quantified by the ratio of the cumulative amplitude of the first harmonic to that of the fundamental for the direct arrival only. Hence a practical question arises over the interpretation of ultrasonic measurements of material nonlinearities in the presence of reflected nonlinear waves. Thus, this article investigates the reflection problem of P or R waves at the edge of a homogeneous plate with quadratic nonlinearity using both a theoretical formulation, based on perturbation analysis, and direct numerical simulations using a Cellular Automata formulation. The numerical approach is first validated against an existing theoretical formulation for reflecting nonlinear P waves. It is then used to simulate the nonlinear reflection of R waves at a plate's edge for which no closed-form formulation is presently available.     

Vibrations of narrow microbeams predeformed by an electric field

Vibrations of a fixed–fixed narrow microbeam electrostatically actuated by applying a voltage difference to it and a parallel rigid conductor are analyzed. For gaps between the two conductors that are comparable to the beam's thickness, the fundamental frequency of the beam may first increase with increasing applied voltage, before suddenly dropping at the pull-in voltage. Available models fail to accurately describe this behavior of the frequency versus voltage diagram for narrow microbeams, that results from a combination of strain-hardening and electrostatic softening effects. A distributed electromechanical model, that accounts for electrostatic fringing fields, finite deflections and residual stresses, is proposed. A recent estimate of the electrostatic force incorporating fringing fields due to both finite width and finite thickness of the microbeam is employed. The lowest frequency is extracted with a simple and computationally efficient one degree-of-freedom model obtained by approximating the deflection field with the static deflection of a fixed–fixed microbeam loaded by a uniformly distributed force. The model's predictions are in good agreement with those from three-dimensional finite-element simulations.