An improved mixed numerical-experimental method for stress field calculation

In this work a numerical-experimental method is used to study the dynamic behavior of an aluminum plate subjected to a small mass impact. The out-of-plane displacements, due to transient bending wave propagation, were assessed for successive time instants, using double pulse TV-holography, also known as pulsed ESPI. The experimental setup and the image processing methods were improved to allow the calculation of the plate transient stress field. Integral transforms are used to obtain the strain fields from spatial derivatives of displacements noisy data. A numerical simulation of the plate transient response was carried out with FEM Ansys^®. For this purpose a PZT transducer was used to record the impact force history, which was inputted in the numerical model. Finally, the comparisons between numerical and experimental results are presented in order to validate the present methodology.     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

高速气流作用下能量加载金属蜂窝板数值模拟

数值模拟研究了高速气流作用下能量加载金属蜂窝板温度场。针对金属蜂窝典型单元,构造了蜂窝核细观导热数值计算分析模型。采用流固耦合计算方法,使用两相流模型和凝固/熔化模型模拟气流对烧蚀物的剥蚀,较完整地模拟了能量加载金属蜂窝板的物理变化过程,计算得到了金属蜂窝板的温度分布以及烧蚀形貌。结果表明两相流方法能够较全面地模拟能量加载金属蜂窝板过程中的对流换热、熔化与凝固过程以及金属液体在气流冲刷下的动力学过程,能获得较为合理的物理图像。     

Structural partitioning of complex structures in the medium-frequency range. An application to an automotive vehicle

In a recent work [Journal of Sound and Vibration 323 (2009) 849-863] the authors presented an energy-density field approach for the vibroacoustic analysis of complex structures in the low and medium frequency ranges. In this approach, a local vibroacoustic energy model as well as a simplification of this model were constructed. In this paper, firstly an extension of the previous theory is performed in order to include the case of general input forces and secondly, a structural partitioning methodology is presented along with a set of tools used for the construction of a partitioning. Finally, an application is presented for an automotive vehicle.     

A fractional calculus approach to nonlocal elasticity

If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen nonlocal elastic model. Aim of the present paper is to provide a mechanical interpretation to this nonlocal fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; the static, kinematic and constitutive equations are presented and the governing fractional differential equation highlighted. Two numerical procedures to solve the fractional equation are finally implemented and applied to study the strain field in a finite bar under given edge displacements.     

Recording receptance of flat plates by holographic interferometry

In the study of mechanical vibrations of structures, the complex ratio of the displacement of the structure at a point divided by the force input to the structure at the same point or a different point is called receptance. This ratio is usually recorded in magnitude and phase by using piezoelectric transducers attached to the structure. This paper describes a study of the feasibility of recording the displacement of a square cantilevered plate not just at one point but over the entire plate surface, by using holographic interferometry. For purposes of comparison of the two techniques a piezoelectric transducer was attached to a free corner of the plate and the displacements at that point were recorded over the frequency range of interest. Although the dynamic range of the holographic technique was found to be somewhat limited, it was found that it is quite feasible to calculate at least the magnitude of the receptance by recording displacements holographically. Since the holographic fringe formation is an integrated effect in time, it was not possible to record the phase by holographic means. The displacements recorded at the corner of the plate by the two methods agreed very well.     

Influence of wall vibrations on the behavior of a simplified wind instrument

The issue of the influence of wall vibrations on the behavior of wind instruments is still under debate. The mechanisms of vibroacoustic couplings involved in these vibrations are difficult to investigate, as fluid-structure interactions are weak. Among these vibroacoustic interactions, the present study is focused on the coupling between the internal acoustic field and the mechanical behavior of the duct. For this purpose, a simplified single reed instrument consisting of a brass tube connected to a clarinet mouthpiece has been studied. A theoretical model of coupling between the plane inner acoustic wave and mechanical modes is developed and suggests that in order to obtain measurable effects of wall vibrations, the geometrical parameters of the studied tube have to be unusual compared to that of real instruments. For a slightly oval-shaped and very thin brass tube, it is shown theoretically and experimentally that a coupling between the inner plane acoustic wave and ovalling mechanical modes occurs and results in disturbances of the input impedance, which can slightly affect the tone color of the sound produced. It is concluded that the reported effects are unlikely to occur in real instruments except for some organ pipes.     

Free vibration analysis of piezoelectric coupled circular plate with open circuit

A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer.     

Periodic shunted arrays for the control of noise radiation in an enclosure

This work presents numerical and experimental investigations of the application of a periodic array of resistive-inductive (RL) shunted piezoelectric patches for the attenuation of broadband noise radiated by a flexible plate in an enclosed cavity. A 4×4 lay-out of piezoelectric patches is bonded to the surface of a rectangular plate fully clamped to the top face of a rectangular cavity. Each piezo-patch is shunted through a single RL circuit, and all shunting circuits are tuned at the same frequency. The response of the resulting periodic structure is characterized by frequency bandgaps where vibrations and associated noise are strongly attenuated. The location and extent of induced bandgaps are predicted by the application of Bloch theorem on a unit cell of the periodic assembly, and they are controlled by proper selection of the shunting circuit impedance. A coupled piezo-structural-acoustic finite element model is developed to evaluate the noise reduction performance. Strong attenuation of multiple panel-controlled modes is observed over broad frequency bands. The proposed concept is tested on an aluminum plate mounted in a wooden box and driven by a shaker. Experimental results are presented in terms of pressure responses recorded using a grid of microphones placed inside the acoustic box.     

Defect detection and localization in orthotropic wood slabs by inversion of dynamic surface displacements

The nondestructive evaluation inversion and generalized force-mapping techniques developed and demonstrated for isotropic thin plates by Bucaro et al. [(2004). "Detection and localization of inclusions in plates using inversion of point actuated surface displacements," J. Acoust. Soc. Am. 115, 201-206] are extended to the case of orthotropic plates. The extended techniques are applied to a finite-element generated numerical database for point excited wooden slabs with and without an internal defect at 5 and 10 kHz. Operation of the original isotropic algorithms on the wood surface displacements is shown to fail in recovering the uniform elastic parameters or in detecting and locating the defect. The new algorithms based on the wave equation for a thin, orthotropic plate successfully convert the surface displacements on the uniform wooden slab to elastic parameter maps which serve to detect and localize the defect in the flawed plate. The results, particularly at the higher frequency, indicate that the onset of failure in the thin plate approximation impacts both the inversion and the generalized force-mapping accuracy. However, in this case use of the inversion algorithm to obtain modified wave equation coefficients followed by operation of the force-mapping algorithm with these new parameters inserted is shown to successfully mitigate this effect.     

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Acoustic waves generated by a laser point pulse in a transversely isotropic cylinder

A three-dimensional (3D) model is presented to predict the acoustic waves generated by a laser point pulse in a transversely isotropic cylinder. The Fourier series expansion and the two-dimensional Fourier transform are introduced to calculate the 3D transient response under either the ablation or the thermoelastic generation. The presented physical model and the numerical inverse scheme are applied to a fiber reinforced composite cylinder with a strong anisotropy. Experimental radial displacements of the cylinder surface are detected by the laser ultrasonic technique and analyzed by the ray trajectories for both generation regimes. Corresponding theoretical displacements are obtained numerically and compared to the experimental signals. Good agreement is found between theoretical and experimental results. The focusing effects that anisotropy gives rise to are observed in both theory and experiment under either regime.     

A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses

This paper presents the evaluation of a method to cancel rigid body displacements that can be introduced when a hole drilling and digital speckle pattern interferometry (DSPI) combined system is used to measure residual stresses. The proposed method is based on a least-square calculation of three correction parameters determined from two evaluation lines located near the edge of the phase map where the displacement field generated by the drilling process is supposed to be negligible. The errors introduced by the method for different residual stress levels and rigid body displacements are analysed using a numerical simulation. An application of the method to experimental data is also presented.     

Acoustic and vibration fields generated by ribs on a fluid-loaded panel,I: Plane-wave problems for a single rib

This paper presents an analytical study of the interaction between incident wave fields, and a single rib on a fluid-loaded panel. The panel is modelled as an infinite membrane (with frequency dependent tension to partially simulate the dispersion characteristics of a thin elastic plate), and the incident waves are taken as plane structural or acoustic waves at normal and oblique incidence on the rib. Our principal concern is with the structural wave field transmitted across the rib (in the case of infinite mechanical impedance and finite non-local rib impedance) through the non-specular acoustic field scattered by the panel-plus-rib is also examined. Matched asymptotic expansions are used to construct analytical approximations covering the entire frequency range, advantage being taken of the smallness of a “fluid-loading-at-coincidence” parameter. The analytical results recover numerical results obtained elsewhere in appropriate regions of parameter space, complement them by providing simple approximations in those regions (typically of rapid variation or of heavy fluid loading) where numerical methods are difficult to implement, and reveal the physical aspects of fluid loading in effecting energy transfer across ribbed structures.     

New achievements and perspectives of optical methods in experimental solid mechanics

Because of the modern achievements in measuring techniques as well as in experimental methods, especially the optical methods, and because of the advances in data recording and the evaluation procedures, combining experimental and numerical methods, optical experimental methods have experienced a kind of renaissance, thus enabling the analysis of new and much more complex problems. Beside classical and conventional fields now, for example, the influence of non-linear problems such as physical and geometrical non-linearity as well as the rheological response of a material can be taken into consideration. As measurements only yield information on displacements or their derivatives, advanced theories and proper algorithms based on these numerical procedures are derived to calculate the finally wanted informations on the stress state. The presented statement will demonstrate the objectives and perspectives of modern experimental techniques and their inalienability to meet the extended requirements by modern technical developments. It will be shown how it is possible to analyse, for example, non-linear mechanical problems according to recent perceptions in hybrid techniques.     

Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions

In this paper, we study the free vibration of multilayered magneto-electro-elastic plates under combined clamped/free lateral boundary conditions using a semi-analytical discrete-layer approach. More specifically, we use piecewise continuous approximations for the field variables in the thickness direction and continuous polynomial approximations for those within the plane of the plate. Group theory is further used to isolate the nature of the vibrational modes to reduce the computational cost. As numerical examples, two cases of the lateral boundary conditions combined with the clamped and free edges are considered. The non-dimensional frequencies and mode shapes of elastic displacements, electric and magnetic potentials are presented. Our numerical results clearly illustrate the effect of the stacking sequences and magneto-electric coupling on the frequencies and mode shapes of the anisotropic magneto-electro-elastic plate, and should be useful in future vibration study and design of multilayered magneto-electro-elastic plates.     

Piezoelastic vibrations of composite Reissner-Mindlin-type plates

Linear vibrations of Reissner-Mindlin-type composite plates in the presence of piezoelectric eigenstrains are studied. Piezoelectric eigenstrains are produced by applying electrical loads to piezoelectric layers embedded in or attached to substrate layers. The influence of the mechanical field upon the electric field is taken into account in the modelling, ending up with electro-mechanically coupled field equations and boundary conditions, which describe the mechanical and the electrical dynamic response of the plate.The mechanical displacements are approximated by means of the kinematic hypothesis of Hencky. The electric potential distribution is assumed to be composed of a superposition of a linear and a parabolic distribution in the thickness direction. The linear part accounts for the electric potential difference between the electrodes of the totally electroded piezoelectric layers. The parabolic part is considered in order to take into account the influence of the mechanical field upon the electric potential by means of the direct piezoelectric effect. A weak two-dimensional formulation of the three-dimensional field equations is obtained by utilizing mechanical and electrical variational principles. This formulation is characterized by resultants of stress and electric displacement. The electro-mechanically coupled behaviour comes into play by means of the constitutive relations. In case the electric potential difference is not prescribed, it can be calculated from a relation, which connects the total electric charge and the electric potential difference to each other. Because this relation is obtained from the Gauss law of electrostatics, requiring integration with respect to the area of the electrode, non-local constitutive relations for the plate are found. The non-local constitutive relations bring a new aspect into the theory of plates. An analysis for the practically interesting one-dimensional case of composite, piezoelectric plates in cylindrical motion completes the paper.     

Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part II: Parametric studies

The possible usage of nanoplates in transporting of nanovehicles encouraged the author to propose some nonlocal plate models in the companion paper where the nanovehicle (i.e., moving nanoparticle) was modeled by a moving point load by considering its friction with the upper surface of the nanoplate. In this paper, a comprehensive parametric study is carried out to study the effects of length to thickness ratio of the nanoplate, small-scale parameter, and velocity (or angular velocity) of the moving nanoparticle on dynamic response of nonlocal Kirchhoff, Mindlin, and higher-order plates subjected to a moving nanoparticle. Herein, dynamic response of the nanoplate covers both time histories and dynamic amplitude factors of the in- and out-of-plane displacements. The capabilities of various nonlocal plate models in predicting the displacement field caused by friction and mass weight of the moving nanoparticle are then explored through various numerical analyses for two cases: (i) the moving nanoparticle moves along a diagonal of the nanoplate; (ii) the moving nanoparticle orbits on an ellipse path whose center is coincident with the nanoplate's center. The obtained results indicate that due to the incorporation of small-scale effect into shear strain energy of the nanoplate, an appropriate nonlocal plate model should be used. The results show that the choice of the nanoplate model to use relies on the small-scale parameter, geometrical properties of the nanoplate, and velocity of the moving nanoparticle.     

Elastic wave field computation in multilayered nonplanar solid structures: a mesh-free semianalytical approach

Multilayered solid structures made of isotropic, transversely isotropic, or general anisotropic materials are frequently used in aerospace, mechanical, and civil structures. Ultrasonic fields developed in such structures by finite size transducers simulating actual experiments in laboratories or in the field have not been rigorously studied. Several attempts to compute the ultrasonic field inside solid media have been made based on approximate paraxial methods like the classical ray tracing and multi-Gaussian beam models. These approximate methods have several limitations. A new semianalytical method is adopted in this article to model elastic wave field in multilayered solid structures with planar or nonplanar interfaces generated by finite size transducers. A general formulation good for both isotropic and anisotropic solids is presented in this article. A variety of conditions have been incorporated in the formulation including irregularities at the interfaces. The method presented here requires frequency domain displacement and stress Green's functions. Due to the presence of different materials in the problem geometry various elastodynamic Green's functions for different materials are used in the formulation. Expressions of displacement and stress Green's functions for isotropic and anisotropic solids as well as for the fluid media are presented. Computed results are verified by checking the stress and displacement continuity conditions across the interface of two different solids of a bimetal plate and investigating if the results for a corrugated plate with very small corrugation match with the flat plate results.