Heterogeneous elastic solids: a mixed homogenization-rigidification technique

A homogenization technique for heterogeneous elastic solids made up by a matrix containing inclusions modelled as rigid in the limit, is proposed. It is shown that the approach can cause considerable simplifications with respect to the use of standard homogenization procedures. The case of a masonry panel set across on an opening is analysed by applying the proposed technique and some numerical results are given. They are compared first with those obtained by considering the panel as a heterogeneous body and, in turn, by using standard homogenization.     

Design of an Active Noise Control System Using a Distributed Actuator

A distributed acoustic actuator for active noise control, consisting of a piezoelectric PVDF film, bonded at each side of a carrier structure, is simulated and built. The piezoelements are driven in anti-phase, resulting in a bending motion of the actuator, and thus in the necessary out-of-plane displacement for sound radiation. An analytical model for the acoustic actuator is derived, relating the actuator's displacement to the applied voltage, taking into account the influence of the piezoelectric film on the actuator's stiffness. The model is used to optimise the specifications for the piezoelectric film and the carrier structure, resulting in the highest sound power output in a frequency range from 30–500 Hz. An analytical model for the behaviour of a double panel partition is derived. The analytical model is combined with the model for the acoustic actuator, describing an actively controlled double panel partition with a distributed acoustic actuator integrated in the cavity. A controller is added to the system to control the sound power transmitted through the double panel partition. Simulation results show that a substantial increase of transmission loss can be achieved in the low frequency region (30–500 Hz) with this configuration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical-experimental method for elastic parameters identification of a composite panel

A hybrid numerical-experimental approach to identify elastic modulus of a textile composite panel using vibration test data is proposed and investigated. Homogenization method is adopted to predict the initial values of elastic parameters of the composite, and parameter identification is transformed to an optimization problem in which the objective function is the minimization of the discrepancies between the experimental and numerical modal data. Case study is conducted employing a woven fabric reinforced composite panel. Three parameters (E₁₁, E₂₂, G₁₂) with higher sensitivities are selected to be identified. It is shown that the elastic parameters can be accurately identified from experimental modal data.     

The forced transversal vibrations and vibroheating of a cylindrical bimorph panel made from a dissipative piezomaterial

The forced vibrations and dissipative heating of a bimorph cylindrical shell are considered. The shell is made from a dissipative piezomaterial and subjected to a harmonic potential difference. The edges of the panel are assumed hinged and perfectly heat-insulated. The dissipative properties of the material are considered on the basis of the concept of complex characteristics. The analystical solution of this problem is found. A finite-element method is developed to study the dynamic behavior and vibroheating temperature of bimorph shells, which are made from viscoelastic material and subjected to harmonic loading. The results of the analyses of the electromechanical vibrations of the panel performed by the finite-element method and by analytically solving the problem are compared. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 89–97, Mary, 2000     

In-plane modal testing of a free isotropic rectangular plate

In-plane vibration modes of an aluminum panel were experimentally identified from frequency response tests. Responses were measured on the panel edges and at selected locations on the panel surface. The measurements on the surface were made by attaching accelerometers oriented parallel to the panel plane. Resonance frequencies, relative damping ratios and mode shapes were established for the lowest 12 in-plane modes found in the frequency range between 1600 and 7000 Hz. A damping ratio of less than 0.05 percent of critical damping is proved to be valid for the aluminum panel. A finite element software was used to calculate 12 corresponding theoretical in-plane eigenfrequencies and mode shapes. An outline for a nondestructive procedure is suggested to estimate the input data for the elastic constants of an isotropic plate model. Two of the modes were used in analogy with the flexural vibration of beams and plates. The modes illustrate the deformation pattern including shear deformations, through the thickness, for the bending modes of thick beams or plates. The Rayleigh-Timoshenko theory also was used for the calculation of these two eigenfrequencies.     

Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

An analytic solution is obtained to describe the vibrations and dissipative heating of a simply supported infinite cylindrical panel under periodic normal loads moving over its surface with a constant velocity. Special attention is focused on resonant vibrations, which result in the most intensive dissipative heating. It is additionally assumed that the material of the panel is viscoelastic, its properties are independent of temperature, and Poisson’s ratio is real. The influence of thickness, radius of curvature, load velocity, and viscoelastic properties on the thermal state of the panel is analysed against the thermal state of the plate__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 100–109, April 2005.     

Thermoplastic damage of a stretched plane caused by a moving energy source

A thermoplastic stress and strain calculation is made to analyze the energy distribution around an energy source traveling in a prestretched panel. The technique of finite element is applied such that the motion of the energy source is discretized into a finite number of time increments. Remeshing of the grid pattern is carried out for every time increment.The energy source may represent a welding torch or laser beam with a high local intensity that causes the material to deform beyond its elastic limit and experience permanent damage by evaporation. This reduces the local stiffness and can lead to global instability. The failure analysis is based on the application of the strain energy density theory which is into the incremental theory of thermoplasticity. The specific example involves examining the experimental data of a 7075-T651 aluminum panel subjected to tensile loading. The energy source is assumed to have a finite radius and travels along the line of symmetry being normal to the direction of applied tension. The possible failure location is predicted for each time increment by analyzing the fluctuation of the local strain energy density field. A critical point corresponding to incipient fracture is found. The panel has a width of 45.72 cm and length of 55.88 cm. The prediction is consistent with the experimental observation.     

Nonlinear stability analysis of a sandwich shallow cylindrical panel with orthotropic surfaces

In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthotropic surfaces. The critical point is determined and the postbuckling behaviour of the panel is studied.     

Temperature-dependence of acoustic fatigue life for thermal protection structures

Acoustic fatigue life evaluation is essential for thermal protection structures due to the severe thermo-acoustic load in service. A study on temperaturedependence of acoustic fatigue life for a C/SiC panel is presented in this paper. Effects of temperature on both the structural responses and the S-N curves are investigated. The Dirlik method is adopted to predict the fatigue life of a C/SiC panel at three different temperatures respectively. Significant differences are observed from the results of numerical simulations between the fatigue lives of the panel in the three cases. The temperature-dependence of acoustic fatigue life of a C/SiC panel is verified, and fatigue test of the material needs to be more attentively performed.     

Nonlinear dynamics analysis of a two-dimensional thin panel with an external forcing in incompressible subsonic flow

Based on the potential theory of incompressible flow and the energy method, a two-dimensional simply supported thin panel subjected to external forcing and uniform incompressible subsonic flow is theoretically modeled. The nonlinear cubic stiffness and viscous damper in the middle of the panel is considered. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin method. The stability of the fixed points of the panel system is analyzed. The regions of different motion types of the panel system are investigated in different parameter spaces. The rich dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincaré maps and maximum Lyapunov exponents based on carefully numerical simulations.     

工业广场保护煤柱开采的相似材料模拟研究

本文用相似材料模拟原理对辽源矿务局西安立井煤柱一采区开采进行了相似模型模拟，作了材料配比方面的研究；同时进行了位移和应力两种观测。     

Stability of a thin panel with added elements in a supersonic gas flow

Thin elastic panels subjected to compression in the median plane and to supersonic gas flow are considered. An element is attached to the panel by an elastic spring and linear dashpot. The stability of the initial planar state of the panel is studied as a function of the main control parameters—such as the gas velocity and membrane force—and the parameters of the attached element. The evolution of the stability regions in the control-parameter plane is considered. Special attention is paid to compound bifurcation points and stabilization islets. Institute of Machine Science, Russian Academy of Sciences, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3–10, December, 1999.     

超音速气流中受热壁板的稳定性分析

采用Galerkin方法建立二维壁板的非线性气动弹性运动方程,用一阶活塞理论模拟壁板 受到的气动力. 基于李雅普诺夫间接法分析了平壁板的稳定性,得到了壁板失稳的边界 曲线;采用牛顿迭代法分析了壁板的屈曲变形,进而分析了后屈曲状态下壁板的稳定性; 在时域中分析了后屈曲状态下壁板的颤振边界. 分析结果表明,为了保证计算精度, 在二维壁板的静态失稳及过屈曲变形分析中,至少要取二阶谐波模态;在平壁板的超音速颤 振(动态失稳)边界分析中至少应取四阶模态. 还对壁板的温升,壁板长厚比、壁板密 度和气流马赫数作了无量纲变参分析,研究了这些参数的变化对壁板稳定性的影响规律. 研 究中发现,当气流速压较低时壁板一般会稳定在低阶谐波模态的屈曲变形位置,但是如果系 统出现多个渐近稳定的不动点,即使作用在壁板上的气流速压很低,壁板也有可能在较低速 压下发生二次失稳型颤振.     

Thermo-piezoelectric effects on the postbuckling of axially-loaded hybrid laminated cylindrical panels

IntroductionCompositelaminatedcylindricalpanelhasbeenusedextensivelyasastructuralconfiguration,mainlyintheaerospaceindustry .Oneoftherecentadvancesinmaterialandstructuralengineeringisinthefieldofsmartstructureswhichincorporatesadaptivematerials.Bytakingadvantageofthedirectandconversepiezoelectriceffects,piezoelectriccompositestructurescancombinethetraditionalperformanceadvantagesofcompositelaminatesalongwiththeinherentcapabilityofpiezoelectricmaterialstoadapttotheircurrentenvironment.Therefore…     

To a formulation of the flutter problem for a conical shell with a small apex angle

The well-known piston theory formula for the excess aerodynamic pressure is used in the majority of works devoted to the panel flutter of shells. In this paper a refined expression for the excess pressure is proposed to take into account the irregularity of undisturbed flow parameters. The case of moderate supersonic velocities is studied in detail. The critical velocity problem is reduced to a new eigenproblem in the panel flutter theory.     

Stochastic non-linear flutter of a panel subjected to random in-plane forces

—An analysis of non-linear flutter of a simply-supported panel exposed to supersonic gas flow and random in-plane forces is presented for two- and three-mode interactions. A first order quasi-steady state aerodynamic piston theory is used to model the aerodynamic loading. The Fokker-Planck equation is used to derive a general moment equation for two- and three-mode interactions. For stability analysis the moment equation is consistent and the mean square stability boundaries of the equilibrium are obtained in terms of the system parameters. The stability boundaries reveal common features to those predicted by the deterministic theory of panel nutter. For the non-linear response the moment equation is found inconsistent and a cumulant-neglect closure is used by setting cumulants of fifth and sixth orders to zero. This first order non-Gaussian closure is carried out to solve for the response statistics in terms of the air-to-plate mass ratio, aerodynamic pressure, modal damping, and in-plane random force spectral density. It is found that the non-Gaussian solution yields higher levels for the response statistics than those obtained by the Gaussian solution. The inclusion of more modes results in a reduction of the response levels and expands the stability region.     

Homogenization of thick periodic plates: Application of the Bending-Gradient plate theory to a folded core sandwich panel

In a previous paper from the authors, the bounds from Kelsey et al. (1958) were applied to a sandwich panel including a folded core in order to estimate its shear forces stiffness (Lebée and Sab, 2010b). The main outcome was the large discrepancy of the bounds. Recently, Lebée and Sab (2011a) suggested a new plate theory for thick plates – the Bending-Gradient plate theory – which is the extension to heterogeneous plates of the well-known Reissner–Mindlin theory. In the present work, we provide the Bending-Gradient homogenization scheme and apply it to a sandwich panel including the chevron pattern. It turns out that the shear forces stiffness of the sandwich panel is strongly influenced by a skin distortion phenomenon which cannot be neglected in conventional design. Detailed analysis of this effect is provided.     

The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity

Theoretical analysis of the nonlinear vibration effects on the sound absorption of a panel absorber and sound transmission loss of a panel backed by a rectangular cavity is herein presented. The harmonic balance method is employed to derive a structural acoustic formulation from two-coupled partial differential equations representing the nonlinear structural forced vibration and induced acoustic pressure; one is the well-known von Karman??s plate equation and the other is the homogeneous wave equation. This method has been used in a previous study of nonlinear structural vibration, in which its results agreed well with the elliptic solution. To date, very few classical solutions for this nonlinear structural-acoustic problem have been developed, although there are many for nonlinear plate or linear structural-acoustic problems. Thus, for verification purposes, an approach based on the numerical integration method is also developed to solve the nonlinear structural-acoustic problem. The solutions obtained with the two methods agree well with each other. In the parametric study, the panel displacement amplitude converges with increases in the number of harmonic terms and acoustic and structural modes. The effects of excitation level, cavity depth, boundary condition, and damping factor are also examined. The main findings include the following: (1)?the well-known ??jump phenomenon?? in nonlinear vibration is seen in the sound absorption and transmission loss curves; (2)?the absorption peak and transmission loss dip due to the nonlinear resonance are significantly wider than those in the linear case because of the wider resonant bandwidth; and (3)?nonlinear vibration has the positive effect of widening the absorption bandwidth, but it also degrades the transmission loss at the resonant frequency.     

Stiffened Composite Panels with a Stress Concentrator Under in-Plane Compression

The in-plane compressive strength of a stiffened thin-skinned composite panel with a stress concentrator is examined. Two possible in-plane failure mechanisms are investigated. The first one is near-surface instability at the edge of the cutout, where high stress gradients are expected because of the stress concentration and the thickness heterogeneity of the laminated skin. Analytical 3D formulas allowing simple parametrical investigation of the phenomenon under consideration are derived. The second failure mechanism is fiber microbuckling in 0°-plies. An equivalent crack model is used to predict the compressive strength of a multidirectional composite laminate. How a stiffener affects the compressive strength of the thin-skinned panel with a hole is studied for both mechanisms. Experimental and predicted values of the critical load are in good agreement.