Debonding detection of honeycomb sandwich structures using frequency response functions

A vibration-based non-destructive evaluation (NDE) method is proposed to determine the location and size of debonding in honeycomb sandwich beams. Although most of the existing vibration-based NDE methods need many measurement points, the method proposed here only utilizes the frequency response function (FRF) measured at one point. A parameterized damaged Timoshenko beam model is developed with the method of reverberation-ray matrix (MRRM) for the first time, and combined with the genetic algorithm (GA) to inverse the damage parameters from the measured FRF. The detection of a honeycomb sandwich beam can be divided into two steps: (1) identifying the equivalent elastic moduli and other parameters of the intact sandwich beam. (2) Identifying the debonding location and size of the damaged sandwich beam with the predetermined parameters. It is demonstrated experimentally that the method can inverse damage parameters with acceptable precision.     

Structural synthesis of sandwich beams with outer layers of box-section

It is proved by model measurements that, for sandwich beams constructed from two rectangular tubes and a damping layer glued between them, the following calculation methods can be applied. Static bending and shear stresses as well as deflections of simply supported beams may be calculated by Allen's formulae for sandwich beams with flexurally stiff faces. The first eigenfrequency and the loss factor can be determined by using the diagrams given in reference [1]. For the loss factors Ungar's formula gives a suitable approximation. A minimum cost design procedure is presented for a sandwich beam with constant cross-section. The unknown dimensions of the cross-section are determined which satisfy the design constraints and minimize the material costs. In a numerical example, constraints relating to the maximal dynamic stresses and deflection as well as local buckling of plate elements are considered. In the optimization the backtrack combinatorial discrete programming method is applied. A numerical comparison shows that the material costs of a sandwich beam are lower than those of a homogeneous box one.     

Vibration and stability of sandwich beams with elastic bonding

This paper is a study of the vibration and stability of symmetrical sandwich cantilevers with elastic bonding. The horizontal displacements of the face layer and the core are discontinuous due to the elasticity of the interface bond. The shear traction at the interface is assumed to be proportional to the relative horizontal displacement of the layers. The core layer is subjected to a horizontal (conservative) or tangential (non-conservative) axial force at its free end. It is shown that a symmetrical sandwich beam with elastic bonding has two kinds of vibration modes: i.e., bending modes and longitudinal modes. Numerical results are given for a beam composed of FRP face layers and a syntactic-foam core layer. It is shown that the divergence and the flutter type instability loads, as well as the natural frequency, are affected considerably by the stiffness of the interface bond.     

Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core

In this study, magneto-rheological elastomers (MREs) are adopted to construct a smart sandwich beam for micro-vibration control of equipment. The micro-vibration response of a smart sandwich beam with MRE core which supports mass-concentrated equipment under stochastic support-motion excitations is investigated to evaluate the vibration suppression capability. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of the smart sandwich beam supporting mass-concentrated equipment is developed based on the Galerkin method and random vibration theory. First, the displacements of the beam are expanded as series of spatial harmonic functions and the Galerkin method is applied to convert the partial differential equations of motion into ordinary differential equations. With these equations, the frequency-response function matrix of the beam–mass system and the expression of the velocity response spectrum are then obtained, with which the root-mean-square (rms) velocity response in terms of the one-third octave frequency band can be calculated. Finally, the optimization problem of the complex modulus of the MRE core is defined by minimizing the velocity response spectrum and the rms velocity response of the sandwich beam, through altering the applied magnetic fields. Numerical results are given to illustrate the influence of MRE parameters on the rms velocity response and the response reduction capacity of the smart sandwich beam. The proposed method is also applicable to response analysis of a sandwich beam with arbitrary core characterized by a complex shear modulus and subject to arbitrary stochastic excitations described by a power spectral density function, and is valid for a wide frequency range.     

Flexural effects of sandwich beam with a plate insert under in-plane bending

The local stress concentrations in sandwich beam with a plate insert under in-plane bending are concerned in the study. An improved six-step phase shifting method in digital photoelasticity is employed to calculate the whole-field shear stress.The shear load transfer is realized by shear bands which connect the top and bottom sheet faces through adhesively-bonded interfaces. The plate insert plays a role in load transfer in the sandwich structure, and the fact that debonding might occur at more sites of the interfaces may also leads to the failure of the structure. The local stress concentrations at the insert end change with the load under three-point bending loads, while they remain as the initial residual shear stress under four-point bending loads. The local stress concentration effects generated by the plate insert is essentially caused by the mismatch of elastic properties of the core materials and the irrational geometry of the insert.     

非惯性系下考虑剪切变形的柔性梁的动力学建模

研究非惯性坐标系下考虑剪切变形的柔性梁的动力学建模. 首先借鉴Euler-Bernoulli梁的几何非线性变形模式,考虑了Timoshenko梁弯曲以及剪切变形产生的几何非线性效应对纵向、横向变形位移的影响,在考虑两个方向的变形耦合项后,利用有限元法对柔性梁进行了离散,采用Lagrange方程建立了柔性梁的动力学模型,首次建立了包含变形二次耦合量的Timoshenko梁的动力学方程. 关键词： 非惯性坐标系 剪切变形 柔性梁 动力学建模     

A new rectangular beam theory

A new theory for beams of rectangular cross-section which includes warping of the cross-sections is presented in the present work. By satisfying the shear-free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required. It is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in Timoshenko beam theory provided that for the Timoshenko equation the shear coefficient is taken to be $\text{5}\text{6}$; this value lies within the range of values, 0·822–0·870, appearing in the literature for the beam of rectangular cross-section. Results for two typical static examples are given for both the new theory and Timoshenko beam theory. These results are compared with the solutions of the comparable problems in the linear theory of elasticity. For the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while Timoshenko beam theory underestimates the shear correction term by 20%. For the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution.     

Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories

Dynamic analysis of nanotube structures under excitation of a moving nanoparticle is carried out using nonlocal continuum theory of Eringen. To this end, the nanotube structure is modeled by an equivalent continuum structure (ECS) according to the nonlocal Euler-Bernoulli, Timoshenko and higher order beam theories. The nondimensional equations of motion of the nonlocal beams acted upon by a moving nanoparticle are then established. Analytical solutions of the problem are presented for simply supported boundary conditions. The explicit expressions of the critical velocities of the nonlocal beams are derived. Furthermore, the capabilities of various nonlocal beam models in predicting the dynamic deflection of the ECS are examined through various numerical simulations. The role of the scale effect parameter, the slenderness ratio of the ECS and velocity of the moving nanoparticle on the time history of deflection as well as the dynamic amplitude factor of the nonlocal beams are scrutinized in some detail. The results show the importance of using nonlocal shear deformable beam theories, particularly for very stocky nanotube structures acted upon by a moving nanoparticle with low velocity.     

Radiation force and shear motions in inhomogeneous media

An action of radiation force induced by ultrasonic beam in waterlike media such as biological tissues (where the shear modulus is small as compared to the bulk compressibility) is considered. A new, nondissipative mechanism of generation of shear displacement due to a smooth (nonreflecting) medium inhomogeneity is suggested, and the corresponding medium displacement is evaluated. It is shown that a linear primary acoustic field in nondissipative, isotropic elastic medium cannot excite a nonpotential radiation force and, hence, a shear motion, whereas even smooth inhomogeneity makes this effect possible. An example is considered showing that the generated displacement pulse can be significantly longer than the primary ultrasound pulse. It is noted that, unlike the dissipative effect, the nondissipative action on a localized inhomogeneity (such as a lesion in a tissue) changes its sign along the beam axis, thus stretching or compressing the focus area.     

Transverse vibrations of pre-twisted sandwich beams

A set of equations of motion governing the bending and extensional displacements of a pre-twisted sandwich beam of rectangular cross-section are derived by using Hamilton's principle. The middle viscoelastic core is assumed to deform mainly through the classical shearing mechanism. The eigenvalues and loss factors of simply supported pre-twisted sandwich beams are computed by using the variational method. Analysis of the results revealed that pre-twisting the beam increases the real part of the eigenvalue by as much as 20% while reducing the loss factor by as much as 30 %. The loss factor of very soft, thickcored beams is especially sensitive to even small angles of pre-twist: e.g., a 22· 5° pre-twist may reduce the loss factor by as much as 80%. The effect of pre-twist is, however, shown not to be appreciable for soft, thin-cored beams. In any case, pre-twisting of the beam has a detrimental effect on the maximum loss factor that one can obtain for a specific size of the beam when only the shear parameter of the beam is changed.     

Reply to the comments of M.E. Golmakani and J. Rezatalab,Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates” (by R. Aghababaei and J.N. Reddy,Journal of Sound and Vibration 326 (2009) 277–289), Journal of Sound Vibration, 333 (2014) 3831–3835

Golmakani and Rezatalab [1] suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms. They based their proof on the use of Navier?s method using a sinusoidal-based deflection solution. This insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of Eringen?s model is not correct, as already detailed in the literature (for example, see [2] for beam problems). In fact, the deflection of the nonlocal plate (in the Eringen sense) is larger than the one of the local case, as shown in many papers available in the literature. We prove in this reply to the authors that the Navier?s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution, as compared to exact analytical solution.     

Toughening through multilayering in TiN–AlTiN films

The damage response of columnar multilayers of TiN and AlTiN to Vickers indentation is studied through focused ion beam machining and elastic modelling. Multilayers display an enhanced resistance, which increases with layer refinement, to the multiple fracture modes that appear at high loads in these materials, including edge (nested) cracks and inclined shear cracks. Measurements of layer thickness reveal that multilayers display additional modes of plastic deformation that lead to permanent compression and bending of the film. An elastic model of contact deformation in a bilayer where plasticity is mimicked by greatly enhanced elastic compliance of the film is used to rationalize the trends in crack resistance. It is shown that the enhanced toughness is not due to any increase in the strain capacity (hardness/modulus) of the film material, brought about by multilayering.     

Kink instability of a highly deformable elastic cylinder

When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears catastrophically at its compressed side while the tensile side remains smooth. The critical radius increases linearly with the diameter of the cylinder but remains independent of its material properties such as modulus; the maximum deflection at the location of the kink depends on both the material and geometric properties of the cylinder. The catastrophic dynamics of evolution of the kink depicts propagation of a shear wave from the location of the kink towards the edges signifying that kinking is an elastic response of the material which results in extreme localization of curvature. We have rationalized this phenomenon in the light of the classical Euler's buckling instability in slender elastic rods.     

Vibration of an excitation system supported flexibly on a viscoelastic sandwich beam at its mid-point

A vibration analysis of an excitation system supported flexibly on a three layer sandwich beam is presented in this paper. The flexibly supported excitation system, which is essentially the primary system, consists of a mass, a spring and a dash-pot. The beam is analyzed separately as a continuous system in a classical way and then its dynamic stiffness at the junction point is combined with that of the primary system to obtain the resultant dynamic stiffness, which in turn is used to develop the expressions for the response of the primary system and the transmissibility provided by the whole system. Both response and transmissibility are evaluated for different geometrical and physical parameters of the sandwich beam. The solution to this problem is also obtained by approximating the sandwich beam by a lumped mass supported on a spring and dash-pot. The results in the two cases are compared. Results obtained from an experimental test-rig substantiate the theoretical results.     

Elastic properties of single-layered graphene sheet

An atomistic simulation method is adopted to investigate the elastic characteristics of defect-free single-layered graphene sheet (SLGS). To this end, the equivalent structural beam is employed to model interatomic forces of the covalently bonded carbon atoms. The beam properties are computed by considering the covalent bond stiffnesses. To calculate the Young’s modulus, shear modulus and Poisson’s ratio of the SLGS, the equivalent continuum sheet model is proposed and the effect of chirality on the SLGS elastic properties is examined. It is perceived that there exists a good agreement between the atomistic modeling results and the data available in the literature.     

基于3.5 MeV射频四极质子加速器硼中子俘获治疗装置的束流整形体设计

在硼中子俘获治疗(BNCT)装置中,束流整形体(BSA)的作用是将中子源产生的快中子束流慢化至超热中子能区(0.5 eVE10 keV),并尽可能减弱快中子、热中子和γ射线的成分,同时保证中子的方向性,其设计与优化是BNCT装置设计工作的核心内容之一.本文采用3.5 MeV,10 mA的质子束轰击锂靶,由核反应~7Li(p,n)~7Be产生的中子为源项,针对BSA的慢化体材料和结构、γ屏蔽层和热中子吸收层的厚度等参数进行蒙特卡罗模拟设计与优化.研究发现,采用Fluental和LiF两种慢化材料间隔2 cm层状堆叠的三明治BSA构型,在保证快中子剂量成分(D_f/φ_(epi)),γ剂量成分(D_γ/φ_(epi))和热中子比例φ_(th)/φ_(epi)满足IAEA-TECDOC-1223报告推荐要求的同时,在BSA出口处超热中子注量率优于单独使用Fluental和单独使用LiF的BSA设计.BSA出口处修正的Synder人头几何模型中的剂量分布计算结果显示:上述三明治构型的深度剂量分布与单独使用Fluental材料构型的结果基本相当,优于单独使用LiF构型,表明Fluental和LiF层状堆叠的三明治BSA构型是一种可行的BSA结构.     

Identification of material properties of orthotropic elastic cylinders immersed in fluid using vibroacoustic techniques

A numerical study is presented to show the potential for using vibroacoustic-based experiments to identify elastic material properties of orthotropic cylindrical vessels immersed in fluids. Sensitivity analyses and a simulated inverse problem are shown to quantify the potential for material characterization through the use of acoustic emissions. For comparison purposes, the analyses are also shown with the normal component of the velocity at the surface of the cylinder as the measured response in place of the acoustic pressure. The simulated experiment consisted of an orthotropic cylinder immersed in water with an impact force applied to the surface of the cylinder. The material parameters of the cylinder considered in the analyses were the circumferential and longitudinal elastic moduli, and the in-plane shear modulus. The velocity response is shown to provide sufficient information for characterizing all three moduli from a single experiment. Alternatively, the acoustic pressure response is shown to provide sufficient information for characterizing only the two elastic moduli from a single experiment. The analyses show that the acoustic pressure response does not have sufficient sensitivity to the in-plane shear modulus for characterization purposes.     

非对称夹芯板隔声量的解析计算模型及影响因素

提出了一种计算上下面板非对称的三明治夹芯板隔声性能的方法。通过对非对称夹芯梁表观抗弯曲刚度的计算,得到对应夹芯板随频率变化的表观抗弯刚度,代入4阶的控制方程,应用模态展开法可以方便地计算简支非对称夹芯板的隔声量。对4种定制的3层非对称碳纤维夹芯板进行了理论计算和实验测试对比,在频率范围100~3150 Hz内,计权隔声量误差在3 dB以内。着重分析了面板对称性、芯层剪切模量对隔声性能的影响,发现在夹芯板面密度一定时,芯层剪切模量对夹芯板的隔声性能影响最为显著。当芯层剪切模量较小时,上下面板非对称分布导致吻合频率显著降低,对夹芯板的整体隔声亦不利。     

金属蜂窝夹芯结构抗水下冲击性能

为揭示高强度水下爆炸冲击载荷作用下金属夹芯结构的抗冲击性能,在实验室开展小尺寸水下爆炸加载技术对金属蜂窝夹芯结构性能影响的实验研究。基于实验结果,开展了全尺寸数值模拟金属蜂窝夹芯结构在水下冲击载荷作用下的动态响应和抗冲击性能研究。结果表明,数值模拟、实验和理论模型计算的结果具有良好的一致性。由于蜂窝芯材相对密度对夹芯结构能量耗散方式和载荷传递机制的影响,结构动态响应、失效模式以及抗冲击性能随着冲击强度的变化表现出较为明显的不同。通过抗冲击参数分析,建立了反映金属蜂窝夹芯结构抗冲击性能的结构横向变形、固支反力、透射脉冲和塑性能耗随冲击强度和芯材相对密度变化的结构-载荷-性能量化关系。     

Non-linear vibrations of three-layer beams with viscoelastic cores,II: Experiment

Experimental results are presented for large amplitude, forced motion of damped, three-layer beams. The beams are constructed with a viscoelastic material constrained between stiff, elastic, outer layers. The sandwich beam is axially restrained; therefore large amplitude displacements cause non-linear response. When the beam is forced at one-half of the lateral vibration resonant frequency, superharmonic response occurs. The experiment is briefly described and frequency response characteristics, spatial shapes and a measure of superharmonic response are presented. The results are compared with predictions from a previously developed theory.