Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Dynamic stability of thermoelastic coupling moving plate subjected to follower force

The dynamic characteristics and stability of the moving thermoelastic coupling rectangular plate subjected to uniformly distributed tangential follower force are investigated. Based on the heat conduction equation containing the thermoelastic coupling term and the thin plate theory, the thermoelastic coupling differential equation of motion of the rectangular plate under the action of uniformly distributed tangential follower force is established. Dimensionless complex frequencies of the moving thermoelastic coupling rectangular plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor and dimensionless moving speed on the stability and critical load of the moving plate are analyzed. The results show that the divergence loads of the first order mode increase with the increase of the dimensionless thermoelastic coupling factor, and decrease with increasing the dimensionless moving speed.     

大剪切实时干涉系统的火焰条纹分析

使用平行平晶做分光元件建立了剪切量随平行平晶偏转角可调的横向剪切实时干涉系统,该系统在最佳偏转角下所得最大剪切量与平行平晶的厚度成正比。实验表明,当系统的横向剪切量大于被测火焰畸变波面宽度的一半时,剪切域中的非核心剪切区将出现半幅以上的双曝光条纹,以之进行干涉测温处理可以避开传统剪切干涉测量技术所必需的剪切相位还原算法。这意味着实时双曝光条纹可以简单地通过大剪切量横向剪切干涉系统得到。     

Analysis of coherent gradient sensing (CGS) by fourier optics

A coherent laser beam reflected or transmitted from a deforming plate specimen acquires an optical path difference (phase change) which is related to the deformation and stress field. The optical method of Coherent Gradient Sensing (CGS) uses two parallel grating plates to displace (shear) and recombine the distorted light beam emerging from the specimen. Fringes are produced on the image plane by the interference of the shifted and unshifted beams. The fringe pattern is related to the spatial difference of the phase in the shearing direction. If the shearing distance is small enough, the spatial difference of the phase approximates to its gradient. Each fringe in the image represents a locus of equal gradient component of the phase in the shearing direction. The technique is interpreted by means of wave optics, using the Fraunhofer approximation and the paraxial theory of lenses. The assumptions made in earlier analyses have been removed here. A more precise analysis based on Fourier optics is presented. The simplicity of the optical setup and variable resolution of the technique have led to its frequent use in the area of solid mechanics, including fracture mechanics. Some examples are discussed in the second half of this paper.     

Response of an elastically supported plate strip to a moving load

A theoretical analysis is presented of the steady state response of a plate strip constrained elastically along its edges against rotation and translation under the action of a moving transverse line load. Within the classical plate theory the solutions are obtained by using Fourier and Laplace transformation methods with respect to space variables. Numerical results are given for a plate strip with both edges identically constrained and a normal line load of constant intensity travelling along the plate strip with a constant speed. The first five speeds of the applied load for which a resonance effect occurs in the system are plotted as functions of the edge constraint parameters. The profiles of the displacement and the moment of the plate are also shown graphically for several values of the load speed and the edge constraint parameters.     

一种全方位激光束检测仪

基于单平板的两种旋转特性（绕表面中心法及绕入射光束光轴旋转）作者提出了一种任意剪切方向的全方位剪切干涉仪，这不仅对于旋转对称发光，尤其对于非旋转对称激光束的定量检测具有十分重要的应用价值，文中描述了该仪器原理，参数及应用实例。     

Dynamic response of a prestressed,orthotropic thick plate strip to a moving line load

This paper is a study of the steady state response of an orthotropic plate strip to a moving line load. The plate is of infinite length and subjected to initial in-plane stresses parallel and perpendicular to the edges. The solution is obtained on the basis of a thick plate theory which takes into account the effects of shear deformation and rotatory inertia. The critical speed of the load which brings about a resonance effect in the system is determined. Further, the bending moment in the plate is calculated for several values of the load speed and the initial stress parameters and shown graphically as a function of the space variable moving with the load.     

Rayleigh-Ritz vibration analysis of rectangular Mindlin plates subjected to membrane stresses

A previously developed analysis of the flexural vibration of isotropic rectangular plates is extended to include the presence of a membrane stress system. The method of analysis is the Rayleigh-Ritz method and Mindlin plate theory is used which takes into account effects which are disregarded in the classical plate theory. As in the aforementioned earlier analysis the spatial variations of the deflection and two rotations over the plate middle surface are based on the use of Timoshenko beam functions. The membrane stress system comprises biaxial direct stress plus in-plane shearing stress and is uniform throughout the plate. Numerical results are presented for a number of types of plate and of applied stress which show the manner of variation of the frequencies of vibration as the intensity of stress changes. This manner of variation is similar in form to that demonstrated elsewhere by analyses based on the use of the classical plate theory but the magnitudes of the present calculated frequencies are considerably reduced for moderately thick plates.     

Vibration and stability of elasticity supported circular plates under conservative and non-conservative loads

This paper deals with the vibration and stability of circular plates elastically restrained against translation and rotation along concentric intermediate circles as well as at the outer edge. The plate is subjected to a horizontal or tangential radial load at the periphery. Both axisymmetric and non-axisymmetric vibrations are considered. It is assumed that the plate is thin, elastic, and isotropic. The solutions are obtained in terms of Bessel functions for both the complete and annular plate sections. The effect of the support stiffnesses on the plate natural frequency and the divergence and flutter instability loads are studied in detail.     

基于有限元方法的Kirchhoff板上动态分布载荷的辨识

借助有限元法研究Kirchhoff板上动态分布载荷的辨识问题.为了反演右端载荷,选择板表面的应变作为已知的附加信息.使用基于FFT算法的Laplace数值变换及其逆变换,以方便处理系统的动态行为.根据Kirchhoff板的应变-位移关系得到的线性控制系统是病态的,为此使用Tikhonov正则化和L-curve方法进行求解.数值算例结果表明,载荷反演策略是行之有效的.     

Study of the shear-rate dependence of granular friction based on community detection

In this study, computer simulations are performed on three-dimensional granular systems under shear conditions. The system comprises granular particles that are confined between two rigid plates. The top plate is subjected to a normal force and driven by a shearing velocity. A positive shear-rate dependence of granular friction, known as velocity-strengthening, exists between the granular and shearing plate. To understand the origin of the dependence of frictional sliding, we treat the granular system as a complex network, where granular particles are nodes and normal contact forces are weighted edges used to obtain insight into the interiors of granular matter. Community structures within granular property networks are detected under different shearing velocities in the steady state. Community parameters, such as the size of the largest cluster and average size of clusters, show significant monotonous trends in shearing velocity associated with the shear-rate dependence of granular friction. Then, we apply an instantaneous change in shearing velocity. A dramatic increase in friction is observed with a change in shearing velocity in the non-steady state. The community structures in the non-steady state are different from those in the steady state. Results indicate that the largest cluster is a key factor affecting the friction between the granular and shearing plate.     

Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

The governing equation for the finite element analysis of the panel flutter of composite plates including structural damping is derived from Hamilton's principle. The first order shear deformable plate theory has been applied to structural modelling so as to obtain the finite element eigenvalue equation. The unsteady aerodynamic load in a supersonic flow is computed by using the linear piston theory. The critical dynamic pressures for composite plates have been calculated to investigate the effects of structural damping on flutter boundaries. The effects are dependent on fiber orientation because flutter mode can be weak or strong in the fiber orientation of composite plates. Structural damping plays an important role in flutter stability with low aerodynamic damping but would not affect the flutter boundary with high aerodynamic damping.     

Impulse response of an infinitely long thick strip plate

This paper is a study of the dynamic response of an infinitely long thick strip plate subjected to an impulsive load. The plate is simply supported along the edges and resting on an elastic foundation. The problem is studied on the basis of a plate theory in which the effects of rotatory inertias and shear deformations are retained. Governing equations are solved by applying the methods of the Laplace transform with respect to time and the Fourier transform with respect to a longitudinal space variable. Dynamic coefficients (maximum dynamic displacement/static displacement, maximum dynamic bending moment/static bending moment) are calculated numerically for plates subjected to a step line load and shown graphically for various values of the parameters included.     

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.     

A new lateral shearing interferometer for precision surface measurement

A new lateral shearing interferometer is proposed for precision surface measurement. In this shearing interferometer, a novel shear generator made of a single birefringence crystal plate is utilized. The shear adjustment is realized through the change of angle at which tested wavefront is incident into the crystal plate. By changing the orientation of the principal section of the plate, the generator can adjust the shearing direction. With the incident beam being circularly polarized, the generator can equalize the intensities of two shearing beams to make a good contrast interference pattern. The interferometer is simple and compact in terms of mechanism and has a complete common optical path structure. Phase shifting can be realized conveniently. The interferometer is insensitive to external vibrations and environmental disturbances, and hence has good stability and reliability with high measurement accuracy. To examine the performance of the proposed interferometer, experimental testing was conducted. High accuracy and repeatability are demonstrated.     

Transverse Vibration and Stability Analysis of Circular Plate Subjected to Follower Force and Thermal Load

Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed . B ased on the thin plate theory in involving the variable temperature, the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established. Then, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the generalized eigenvalue under three different boundary conditions are calculated. In this case, the change curve of the first order dimensionless complex frequency of the circular plate subjected to the follower force in the different conditions with the variable temperature coefficient and temperature load is analyzed. The stability and corresponding critical loads of the circular plate subjected to follower force and thermal load with simply supported edge, clamped edge and free edge are discussed. The results provide theoretical basis for improving the dynamic stability of the circular plate.     

Investigation of interference field phase distribution with a lateral shearing interferometer

Problems of investigating the interference field are discussed. An investigation method is suggested which is based on using an imperfect plane-parallel plate lateral shearing interferometer for comparing aberrations in the arms of the two-beam interferometer which generates the interference field. It is demonstrated that equipartition of interference field fringes can be analyzed to an accuracy of λ/100 which exceeds the manufacturing accuracy of the lateral shearing interferometer.     

On flow of an elastico-viscous fluid past an oscillating porous plate

A solution for the flow problem of an elastico-viscous fluid (Walters liquid B) due to an oscillating infinite porous plate with constant suction has been obtained. It has been observed that the magnitude of velocity decreases with increase in suction velocity. The shearing stress increases with increase in suction.We thank the referee for his useful suggestions.     

剪切散斑干涉术的无损检测研究

剪切散斑干涉术用于复合材料的光学无损检测具有较宽的加载范围,便于实现缺陷的全场记录,防止漏检。本文从理论上推导了剪切散斑干涉条纹(等应变条纹)的强度分布,并证明随着加载量的增大,条纹变密的程度较全息干涉条纹(等位移条纹)缓慢。加之,剪切散斑干涉条纹灵敏度具有可调性,加载范围大为加宽。实验观察与理论分析一致。