Pitch change during reverberant decay

The natural frequencies and mode shapes of a number of box beams are calculated by using the finite element displacement method. The structures are considered as assemblages of plates, and in general it is necessary to consider both the in-plane and transverse motion of the plates. A method of representing these two types of motion in the analysis of the vibrations of box beams is presented. A number of box beams of varying sectional parameters are analysed as systems of plates and the results compared with the predictions of Euler and Timoshenko beam theories. The comparisons show that for short beams constructed of thin plates, the new method can successfully represent the localized plate deformations, which cannot be described by beam theory.     

Flexural waves on narrow plates

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories, and isotropic plates are considered for Mindlin's theory with and without rotational inertia. A frequency-dependent Young's modulus for beams or strips of finite width is suggested, although the form of the correction to the modulus is not unique and depends on the theory used. The sign of the correction for the Kirchhoff theory is opposite to that for the Mindlin theory. These results indicate that the different plate and beam theories can produce quite distinct behavior. This divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural, or torsional, modes on narrow plates. The four classical theories predict limiting wave speeds as the plate width vanishes, but the values are different in each case. The deviations can be understood in terms of torsional waves and how each theory succeeds, or fails, in approximating the effect of torsion. Dispersion equations are also derived, some for the first time, for the flexural edge wave in each of the four "engineering" theories.     

POWER FLOW ANALYSIS OF REINFORCED BEAM-PLATE COUPLED STRUCTURES

A power flow analysis method was developed to predict the vibrational responses of reinforced beam-plate coupled structures in frequencies ranging from medium to high. This analysis method was successfully applied to simply supported rectangular plates reinforced with multi-parallel beams by utilizing the power flow coupling relationships at the beam-plate junctions and the zero intensity conditions at the plate edges. Through numerical simulations, the power flow energy density and intensity fields of two different plates, consisting of single beam and eight beams, were compared with those of classical displacement solutions, and they show good agreement in terms of the global decay and the attenuation patterns of the energy density.     

平板式螺旋相位板的设计与应用

传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件,由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数.本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板.通过理论分析与数值模拟,发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束,而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节.为了实际应用的需要,可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束.这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.     

基于高级统计能量分析的周期加筋板振动特性研究

统计能量分析(statistical energy analysis, SEA)是复杂耦合系统中、高频动力学特性计算的有力工具. 本文以波传播理论和SEA的基本原理为基础, 研究周期加筋板中弯曲波传播特性. 分析了周期结构的频率带隙特性和加强筋对板上弯曲波的滤波特性对SEA计算结果的影响规律, 发现经典SEA由于忽视了加筋板中物理上不相邻子系统间存在的能量隧穿效应, 而导致响应预测结果产生最高近 40 dB的误差. 为了解决这一问题, 本文应用高级统计能量分析(advanced statistical energy analysis, ASEA)方法, 考虑能量在不相邻子系统间的传递、转移和转化的物理过程, 从而大幅提高子系统响应的预测精度, 将误差在大部分频段降低至小于5 dB. 设计了模拟简支边界条件的加筋板振动测试实验装置, 实验测试结果与有限元结果符合较好, 对理论模型进行了验证.     

加筋板结构声导纳的面接触判据

通过采用有限元方法建立加筋板模型,计算不同边界条件下具有不同加筋形式的薄板在不同加载面尺寸下的导纳差值,进而得到与频率相关的加筋板面接触判据,揭示了加筋板面导纳和点导纳之间的相关关系,得到了“点”和“面”是否能够等效处理的面接触判据。进一步通过考察薄板的不同加筋形式和加载面形状以及加筋板的速度分布,可以发现:在不加筋、单加筋和十字加筋3种情况中不加筋平板的面接触判据最严格,而十字加筋板的面接触判据最宽松;单加筋板的速度差值与导纳差值的计算结果较为吻合;单加筋板的加载面沿垂直加筋方向的边长越长导纳差值越大。      

Prediction of airborne sound transmission across a timber–concrete composite floor using Statistical Energy Analysis

This paper concerns the development and experimental validation of prediction models using Statistical Energy Analysis (SEA) to calculate the airborne sound insulation of a timber–concrete composite floor. The complexity in modelling this floor is due to it having (1) a multilayer upper plate formed from concrete and Oriented Strand Board (OSB), (2) multiple types of rigid connector between the upper plate and the timber joists and (3) a resiliently suspended ceiling. A six-subsystem model treats the concrete–OSB plate as a single subsystem and three different five-subsystem models treat the combination of concrete, OSB and timber joists as a single orthotropic plate subsystem. For the orthotropic plate it is suggested that bending stiffnesses predicted using the theories of Huffington and Troitsky provide a more suitable and flexible approach than that of Kimura and Inoue. All SEA models are able to predict the weighted sound reduction index to within 2 dB of the measurement. The average difference (magnitude) between measurements and predictions in one-third octave bands is up to 4 dB. These results confirm that SEA can be used to model direct transmission across relatively complex floor constructions. However, this requires the inclusion of measured data in the SEA model, namely the dynamic stiffness of the resilient isolators and the cavity reverberation time.     

Negative refraction and dispersion phenomena in platonic clusters

We consider the problem of Gaussian beam scattering by finite arrays of pinned points, or platonic clusters, in a thin elastic plate governed by the biharmonic plate equation. Integral representations for Gaussian incident beams are constructed and numerically evaluated to demonstrate the different behaviours exhibited by these finite arrays. We show that it is possible to extend the scattering theory from infinite arrays of pinned points to these finite crystals, which exhibit the predicted behaviour well. Analytical expressions for the photonic superprism parameters p, q and r, which are measures for dispersion inside the crystal, are also derived for the pinned plate problem here. We demonstrate the existence of negative refraction, beam splitting, Rayleigh anomalies, internal reflection, and near-trapping on the first band surface, giving examples for each of these behaviours.     

A note on the dynamical behaviour of uniform beams having open channel section

Theoretical predictions of the natural frequencies and mode shapes of beams depend on the choice of beam theory (Bernoulli-Euler [1], Timoshenko [1], Vlasov [2, 3], Wagner-Kappus [4]) adopted in the mathematical model. The various theories are developed from differing assumptions. Alternatively, the finite element approach may be used and this, in its way, depends on the mathematical modelling of the structure. Many writers have investigated the dynamic characteristics of coupled lateral bending and twisting in uniform beams of channel section, and the purpose of this paper is to bring much of the relevant data together. Wherever possible, a comparison is made between theoretical predictions and measured natural frequencies.     

Stop-pass behavior of acoustic waves in a 1D fractured system

This study examines the dispersion and the stop-pass band behavior of acoustic waves propagating across periodically spaced and non periodically spaced parallel fractures. Laboratory ultrasonic wave measurements performed on a stack of synthetic fractures (identical steel plates with roughened interfaces) and numerical propagator matrix simulations show spectra with distinct stop-pass band structures that develop with decreasing fracture stiffness. To understand the physics behind these observations, an exact dispersion equation for wave propagation through an infinite series of equally spaced fractures is derived using displacement-discontinuity boundary conditions to model the constitutive behavior of the fractures and Floquet's (Bloch's) theory for the periodic boundary conditions. Both the measured and numerically simulated stop-pass band structures show good agreement with the theoretical predictions. Furthermore, the theory reveals that the left boundary of the stop-bands contains information about the fracture stiffness, suggesting the possibility of determining the stiffness of the parallel fractures from seismic waves. This paper also discusses the effects of fractured systems with random distributions of fracture spacings and stiffnesses on the stop-pass band structures of seismic waves in fractured rock.     

Point and transfer mobility of point-connected ribbed plates

The work reported in this paper addresses the problem of structure-borne sound transmission between vibrating sources and ribbed-plate receiver structures. Vibrating sources, such as pumps, motors, fans, etc., transmit vibro-acoustic power, causing noise complaints by occupants in cars, trains, aircraft, buildings and/or material fatigue and damage. The transmission process is complicated in that sources transmit power through several contacts and by up to six components of excitation at each contact. The structure-borne sound power is a function of source activity, source mobility and receiver mobility, and all three quantities must be known to some degree. For non-homogeneous receiver structures, such as thin-plate cavity constructions or lightweight framed constructions, the sheathing plates are typically fastened to the framing members using bolts, screws or spot-welded joints. Hence the resulting system is a point-connected ribbed plate structure and the receiver mobility is expected to vary significantly with position. Since measured receiver data seldom is available for prediction purposes, a method of estimating the point and transfer mobility of point connected ribbed plates is required. In this paper, an approximate approach, based on substitution forces, is described. The model uses infinite beam and infinite plate behaviour as input quantities. Estimates of point and transfer mobility are compared with measured results using a timber joist floor construction as an example.     

相位片角向衍射产生拉盖尔-高斯光束的实验研究

设计了一种角向分布的相位片,利用离子束刻蚀技术加工成0和π二级的相位片.利用角向衍射理论对相位片的衍射场分析表明,衍射场为拓扑指数相反的两束拉盖尔-高斯光束的叠加场.用直径为4 mm的近平行光照射相位片,获得径向指数为零,拓扑荷相反的叠加拉盖尔-高斯光场.采用较大孔径的光束入射时,仍为拓扑荷相反的两束光的叠加,但径向指数会发生变化. 关键词： 信息光学 拉盖尔-高斯光束 相位片 离子束刻蚀     

Interfacial stress concentrations in FRP-damaged RC hybrid beams

This paper presents a careful theoretical investigation into interfacial stresses in damaged RC beams strengthened with externally bonded FRP plate. The model is based on equilibrium and deformations compatibility requirements in and all parts of the strengthened beam, i.e. the damaged concrete beam, the FRP plate and the adhesive layer. The theoretical predictions are compared with other existing solutions. This research is helpful for the understanding on mechanical behaviour of the interface and design of the FRP-damaged RC hybrid structures.     

Natural frequencies and mode shapes of flexural vibration of plates: laser-interferometry detection and solutions by Ritz's method

This paper presents an experimental and theoretical study of flexural symmetric vibration modes of a linear elastic plate. A laser interferometer is used as detector of the free vibration of a rectangular parallelepiped-shaped aluminium plate. The vibration spectrum gives the lowest natural frequencies of the sample. Assumption that the vibration of the plates may be described by some approximate theories is proven to be inconsistent. The Ritz method, with products of powers of the co-ordinates as basis functions, is applied to obtain the lowest flexural natural frequencies. Three-dimensional solutions are obtained, unlike those provided by simpler theories. The experimental results are compared with the numerical predictions and a good agreement is obtained. Finally, forced motion is applied to the centre of the plate and the out-of-plane and in-plane displacement components for the first symmetric mode are measured. A good fit of the calculated values to the experimental values is found.     

Adhesive fracture of heterogeneous interfaces

We have studied the effect of interface heterogeneity on fracture, at both local and global scales. The single cantilever beam adhesion test was used to investigate interfacial fracture between polycarbonate plates and an elastic/fragile epoxy adhesive. Two surface treatments were applied to a (given) polycarbonate plate giving zones of strong and weak adhesion parallel to the crack direction. Calculated fracture energies differed from those expected from a simple rule-of-mixtures. A perturbation method, proposed by Rice, was used and results compared with crack fronts observed in situ. The technique was applied successfully but the difference in values of stress intensity factor between the zones was found substantially different from the experimental value. In an attempt to explain discrepancies, specimens with discontinuous crack fronts (adhesive and/or plates severed along the strong/weak adhesion frontier) were tested. Good agreement was found with the rule-of-mixtures predictions raising questions about the role of crack front continuity in load transfer.     

Structural waveguide behaviour of a beam–plate system

Structures which have a constant cross-section normal to a longitudinal axis can be considered as waveguides in which vibration can propagate in the form of various waves in the longitudinal direction. The dynamic behaviour of such systems can be found by using a Fourier transform approach in terms of wavenumbers in the longitudinal direction. Analytical solutions are available for simple, infinitely long waveguides, whereas for more complex waveguides numerical approaches have been developed using finite element techniques to describe the cross-section. In the present paper an analytical Fourier transform approach is used to find the dynamic behaviour of a system consisting of two parallel beams coupled by a plate, when a point force is applied to one of the beams. Multiple waves occur in the longitudinal direction, the number of waves depending on the number of modes of the equivalent cross-section. However, the motion of the driven beam is shown to be dominated by the contribution from only one or two waves at each frequency, these having wavenumbers closest to that of the uncoupled beam. The motion of the plate is also shown to be dominated by these wavenumbers for excitation on the beam. Experimental results are obtained on beam–plate–beam systems with identical and non-identical beams, which show good agreement with the predictions. In particular, these confirm that the plate response is dominated by waves with wavenumbers in the beam direction that follow those of the excited beam.     

Estimation of structural wave numbers from spatially sparse response measurements

A method is presented for estimating the complex wave numbers and amplitudes of waves that propagate in damped structures, such as beams, plates, and shells. The analytical basis of the method is a wave field that approximates response measurements in an aperture where no excitations are applied. At each frequency, the method iteratively adjusts wave numbers to best approximate response measurements, using wave numbers at neighboring frequencies as initial estimates in the search. In comparison to existing methods, the method generally requires far fewer measurement locations and does not require evenly spaced locations. The number of locations required by the method scales with the number of waves that propagate in the structure, whereas the number of locations required by existing methods scales with the minimum wavelength. In addition, the method allows convenient inclusion of the analytic relationships between wave numbers that exist for flexural vibrations of beams and plates. Advantages of the method are illustrated by an example in which a beam is excited by a transverse force at one end. Using analytic data and experimental measurements, the method produces a wave field that matches response measurements to within 1 percent. One interesting feature of the new method is that, when applied to analytic data, it supplies more robust wave number estimates using responses at unevenly spaced locations.     

Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary.     

基于自适应遗传算法部分相干光整形位相板的优化设计

基于自适应遗传算法,对部分相干光整形的相位板做了优化设计.以高斯-谢尔模型(GSM)光束为例,推导出远场光强的解析表达式.最优化设计的位相板能将GSM光束变为平顶光束.数值计算例表明空间相干性对光束整形效果的影响.与已有工作相比较说明自适应遗传算法用于部分相干光整形的优点. 关键词： 自适应遗传算法 光束整形 部分相干光 位相板