3-D electrostatic hybrid element model for SAW interdigital transducers

In this work, the singular behavior of charges at corners and edges on the metallized areas in SAW transducers are investigated. In particular, it is demonstrated that a tensor product of the commonly used Tchebychev bases overestimates the singularities at corners, and, hence, it cannot be used in a proper boundary element method formulation. On the other hand, it is shown that a simple finite element method-like approach is impractical due to the enormous number of unknowns required to model the electrode's large length-to-width ratio. These considerations are then used for defining a hybrid element model, which combines Tchebychev and linear polynomials over differently meshed domains. Such an approach is shown to suitably account for charge singularities while greatly reducing the number of unknowns. Results are obtained for isotropic and anisotropic substrates for non-periodic configurations.     

Dimensional reduction study of piezoelectric ceramics constitutive equations from 3-D to 2-D and 1-D

Accurate performance evaluation is crucial to the design and development of macro/micro-sized piezoelectric devices, and key to this is the proper use of the stiffness/ compliance and piezoelectric coefficients of the piezoelectric ceramics involved. Although the literature points out effective piezoelectric coefficients e_31,f and d_33,f for thin film materials and reduced dimensionality of equations for bulk material, the elastic and piezoelectric coefficients remain unchanged from the 3-D equations in most reported 1-D and 2-D analyses of the macro/micro-sized devices involving the e form of the constitutive equations. The use of unchanged coefficients leads to variations between numerically predicted and experimental results in most devices. To understand effects of the dimensional reduction from 3-D to 2-D and 1-D on stiffness/compliance and piezoelectric coefficients, this paper derives the 2-D and 1-D constitutive equations from the 3-D equations, focusing on the discussion of often-required device configurations for sensor and actuator design and analysis. Two modified coefficients are proposed, termed reduced and enhanced, which enable better understanding of effects of the dimensional reduction and also effects on the design and analysis of sensors and actuators.     

3-D and 2-D Dynamic Green's functions and time-domain BIEs for piezoelectric solids

Dynamic Green's functions for linear piezoelectric solids are derived by using Radon transform. Time-harmonic and Laplace transformed dynamic Green's functions are obtained subsequently by applying the Fourier and the Laplace transform to the time-domain Green's functions. Time-domain boundary integral equation formulations are presented for transient dynamic analysis of linear piezoelectric solids. In particular, hypersingular and non-hypersingular time-domain traction BIEs are derived by two different ways. Their potential application in transient dynamic crack analysis of three-dimensional and two-dimensional piezoelectric solids is discussed.     

Circular edge singularities for the Laplace equation and the elasticity system in 3-D domains

Asymptotics of solutions to the Laplace equation with Neumann or Dirichlet conditions in the vicinity of a circular singular edge in a three-dimensional domain are derived and provided in an explicit form. These asymptotic solutions are represented by a family of eigen-functions with their shadows, and the associated edge flux intensity functions (EFIFs), which are functions along the circular edge. We provide explicit formulas for a penny-shaped crack for an axisymmetric case as well as a case in which the loading is non-axisymmetric. Explicit formulas for other singular circular edges such as a circumferential crack, an external crack and a 3π/2 reentrant corner are also derived. The mathematical machinery developed in the framework of the Laplace operator is extended to derive the asymptotic solution (three-component displacement vector) for the elasticity system in the vicinity of a circular edge in a three-dimensional domain. As a particular case we present explicitly the series expansion for a traction free or clamped penny-shaped crack in an axisymmetric or a non-axisymmetric situation. The precise representation of the asymptotic series is required for constructing benchmark problems with analytical solutions against which numerical methods can be assessed, and to develop new extraction techniques for the edge flux/intensity functions which are of practical engineering importance in predicting crack propagation.     

A green's function method for large deflection analysis of plates

Summary An integral equation method is presented for large deflection analysis of thin elastic plates, whose behaviour is governed by the von Kármán equations. The method uses the Green function of the biharmonic equation to establish integral representations of the deflection and stress function for the linear part of the governing operator while the nonlinearities are treated as loading forces. Six nonlinear domain integral equations are formulated which are solved to yield the curvature tensors of the deflection and stress function surfaces and thereby the deflections and stress resultants. The nonlinear integral equations are solved numerically by developing an effective technique based on Gaussian quadrature over domains of arbitrary shape. For domains of simple geometry ready-to-use Green functions are employed whereas for regions of arbitrary shape the Green function is established numerically using BEM. The efficiency of the method is demonstrated and attested by analyzing a circular clamped plate with movable edge.With 4 Figures     

Design free of stress singularities for bi-material components

Interest in the application of genetic algorithms (GA) to the stacking sequence of composite laminates has grown in recent years. However, the huge calculation time of GA is a major problem for designers. In this study, a local improvement is inserted into a standard GA, and the real calculation, by finite element analysis (FEA) for example, required in the local search is replaced by a regression model. Accordingly, the improved GA converges much sooner than a standard GA and the calculation time is greatly reduced. The regression analysis applies chosen trigonometric functions as base functions, and estimates objective function values accurately using only few sample points. The GA with local improvement is then applied to a sandwich plate and composite propeller, the amount of calculation is reduced by over half.     

3-D Numerical Simulations of Biofilm Flows

We study the biofilm-flow interaction resulting in biofilm growth and deformation in a water channel in a 3-D setting using the phase field model developed recently [28, 29]. In this biofilm model, the biofilm made up of the EPS, bacteria and solvent is tracked using a biofilm volume fraction which vanishes outside the biofilm region. The interface between the biofilm and the solvent is marked by the zero level surface of the volume fraction measured from the biofilm to the solvent. The growth of the biofilm and the solvent-biofilm interaction with the top nutrient feeding condition is simulated in the viscous regime (growth regime) of the biofilm-solvent mixture flow. In quiescent flows, the model predicts growth patterns consistent with experimental findings for single or multiple adjacent biofilm colonies, in which the known mushroom shape growth pattern is obtained. Shear induced deformation in biofilms is simulated in a shear cell, providing a viable numerical evidence for using simulation tool to study biofilm growth and interaction dynamics in aqueous environment.     

Application of synchronous two-port resonators for measurement of SAW parameters in piezoelectric crystals

The synchronous two-port resonator can be used for the determination of SAW parameters, including velocity, electromechanical coupling coefficient, and reflection coefficient of one strip. These parameters can be determined from a comparison between the measured and calculated transfer functions of the resonator. Using this technique, the SAW free surface velocity of the 45 degrees XZ-cut of lithium tetraborate (Li(2)B(4)O(7)) crystal was found to be equal to 3436 m/s. The other measured parameters agree well with the values found in the literature.     

Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method

Among the various possible ways of dealing with notch and crack situations, the scaled boundary finite element method [SBFEM, (Wolf and Song in Finite element modelling of unbounded structures. Wiley, Chichester, 1996; Wolf in The scaled boundary finite element method. Wiley, Chichester, 2003)] has been adopted in this work. This method has been proved to be versatile, much less time consuming than the finite element method and generates highly accurate numerical predictions in cases of structures with notches and cracks. The SBFEM gives the advantage of boundary element method by reducing one dimension in modelling the structures but the mathematical formulations are more related to conventional displacement based finite element method. This method requires a certain scalability of the given structure with respect to a point called similarity center. Like in the case of the boundary element method, the structure needs to be discretized only at the surface where standard displacement based isoparametric finite element formulations are adequate. Unlike in the boundary element method, however, no fundamental solution is required by the scaled boundary finite element method. The similarity or scalability of the method requires separation of coordinates such that in the radial direction (i.e. scaling direction) it yields simple differential equations that can be solved analytically. So this approach can be considered as a semi-analytical method. Several two-dimensional examples have been analysed for crack and notch situations that are well known cases in fracture mechanics. A number of three-dimensional cases have been considered for different crack configurations that yield high order of singularity. The results, according to the authors’ knowledge are up to now unpublished in the open literature. Parametric studies are conducted for structures with bi-material interfaces.     

双丝埋弧焊工艺焊接温度场模拟分析

采用MSC.Marc软件对16 mm厚的E36钢板双丝埋弧焊接温度场进行了数值模拟,系统地分析了焊接速度、双丝间距对焊接温度场形貌的影响,并分析了不同焊接速度下双丝间距对熔池形状、HAZ高温区宽度的影响规律。研究表明,热输入一定时,当焊速增至120cm/min时,双丝间距为50 mm的熔池由分离变为共熔;随着焊速的提高及双丝间距的增加,熔池深度变浅、熔宽变窄,HAZ高温区宽度变窄,实际焊接时可能出现"脊背"现象,需重新调整热输入。     

Elastic green's function for a bimaterial composite solid containing a crack inclined to the interface

An analytical closed-form expression is derived for the elastic Green's function of a bimaterial composite solid containing a planar interface and a straight crack inclined at an arbitrary angle with the interface. The crack tip is assumed to be at the interface. Both the constituent materials of the composite are assumed to anisotropic. The Green's function satisfies the interfacial boundary conditions of continuous tractions and displacements, and zero tractions at the crack surfaces. The boundary conditions are satisfied by using the virtual force technique. The determination of the virtual forces requires solutions of a Hilbert problem which is obtained by using an orthogonal complex transform. The method is illustrated by applying it to a copper/nickel composite. The Green's function should be useful in the boundary-element method of calculating the stress and the displacement field in the solid.     

Evaluation on mass sensitivity of SAW sensors for different piezoelectric materials using finite-element analysis

The mass sensitivity of the piezoelectric surface acoustic wave (SAW) sensors is an important factor in the selection of the best gravimetric sensors for different applications. To determine this value without facing the practical problems and the long theoretical calculation time, we have shown that the mass sensitivity of SAW sensors can be calculated by a simple three-dimensional (3-D) finite-element analysis (FEA) using a commercial finite-element platform. The FEA data are used to calculate the wave propagation speed, surface particle displacements, and wave energy distribution on different cuts of various piezoelectric materials. The results are used to provide a simple method for evaluation of their mass sensitivities. Meanwhile, to calculate more accurate results from FEA data, surface and bulk wave reflection problems are considered in the analyses. In this research, different cuts of lithium niobate, quartz, lithium tantalate, and langasite piezoelectric materials are applied to investigate their acoustic wave properties. Our analyses results for these materials have a good agreement with other researchers' results. Also, the mass sensitivity value for the novel cut of langasite was calculated through these analyses. It was found that its mass sensitivity is higher than that of the conventional Rayleigh mode quartz sensor.     

Evaluation of the Green function for 3-D wave-body interactions in a channel

This study deals with a 3-D boundary-value problem that arises when free-surface waves interact with a stationary body or body system in a channel or wave tank of rectangular cross-section. A consistent asymptotic analysis and an efficient numerical solution is presented of the Green function that satisfies the linear free- surface condition and the non-penetration condition on the channel bottom and the sidewalls. The formulation is based on the open-sea Green function and the complete series of images is evaluated accurately based on the asymptotic analysis. It is demonstrated that the Green function has a square-root singular behavior due to the sidewalls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green function presented in this paper are believed to have an absolute accuracy of 10^–5.     

电子全息高分辨率三维数值重现

对电子全息图进行计算机三维数值重现时,由于样品各层电子衍射的干扰,影响了纵向分辨率的提高。本文提出一种基于多能量电子全息图数值重现像叠加原理的新方法,可以提高电子全息数值重现纵向分辨率,从而实现真正的三维数值重现的含义。还通过计算机模拟研究的手段对该原理和方法的有效性进行了验证,得出了有价值的结果。     

Circuital model for the analysis of the piezoelectric response of A1N films using SAW filters.

In this paper we describe a method to assess the piezoelectric response of a piezoelectric thin film deposited on a conductive substrate. It is based on analyzing the frequency response of a surface acoustic wave (SAW) filter made on the piezoelectric thin film. For this analysis, we use a circuital model that takes into account the theoretical response of the ideal filter along with all the external and internal parasitic effects that deteriorate the response. Using this model, we can obtain the electromechanical coupling factor of the piezoelectric material (k2m) with good accuracy. If parasitic effects are not considered, k2m can be underestimated by a factor of up to 20. We have tested our model using SAW filters made on A1N thin films sputtered on substrates with different conductivities. A discussion on the relation between the different circuital elements and the physical properties of the filters also is provided.     

Numerical and experimental investigations of the influence of corner singularities on 3D fatigue crack propagation

In the case of surface breaking cracks, the typical square-root stress singularity is generally not sustainable and a 3D corner singularity in the vicinity of the intersection of crack front and free surface has to be considered. Only the crack front intersection under a special angle γ_r ensures a valid square-root stress singularity and the applicability of the classical SIF-concept. In this paper, the theory of the numerical determination of the intersection angle γ_r is briefly described and the influence of the 3D corner singularity on fatigue crack growth is experimentally investigated. Therefore, 3D fatigue crack propagation experiments under pure mode-I are performed. Transparent specimens of PMMA are used, in order to be able to observe and to document accurate sequences of real 3D crack front evolution profiles via in situ photographic measurement.     

声表面波压电免疫检测系统的设计

文章报导了一种声表面波压免疫检测系统,它是利用压电元件的质量敏感性质,结合生物免疫识别特性而形成的一种自动化分析传感器检测系统,可对多种抗原或抗体进行实时,快速的定量测定,并可用于反应动力学的研究。具有高特异性,高灵敏度,响应快和小型简便等特点,文中给出了利用该系统进行一些实验研究得到的结果。     

空调室内三维紊流流动与传热的数值模拟

采用三维紊流模型，应用有限容积法计算了室内空调的气固耦合传热问题，并对室内空调的气流组织形式，主要是对流速场，温度场进行了数值模拟计算，为空调室内的气流组织形式的优化设计及舒适性提供了研究依据。     

Numerical study on spectral properties of tungsten one-dimensional surface-relief gratings for spectrally selective devices

Spectral properties of one-dimensional tungsten gratings with various depths and widths of grooves were investigated by means of finite-difference time-domain simulation with a multi-Lorentz model. Shallow gratings showed a strong absorption peak due to surface plasmon polaritons when the oscillation of the electric field was parallel to the grating vector. On the other hand, deep gratings with wide grooves showed a different absorption attributed to the microcavity effect when the oscillation of the electric field was perpendicular to the grating vector. With narrowed grooves, another absorption with d-dependence occurred, which was probably due to vertically oscillating surface plasmons to the grooves.