On the reciprocity relationship between direct field radiation and diffuse reverberant loading

This analysis is concerned with the derivation of a "diffuse field" reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection. Such a relationship has been derived previously for connections described by a single degree of freedom. In the present work it is shown that the diffuse-field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries. Furthermore, it is shown that the existing diffuse-field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom. The present work has application to (i) the calculation of the diffuse field response of structural-acoustic systems modeled by Finite Elements, Boundary Elements, and Infinite Elements; (ii) the general calculation of the Coupling Loss Factors employed in Statistical Energy Analysis (SEA); and (iii) the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries (a generalized "boundary" approach to SEA).     

基于声压场描述的扩散声场多自由度互易原理研究

应用于复杂结构中频声振分析的扩散场多自由度互易原理采用位移变量描述系统,实质为弹性波场互易原理,应用于声波场时会造成模型自由度数不必要的增加。建立基于声压描述的扩散声场受挡模型,利用声辐射模态描述扩散声场中结构的表面受挡声压;据此提出基于声压描述的扩散声场多自由度互易原理,发现扩散声场中结构表面受挡声压的互谱矩阵与该结构在自由空间中振动辐射声波的声阻矩阵成正比。该互易原理与传统的单自由度互易原理表达形式相似,但适用于任意自由度结构。该互易原理可用于扩散声场中复杂结构的表面受挡声压的自谱及相关分析,仿真研究表明当边界元网格尺寸小于声波波长的1/6(线性单元)或1/3(二次单元)时,数值解与理论解完全吻合。      

Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation

A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two recordings of a wave field at different receiver locations at the free surface. Unlike in other derivations, which apply to diffuse wave fields in random media or irregular finite bodies, no assumptions are made about the diffusivity of the wave field. In a second version, it is assumed that the wave field is diffuse due to many uncorrelated sources inside the medium.     

A structural mechanics approach for the phonon dispersion analysis of graphene

A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector.     

Non-diffuseness of vibration fields in ribbed plates

This paper presents numerical simulations of structural intensity in a rib-reinforced plate, investigating the diffuseness. Many prediction models of building and structural acoustics, such as statistical energy analysis or energy flow methods, assume the vibrational wave fields to be diffuse. However, the diffuseness assumption is not always valid. One such example is a rib-reinforced plate typically found in a lightweight floor with wooden joists. Other examples can be found in aircraft and ship structures. The structural intensity of a ribbed plate is computed at low to mid frequencies using the Fourier sine expansion of the transverse displacement of the plate. Hamilton's principle is used in combination with thin plate theory and Euler beam theory. The model takes into account interactions between components. The Fourier sine modes are re-formulated as plane waves in a radial coordinate system, which can express the structural intensity in terms of the angular component of the modes. In the simulations, ensemble averages and rain-on-the-roof excitations are used. The numerical results show that the structural intensity varies significantly as the angle of propagation changes and cannot be assumed to form a diffuse field.     

Response variance prediction in the statistical energy analysis of built-up systems

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.     

振动结构耦合动刚度的间接逆子结构辨识方法

耦合动刚度是复杂耦合结构振动分析中的一个非常关键的参数,其精确辨识对于结构振动特性评估与控制设计非常重要。为将逆子结构动态分析方法推广应用于振动结构耦合动刚度辨识,在建立了耦合动刚度逆子结构分析模型后,提供一种通过频率响应函数反演耦合结构动刚度的方法——间接逆子结构辨识法。最后采用单点和三点耦合二级子结构“质量-胶垫”实验模型,验证了逆子结构辨识方法的理论有效性,包括辨识精度的误差分析.实验与理论分析结果的一致性表明,与现有的直接逆子结构动态分析方法相比,该方法较常规辨识方法具有适用条件范围更宽、辨识精度更高的优点,可以提高工程结构参数的辨识精度,具有更好的工程应用可行性与有效性,为逆子结构动态分析方法辨识振动结构耦合动刚度进一步提供理论依据。      

Lasing without inversion due to cooling subsystem

The new possibility of inversionless lasing is discussed. We have considered the resonant interaction of a two-level system (TLS) with photons and the adiabatic interaction with an ensemble of Bose particles. It is found out that a TLS with equally populated energy levels amplifies the coherent light with Stokes-shifted frequency. This becomes possible as photon emission is accompanied by Bose particles excitation. The energy flow from the TLS to the photon subsystem is realized due to the Bose subsystem being at finite temperature and playing the cooler role. The advantage of this new lasing principle is discussed. It is shown that lasing conditions strongly differ from conventional ones. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamic buckling of columns by biaxial moments and uniform end torque

A new concept of uniform torque is proposed for the dynamic torsional buckling analysis. A dynamic biaxial moments and torque buckling theory is presented for analysis in structural dynamics. Second-order effects of the axial force, biaxial moments and torque are considered. The consistent natural boundary moments and forces are derived to ensure the symmetry of the dynamic stiffness matrix in fulfilling the requirement of the reciprocal theorem and conservation of energy. The exact dynamic stiffness matrix is obtained using power series expansion. The derivatives of the analytical dynamic stiffness matrix with respect to different loading and geometric parameters are derived explicitly for sensitivity and continuation analyses. Generally distributed axial force can be analyzed without difficulty. It is pointed out that non-uniform sections may not be handled by power series due to the convergent problem. Global pictures for all kinds of linear dynamic buckling are given for the first time. The methodology is based on finite element formulation and therefore it can easily be extended to analyze structural frames.     

Semi-analytical finite element analysis of elastic waveguides subjected to axial loads

Predicting the influence of axial loads on the wave propagation in structures such as rails requires numerical analysis. Conventional three-dimensional finite element analysis has previously been applied to this problem. The process is tedious as it requires that a number of different length models be solved and that the user identify the computed modes of propagation. In this paper, the more specialised semi-analytical finite element method is extended to account for the effect of axial load. The semi-analytical finite element method includes the wave propagation as a complex exponential in the element formulation and therefore only a two-dimensional mesh of the cross-section of the waveguide is required. It was found that the stiffness matrix required to describe the effect of axial load is proportional to the mass matrix, which makes the extension to existing software trivial. The method was verified by application to an aluminium rod, where after phase and group velocities of propagating waves in a rail were computed to demonstrate the method.     

Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations

For the spatially coupled free vibration analysis of thin-walled composite I-beam with symmetric and arbitrary laminations, the exact dynamic stiffness matrix based on the solution of the simultaneous ordinary differential equations is presented. For this, a general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing Vlasov's assumption. Next, the equations of motion and force–displacement relationships are derived from the energy principle and the first order of transformed simultaneous differential equations are constructed by using the displacement state vector consisting of 14 displacement parameters. Then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force–displacement relationships. In addition, the finite-element (FE) procedure based on Hermitian interpolation polynomials is developed. To verify the validity and the accuracy of this study, the numerical solutions are presented and compared with analytical solutions, the results from available references and the FE analysis using the thin-walled Hermitian beam elements. Particular emphasis is given in showing the phenomenon of vibrational mode change, the effects of increase of the modulus and the bending–twisting coupling stiffness for beams with various boundary conditions.     

SH-wave propagation and resonance phenomena in a periodically layered composite structure with a crack

This paper presents a dynamic analysis of time-harmonic plane SH-waves propagating in periodically multilayered elastic composites with a strip-like crack. The total wave field in the multilayered elastic structure is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation containing the crack-opening-displacement. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. The paper focuses on resonant and non-resonant regimes of anti-plane wave motion in a stack of elastic layers weakened by a single strip-like crack and wave localization in the vicinity of the crack. The scattered extra displacement induced by the presence of the crack is investigated in detail for both situations of high and low contrast in material properties. Numerical results for the average crack-opening-displacement, the transmission coefficient, the stress intensity factor and the average energy flow are presented and discussed to reveal wave resonance and localization phenomena within the band-gaps and the pass-bands.     

强红外场作用下BCl3振动态传能动力学研究

基于文献[1],本工作在较高泵浦激光能通量范围,测量并研究了BCl₃分子振动激发v_3吸收谱及时间演变,观察了v₃激发弛豫的几种能量转移过程,以及对泵浦激光能量BCl₃气压等参数的依赖关系。表明泵浦光脉冲产生一个振动态非热分布的系综,转动能量转移对引起这种非热分布有重要作用。用简化碰撞动力学模型讨论了BCl₃振动激发吸收谱的演变过程,得到振动态再分布的简单关系;Pτ_v-v≌c/K′(T_v,T₀,q)和等效振动温度、平均吸收光子数的分析表达式,与实验结果定性地符合。 关键词：     

Wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam

The wave propagation in a periodic elastic-piezoelectric axial-bending coupled beam is investigated in this paper by considering the mechanical–electrical coupling behavior. The strain energy and kinetic energy of each sub-cell are first formulated to extract the dynamic stiffness matrices, and then the compatibility and continuity conditions at the interface between the adjacent cells are utilized to derive the transfer matrix that governs the propagation of the wave along the periodic piezoelectric beam. By employing the Lyapunov exponent method, the dynamic behaviors of the periodic beam structure are evaluated with different base beam materials, dimension ratios, piezoelectric constants and elastic stiffness. The results indicate that regardless of the length ratio, there exist certain frequency intervals, where the width and magnitude of the prominent stop band of the aluminum beam with periodic piezoelectric patches are always broader and larger than those of the steel base system. In addition, as the thickness ratio decreases, the location of the stop band tends to move toward a higher frequency. Numerical studies also demonstrate that different piezoelectric constants and elastic stiffness affect the characteristics of wave propagation in completely different fashions. The investigation in the present study provides basic guidelines to design periodic elastic-piezoelectric laminate structures in order to achieve desired filtering characteristics.     

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.     

Analysis of energy distribution in a loaded quantum anharmonic oscillator in a wide temperature range

Analysis of the energy distribution in an ensemble of quantum anharmonic oscillators loaded by an external force in a wide temperature range (from T = 0) is carried out using a general approach based on the virial theorem. At T = 0, anharmonic effects are observed: a linear variation of zero-point energy of an oscillator under loading (energy decrease during extension and increase under compression) and a linear variation of the average kinetic and potential energy components. At high temperatures, at which the dynamics of the oscillators becomes classical, the anharmonic effects are manifested in a linear variation in the vibrational energy and a linear variation in the average kinetic and potential energy components upon an increase in force. Mutually compensating variation in the average kinetic and potential energy components of the internal dynamic energy of an oscillator (energy redistribution upon loading) takes place both at low and high temperatures.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Radiofrequency electrode vibration-induced shear wave imaging for tissue modulus estimation: a simulation study

Quasi-static electrode displacement elastography, used for in-vivo imaging of radiofrequency ablation-induced lesions in abdominal organs such as the liver and kidney, is extended in this paper to dynamic vibrational perturbations of the ablation electrode. Propagation of the resulting shear waves into adjoining regions of tissue can be tracked and the shear wave velocity used to quantify the shear (and thereby Young's) modulus of tissue. The algorithm used utilizes the time-to-peak displacement data (obtained from finite element analyses) to calculate the speed of shear wave propagation in the material. The simulation results presented illustrate the feasibility of estimating the Young's modulus of tissue and is promising for characterizing the stiffness of radiofrequency-ablated thermal lesions and surrounding normal tissue.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."