Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations

An analytical method based on the modal expansion technique was developed to predict the vibro-acoustic response of both unidirectionally and bidirectionally stiffened flat panel. This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance. Numerical results for the dynamic and acoustic responses are compared with finite element method (FEM) and boundary element (BEM) results for stiffened panel with complex and eccentrically shaped stiffeners subject to point force excitation. A theoretical prediction of the transmission loss (TL) is also compared with laboratory measurements conducted on flat panels representing aircraft models as well as with hybrid statistical energy analysis (SEA)-FEM periodic model. The results confirm that the stiffened panel has the same acoustic response as the skin without stiffeners at frequencies where the structural wavelengths are equal to the spacing between the stiffeners. In addition, the transmission loss is lowered by the presence of the stiffeners at some particular region of frequencies below the critical frequency with respect to the unstiffened panel.     

Optical measurement on dynamic buckling behavior of stiffened composite panels under in-plane shear

The buckling behavior and failure mode of a composite panel stiffened by I-shaped stringers under in-plane shear is studied using digital fringe projection profilometry. The basic principles of the dynamic phase-shifting technique, multi-frequency phase-unwrapping technique and inverse-phase technique for nonlinear error compensation are introduced. Multi-frequency fringe projection profilometry was used to monitor and measure the change in the morphology of a discontinuous surface of the stiffened composite panel during in-plane shearing. Meanwhile, the strain history of multiple points on the skin was obtained using strain rosettes. The buckling mode and deflection of the panel at different moments were analyzed and compared with those obtained using the finite element method. The experimental results validated the FEM analysis.     

基于波数域直接求解法的正交加筋板声辐射研究

为了研究正交加筋板的声辐射问题,基于波数域直接求解法,建立了研究正交加筋板声辐射特性的理论模型。先利用傅里叶变换法求解周期结构的声振理论模型,得到波数域中关于结构响应的无限大耦合代数方程组,采用数值方法将其截断成有限项求解,结合稳相法便可快速获得远场辐射声压。该方法对单向和正交加筋板的预测结果与现有文献中的理论结果取得了良好的吻合,验证了理论模型的准确性和可靠性;并进一步通过数值算例研究了作用点位置,加强筋间距及平板厚度对结构声辐射特性的影响。      

Acoustic emission localization in complex dissipative anisotropic structures using a one-channel reciprocal time reversal method

This paper presents an imaging method for the localization of the impact point in complex anisotropic structures with diffuse field conditions, using only one passive transducer. The proposed technique is based on the reciprocal time reversal approach (inverse filtering) applied to a number of waveforms stored into a database containing the experimental Green's function of the structure. Unlike most acoustic emission monitoring systems, the present method exploits the benefits of multiple scattering, mode conversion, and boundaries reflections to achieve the focusing of the source with high resolution. Compared to a standard time reversal approach, the optimal refocusing of the back propagated wave field at the impact point is accomplished through a "virtual" imaging process. The robustness of the inverse filtering technique is experimentally demonstrated on a dissipative stiffened composite panel and the source position can be retrieved with a high level of accuracy in any position of the structure. Its very simple configuration and minimal processing requirements make this method a valid alternative to the conventional imaging Structural Health Monitoring systems for the acoustic emission source localization.     

超高速撞击声发射信号在载人航天器加筋结构的传播特性实验研究

为研究超高速撞击声发射信号经过载人航天器加筋结构后的传播规律,分别在平板结构和加筋结构上模拟高速撞击实验,利用传感器阵列采集高速撞击产生的声发射信号。结合小波和傅里叶分析方法从板波模态、频域以及时域三方面分析加筋结构对声发射信号传播特性的影响,并研究成坑和穿孔损伤模式下声发射信号的传播规律。结果表明:加筋板中的信号高频部分比平板中高频部分能量少,筋体对信号高频部分有滤波效果。加筋结构受高速撞击产生穿孔损伤时,S0模态声波的能量增多。研究成果可为载人航天器结构的高速撞击感知与定位技术提供有利参考。      

Vibro-acoustic response of orthogonally stiffened panels: The effects of finite dimensions

This paper investigates the effects of finite dimensions on the vibro-acoustic response of orthogonally stiffened panels. Three types of excitations are considered: acoustical excitation, point force excitation and random excitation by a turbulent boundary layer. In each case, a spatially windowed periodic model is compared with a Rayleigh-Ritz model where the modes of the un-stiffened panel are used as the basis functions. The latter model accounts for the reflected wave field generated at the boundaries by assuming that the panel is simply supported. On the contrary, the windowed periodic model only accounts for finiteness on sound radiation (the assumption of an infinite periodic structure is used to calculate the panel response). Numerical studies show that when the bending wavelength becomes comparable or smaller than the stiffener spacing, the periodic model is able to reproduce the results obtained with the Rayleigh-Ritz model. To complement the study, the developed models are compared with numerical simulations (finite element method) and with experimental results.     

Decentralized control of sound radiation using iterative loop recovery

A decentralized model-based control strategy is designed to reduce low-frequency sound radiation from periodically stiffened panels. While decentralized control systems tend to be scalable, performance can be limited due to modeling error introduced by the unmodeled interaction between neighboring control units. Since bounds on modeling error are not known in advance, it is difficult to ensure the decentralized control system will be robust without making the controller overly conservative. Therefore an iterative approach is suggested, which utilizes frequency-shaped loop recovery. The approach accounts for modeling error introduced by neighboring control loops, requires no communication between subsystems, and is relatively simple. The control strategy is evaluated numerically using a model of a stiffened aluminum panel that is representative of the sidewall of an aircraft. Simulations demonstrate that the iterative approach can achieve significant reductions in radiated sound power from the stiffened panel without destabilizing neighboring control units.     

Identification of structural systems with full characteristic matrices under single point excitation

The aim of “System Identification” is to determine modal and system properties of structural systems. This is while in “Damage Detection”, the identification of system characteristic matrices is as important as or even more important than the identification of frequency characteristics. Because of various constraints – i.e. difficulties in force excitation of structures due to their large size, geometry, and location – in practice only single excitation and partial measurement, at selected degrees of freedom, is possible. In this paper, a single dynamic load was applied to identify a structural system only along one of the degrees of freedom of the structure. Further, responses corresponding to a few degrees of freedom were also measured. To identify a system with this sort of restricted information, a new approach was introduced enabling identification of the structure?s parameters of mass, damping and stiffness. Taking into account the significant effect of noise reduction in improving system identification accuracy levels, a noise reduction technique was also proposed. The accuracy of the method was also assessed against noise level and location of single excitation. It was shown that as noise level increases, identification errors will also increase (less than 3.5 percent). It was further observed that applying single force at the first storey of the flexural structure would yield the lowest error levels in the identification results. Later, the method?s efficiency and precision were examined through the application of a “closed loop solution” to a six-storey flexural structure, and a four-span Pratt truss. The obtained results showed that the proposed method could act as an effective model in identification of system properties.     

REMOTE IDENTIFICATION OF IMPACT FORCES ON LOOSELY SUPPORTED TUBES: PART 2—COMPLEX VIBRO-IMPACT MOTIONS

In a previous paper, techniques were presented, based on response measurements at remote locations, for the experimental identification of the flexural wave-guide propagation parameters and for recovering the impact forces. Numerical simulations and experiments were presented, for simpleisolated impacts. Those basic results showed that such an inverse problem can be successfully attempted, and a good agreement was found between direct measurements and the remotely identified impact forces. However, when subject to flow-induced vibrations, the loosely supported tubes display verycomplex rattlingmotions—with the impact-generated primary waves completely immersed in countless wave reflections travelling between the tube boundaries. As a consequence, the multiple-impact patterns of tube-support interaction are much more difficult to identify than isolated force spikes. In this paper, the authors move a step further towards the identification of impacts for realistic tube vibrations. To deal with complex vibro-impact regimes, a signal-processing technique is presented for separating the multiple wave sources, which uses the information provided by a limited number of vibratory transducers. This technique can be applied to both non-dispersive and dispersive waves and is therefore useful for all kinds of beam motions. Such a method is instrumental in separating the primary impact-generated flexural waves from severe background contamination. This enables the straightforward identification of complex rattling forces at a loose support. Extensive results are given in order to assert the numerical conditioning of the technique used to identify the impact forces, the optimal location of the transducers used in the identification procedure, and the sensitivity of the identification method to noise contamination. Overall, results are quite satisfactory, as the complex identified impact forces compare favourably with direct measurements.     

Assessing impact force localization by using a particle swarm optimization algorithm

This paper focuses on the inverse problem regarding force localization in the case of impacts not concentrated at a point but which occur on elastic beams. Following the identification approach proposed to solve this problem and which is based on the reciprocity theorem, the impact location characteristics were determined by using particle swarm optimization algorithm. To eliminate numerical trouble due to the trivial solutions appearing in this formulation, the fitness function was customized by introducing a set of weighting coefficients. Four different formulations of the fitness function were considered and their performances with regards to the number of sensors used and their positions were analyzed. They enabled a selection of the best combination of weighting coefficients to be used in the context of an impact force localization process based on the particle swarm optimization technique. Three sensors were found to be required and comparison with a genetic algorithm has revealed the effectiveness of the proposed method in terms of accuracy and computational time.     

抛物型方程的演化参数识别方法

给出了一种利用演化计算方法求解微分方程中的参数识别类型反问题的方法。该方法把参数识别问题转化为泛函的优化问题用演化算法来求解,指定待定参数的函数类形式,用遗传算法(Genetic Algorithms)来演化待求参数的最优估计值,并将该方法运用于线性扩散方程和拟线性对流扩散反方程反问题的数值模拟中。     

碳纤维-泡沫铝夹芯板低速冲击响应

为研究夹芯结构的低速冲击响应,以碳纤维(T700)/环氧树脂复合材料层合板为上下面板,以闭孔泡沫铝为芯层,模拟夹芯板落锤冲击时的损伤演化过程。复合材料层合板采用三维实体单元建模,基于有限元软件ABAQUS中的用户子程序VUMAT,引入三维Hashin失效准则模拟复合材料的损伤破坏;采用二次应力准则,Cohesive单元模拟黏结层的层间失效;闭孔泡沫铝芯层采用3D Voronoi细观模型建模。分析复合材料夹芯结构在落锤冲击下的损伤起始、损伤扩展和最终破坏模式,通过锤头的接触力、位移、夹芯板的内能、后面板的最大位移研究夹层结构的能量吸收情况及抗冲击特性,得出了在质量保持不变的情况下,5种芯层相对密度和厚度的耦合关系中的最优设计是芯层相对密度15.0%,厚度为10 mm,为满足实际工程中的需求提供了设计依据。     

A state space force identification method based on Markov parameters precise computation and regularization technique

A time domain force identification approach for linear system is proposed. This approach can found a highly precise force identification model within the scope of general computer precision while it does not cost much computing time. Although the force identification model is accurate, the force identification process, like other inverse methods, is still ill-posed due to the inversion process and the white noise in measured structural responses. The singular value decomposition is used to reveal the intrinsically matter of the ill-posedness of force identification problem and a regularization technique is utilized to deal with this issue. Finally, the proposed method with the aid of regularization technique is successfully applied to identify the input forces in two numerical simulations.     

Identification of dynamic loading on a bending plate using the Virtual Fields Method

This paper aims at identifying local dynamic transverse forces and distributed pressures acting on the surface of a thin plate, from its measured vibration response. It is related to previous work by other authors on the so-called Force Analysis Technique but uses a different formulation. The paper first presents the theoretical developments based on the Virtual Fields Method and then, numerically simulated data are processed to validate the identification algorithm. Finally, experimental data are used. Both mechanical point load excitation, and distributed acoustic excitation of a bending panel are considered. The force reconstruction results are very satisfactory and the low computational times together with the simple implementation make the Virtual Fields technique attractive for this type of problem.     

Aero-thermo-mechanical characteristics of imperfect shape memory alloy hybrid composite panels

A nonlinear finite element model is provided to predict the static aero-thermal deflection and the vibration behavior of geometrically imperfect shape memory alloy hybrid composite panels under the combined effect of thermal and aerodynamic loads. The nonlinear governing equations are obtained using Marguerre curved plate theory and the principle of virtual work taking into account the temperature-dependence of material properties. The effect of large deflection is included in the formulation through the von Karman nonlinear strain-displacement relations. The thermal load is assumed to be a steady-state constant-temperature distribution, whereas the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The Newton-Raphson iteration method is employed to obtain the nonlinear aero-thermal deflections, while an eigenvalue problem is solved at each temperature step and static aerodynamic load to predict the free vibration frequencies about the deflected equilibrium position. Finally, the nonlinear deflection and free vibration characteristics of a composite panel are presented, illustrating the effects of geometric imperfection, temperature rise, aerodynamic pressure, boundary conditions and shape memory alloy fiber embeddings on the panel response.     

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.     

Sound radiation from shear deformable stiffened laminated plates

Sound radiation from shear deformable stiffened laminated plates is studied theoretically. The equations of motion for the composite laminated plate are derived on the basis of the first-order shear deformation plate theory. Two sets of parallel stiffeners interact with the laminated plate only through the normal line forces. By using the Fourier wavenumber transform and the stationary phase method, the far-field sound pressure is described analytically. Sound pressure given by the first-order shear deformation plate theory and the classical thin plate theory is compared, and the differences of sound pressure are shown in the high frequency range for an isotropic plate. Sound pressure and the transverse displacement spectra are presented to illustrate the effects of force location, stiffeners and angle-ply layers. Sound radiation from symmetric and antisymmetric composite plates with multiple loadings is also investigated.     

A computational method for wave propagation from a point load in an anisotropic material

One approach which is employed to solve dynamic point load problems in plates and laminates is to take integral transforms to reduce the governing equations to a system of ordinary differential equations with respect to the depth variable. The solution of this system leads to expressions for the transforms of the displacement and stress components at any level in the plate and the transient response at any location may then be recovered by inversion of the multiple transforms. The formal transform inversion involves a double infinite integral but by making a change of variable this may be replaced by an infinite integral associated with a line source and a finite integral with respect to the orientation of the line. A first attempt at applying this approach to obtain the point load response of quasi-isotropic fibre composite laminate led to a non-causal predicted signal. This paper deals with an investigation of this proposed method applied to the simpler model problem of wave propagation in a two-dimensional anisotropic medium. Results are obtained for two different time histories of point loads, namely: a delta function; and a single period of a sine function. In the case of the delta function source a comparison is made with the analytic solution and the errors arising from the numerical approach are discussed. Graphs are also presented showing the non-causal contributions to the overall response which arise at individual angles of orientation of the line source.     

Comparison of restoring force models for the identification of structures with hysteresis and degradation

When subjected to events such as earthquakes, engineering structures typically exhibit a nonlinear and hysteretic behaviour with stiffness and strength degradations. Though a reliable evaluation of safety conditions should take into account the nonlinear dynamic and evolutionary nature of the structural response, the experimental identification of a nonlinear behaviour under dynamic and seismic loading is, to date, an open problem. The present research aims at evaluating the potential of different restoring force models for simulating the seismic response of hysteretic structural systems, with special emphasis on the two main problems encountered when applying this approach to full-scale structures under intense excitation: (a) a markedly time-dependent behaviour; (b) need to compare among different restoring force models, either expressed in a parametric or polynomial form. In particular, polynomial models will be formulated both in terms of restoring force and its derivative, in order to present a comprehensive discussion of different strategies. The nonlinear identification technique employed in this paper is required to account for a time-dependent behaviour. In fact, in presence of degradation or any other time-varying characteristics, instantaneous identification certainly constitutes an enhancement of the classical restoring force based approach, and may as well provide checks on the consistency of the assumed models.     

Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading

The dynamic instability characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element analysis. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The method of Hill's infinite determinants is applied to determine the dynamic instability regions. Numerical results are presented to study the effects of various parameters, such as static load factor, aspect ratio, boundary conditions, stiffening scheme and load parameters on the principal instability regions of stiffened plates using Bolotin's method. The results show that location, size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability region.