Second-order wave interaction with a vertical plate

The second-order interaction of monochromatic water waves with a rigid vertical plate is investigated numerically and experimentally. The plate has a finite width and is projected from one of the side-walls of a wave-tank. This geometry reduces the wave cases to normal incidence but permits a semi-analytical resolution based on eigenfunction expansions. Obtained numerical results are shown to be insensitive to the width of the tank beyond some value, and to converge quickly with the truncation orders of the expansions, in spite of the second-order potential having a logarithmic singularity at the plate edge. Second-order free-surface elevations are compared with values derived from experimental measurements at the BGO-First offshore wave-tank. Good agreement is reported. It is with much pleasure and admiration for his achievements that we dedicate this work to Nick Newman.     

A generalized approach to the mechanics of three-dimensional nonlinear ocean waves

The paper suggests a generalized approach to the analysis of second-order three-dimensional random wave fields that can represent either ocean waves in an undisturbed field or standing ocean waves. A nonlinear stochastic family is introduced that has a linear stationary Gaussian random contribution and a second-order correction exact in a Stokes expansion. This family can describe the nonlinear mechanics of a random wave field. Subsequently, in the considered random ocean field, the nonlinear mechanics of wave groups can be investigated conditional to the occurrence of a very high wave. The free-surface displacement and velocity potential may be obtained, as well as the nonlinear wave velocity and acceleration, for both the stochastic family and the very high wave groups. The results are of interest for the analysis of nonlinear wave kinematics when extreme surface wave events occur and thus for Morison′s wave forces on slender structures.     

Levy-type solution for buckling analysis of orthotropic plates based on two variable refined plate theory

This paper presents closed-form solution for buckling analysis of orthotropic plates using two variable refined plate theory. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions are obtained by applying the state space approach to the Levy-type solution. Comparison studies are performed to verify the validity of the present results. The effects of boundary condition, loading condition, and variations of modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of orthotropic plates are investigated and discussed in detail.     

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.     

Strip theory for underwater vehicles in water of finite depth

This paper addresses the need to know the unsteady forces and moments on an underwater vehicle in finite-depth water, at small enough submergences for it to be influenced by sea waves. The forces are those due to the waves themselves, as well as the radiation forces due to unsteady vehicle motions. Knowledge of these forces and the mass distribution of the vehicle allow solution of the equations of motion at a single-frequency. Since the theory is linear, any incident wave field can be decomposed into the sum of many individual single-frequency sinusoidal waves. The motions due to each frequency component can then be added together to obtain the total predicted vehicle motions. The wave forces are due to the undisturbed sea wave plus those due to the diffracted wave necessary to satisfy boundary conditions on the vehicle. The long-used strip theory for ships, with the inviscid-flow approximation, is modified for finite depth and inclusion of lift forces on the vehicle fins. The two-dimensional solutions for the forces on each strip are found by a different method than is commonly used for strip theory. This form of the theory is easier to deal with and requires much less computing time than a fully three-dimensional approach. Experiments are conducted and their results are compared with the theory. Excellent agreement is found between the theoretical and experimental wave forces, including the diffracted wave. It is shown that inclusion of the forces on the fins not only improves the theoretical wave forces, but also brings the results of theory for the radiation forces and moments due to vehicle motions much closer to the experimental values that the theory without inclusion of fin lift forces.     

Nonlinear wave theory in reliability analysis of offshore structures

The reliability analysis of offshore structures under wave and wind actions is considered using second order random wave theory. To represent non-Gaussian properties of the resulting wave kinematics, the Hermite moment transformation is used. Further, the so-called sample-specific linearization method developed already (to be used in conjunction with the directional simulation method and the linear wave theory) will be extended to take into account both (1) non-Gaussianity of wave/wind load due to nonlinear load processes and also (2) the non-Gaussianity of wave kinematics due to the nonlinear wave theory. This allows an out-crossing approach to be used to assess the structural probability of failure and the involving out-crossing rate (which is not generally available for non-Gaussian processes) is required to be estimated. Using the proposed procedure, simple structures are analyzed in one- and multi-dimensional cases and the results for structural probability of failure are compared with those obtained using simple linear wave theory. Outcomes show that the use of nonlinear wave theory may affect the results considerably.     

基于荷载时程分析法的商用飞机撞击钢板混凝土结构安全壳的有限元分析

由于钢板混凝土墙背部钢板能够有效地约束混凝土在撞击方向上的运动以及限制混凝土碎片的飞溅,为了抵御商用飞机撞击,新型核电机组的核岛厂房外墙通常设计为钢板混凝土结构(SC)。本文基于荷载时程分析法,运用经典的显式非线性动力分析软件ANSYS/LS-DYNA,进行了波音707-320型号商用飞机撞击某钢板混凝土结构安全壳的响应分析。计算结果表明,即使在安全壳筒身最不利撞击部位冲击作用下,像波音707-320型号的商用飞机对该安全壳的影响是较小的,且增大钢板的厚度能够有效的减小冲击作用下结构的响应。     

Three-dimensional solution of low-velocity impact on sandwich panels with hybrid nanocomposite face sheets

In this article, a three-dimensional solution based on Fourier's series and the generalized differential quadrature method is presented to model the low-velocity impact on sandwich panels with hybrid nanocomposite face sheets. Navier's equations are derived and displacements are substituted by their corresponding Fourier's series. The contact force is considered as a Fourier's series of impactor displacement and deflection of contact point. To verify the theoretical model, experiments are performed on a polyurethane foam-cored sandwich panel with epoxy/woven-fiberglass/nanosilica hybrid nanocomposite face sheets. Contact force and lateral displacement of contact point histories are compared with the theoretical model.     

应用Poisson板理论求解S0兰姆波在通孔缺陷的散射

为降低3D精确理论散射场求解的复杂性和计算成本,应用Poisson板理论描述面内波模式,给出了S0波在各向同性板中受通孔散射的近似模型。该理论利用波函数展开技术以及孔边缘的边界条件,得到了S0和SH0模式的散射远场。将Poisson板理论与3D精确理论进行比较,两者在低频情况下具有较好的一致性。考察了两个基本导波模式在不同尺寸孔的散射特性,发现它们的散射波幅值在某些散射方向随孔径呈线性变换,该结果为兰姆波无损评价提供了依据。     

K8型单层球面网壳顶点竖向冲击下的冲击荷载特征及荷载简化模型

为简化网壳结构遭受冲击作用时复杂的接触分析过程,基于ANSYS/LS-DYNA建立了单层K8型球面网壳模型,并模拟其在不同冲击作用下的失效过程,辨别网壳的失效模式,并获取了冲击过程中的冲击力曲线。通过对网壳遭受竖向冲击荷载下的这些冲击力曲线特征进行分析,提出了简化的冲击荷载模型,并应用能量守恒定律和动量定理确定了模型相关参数。利用此冲击力模型对网壳结构在冲击荷载下的响应进行分析并与实体冲击物作用下的响应进行了对比,验证了该模型的准确性,应用该模型可以实现对网壳抗冲击性能的简单有效评估。     

An exact analytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory

Based on third-order shear deformation plate theory of Reddy, the authors aim to provide an exact analytical solution for free vibration analysis of thick circular/annular plates, both upper and lower surfaces of which are in contact with a piezoelectric layer. Natural frequencies are determined by the solution of the coupled electromechanical governing equations for a combination of free, soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the plate. The electrodes on each piezoelectric layer are assumed to be short-circuited. The Maxwell electrostatics equation is satisfied by adopting a half-sine distribution of the electric potential in the transverse direction of the piezoelectric layers. A comparison of the present exact natural frequencies for piezoelectric coupled circular/annular plates with different boundary conditions is made with previously published results obtained by the Mindlin plate theory and 3-D modified finite element method. The effects of plate parameters such as host thickness to radius ratios, inner to outer radius ratios and piezoelectric to host thickness ratios on the natural frequencies of laminated circular/annular plates are investigated for different combinations of boundary conditions. Results obtained by the present exact closed-form solutions can be served as benchmark data for investigators to validate their numerical and analytical methods in the future.     

Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory

In this work, analytical solutions are presented for the wave propagation in functionally graded (FG) nanoplates using a nonlocal strain gradient theory and four-variable refined plate theory considering the magnetic field. The size effects are included using nonlocal strain gradient theory that has two length scale parameters, and the nanoplate is modeled as a plate using four-variable refined plate theory. From the knowledge of authors, it is the first time that the influences of magnetic field on the wave propagation in FG nanoplates are investigated based on present methodology.     

Re-examination of the evidence for a failure wave in SiC penetration experiments

Previous work suggested the possibility that the effects of a failure wave, evidenced through a change in the slope of the penetration velocity vs. impact velocity (u–v_p) curve resulting from an increase in target penetration resistance, could be observed in penetration experiments of SiC. However, the previous work had to combine two different sets of experimental data, one using long tungsten rods and the other copper shaped-charge jets. A new set of experiments was conducted to address the uncertainties associated with combining the two disparate data sets. Analysis of the new experiments showed no evidence of a distinct change in the slope of the u–v_p response of SiC, up to an impact velocity of 6.2 km/s. We re-examine the original data and analysis in light of the new experiments to understand the origins of the original misinterpretation.     

基于微观力学失效理论的CFRP多向层合板低速冲击行为预测

基于微观力学失效(MMF)理论对碳纤维增强复合材料(CFRP)多向层合板在低速冲击载荷下失效机制及损伤过程进行分析和预测。建立基于MMF理论的层合板结构冲击损伤行为分析方法。首先, 使用MMF理论对冲击过程中组分的失效类别进行判别; 然后, 根据组分失效的类别制定出相应的材料性能退化方案来实现对复合材料在低速冲击下的逐步失效分析;在ABAQUS平台上开发了基于显示分析的用户材料子程序(VUMAT), 即基于MMF理论的层合板冲击损伤分析程序;最后, 利用MMF理论冲击损伤行为分析方法, 对UTS50/E51碳纤维增强复合材料多向层合板在小能量低速冲击情况下的失效机制和损伤形貌进行预测, 并将预测结果与试验结果进行对比, 分析了利用MMF理论预测冲击损伤这一方法的准确性。结果表明理论预测的凹坑直径与试验测试的凹坑直径误差为4.8%, 预测的失效机制和损伤形貌与实际观察的一致。      

Wave propagation of a gravitated piezo-thermoelastic half-space via a refined multi-phase-lags theory

Abstract

This work presents a refined multi-phase-lags theory for thermoelastic response of half-space medium with the inclusion of gravity. The wave propagation of a gravitated piezo-thermoelastic half-space has been presented. Additional equation for the piezoelectric material is added to get four partial differential equations. All coupled equations have been resolved exactly due to the normal mode model. A harmonic wave solution is adopted to derive the main variables of the medium. The displacements, temperature, and electric potential have been obtained. Consequently, the electric displacements and thermomechanical stresses have been also obtained. A comparison is made to show the dependency of all field on the inclusion of gravity. Most fields are very sensitive to the variation of the gravity factor. Results are tabulated to serve as benchmarks for future comparisons and other results have been displayed to show the physical meaning of the phenomena.     

电锤冲击系统的波动力学研究

电锤是一种利用撞击来产生、传递能量的机械。首先基于电锤的结构特点和波动力学理论,建立电锤三元冲击系统动力学模型;然后应用透反射关系原理,提出电锤冲击系统动力学数值模拟计算方法,最后以某型号电锤为例,进行冲击系统动力学数值仿真分析和试验验证,结果表明数值仿真分析与试验测试结果基本吻合。这为电锤冲击系统的动力学分析、结构设计及优化提供理论基础和方法。     

Damage evaluation of concrete plates by high-velocity impact

This paper describes the evaluation of the local damage of concrete plates by the impact of high-velocity rigid projectiles. A new launching system of mushroom-shaped projectiles has been developed. Impact tests for concrete plates have been conducted by using the system to examine failure modes of the local damage of concrete plates. The damage or failure behavior has been discussed on the basis of the failure process captured by a high speed video camera and the strain histories obtained by strain gauges on the concrete plate. Numerical simulations have been also carried out in order to explain the mechanism of the local damage observed by the experiment. A reasonable numerical model has been discussed in terms of a constitutive model and strain rate effect of concrete material. Mechanism of the local damage of concrete plates has been illustrated schematically.     

An examination of deviations from hydrodynamic penetration theory

The hydrodynamic theory of penetration (HTP) was first developed in the U.S. during WWII, and independently and essentially simultaneously in England. Since then the theory has proved very useful in understanding and predicting results of many penetration experiments. The assumptions and limitations of HTP were well stated in the initial paper. The most obvious limitation is that, strictly speaking, HTP only applies to hydrodynamic materials, i.e., both the projectile and the target have no strength. But for nearly all cases of interest, penetration does depend on material strengths, even at quite high velocities. Consequently, effects of projectile and target strength on penetration physics have been studied by many researchers, and modified versions of HTP have been proposed. While material strength is an important reason for deviations from HTP, it is not the only one. Other assumptions underlying HTP are steady-state behavior and incompressibility. In this paper we present new numerical simulation results that examine and quantify deviations from HTP due to compressibility for several material combinations of interest as a function of impact velocity. For these calculations all the materials are modeled as having zero strength. This is done in order to separate effects of compressibility from effects due to material strength. Some discussion of transient effects is also provided.     

Inverse identification of impact locations using multilayer perceptron with effective time-domain feature

This study presents a novel time-domain feature to identify impact locations using Multilayer Perceptron. This feature is based on the minimum arrival time (MAT) of surface wave at a particular location of an object due to impact. Trial impact forces were made on a Perspex plate structure and corresponding acceleration responses were acquired from six locations. Two other conventional time-domain features – peak arrival time (PAT) and threshold crossing (TC), were compared with the proposed feature. Each feature was used separately as network inputs to identify 15 fixed impact locations. The results showed that impact localization with MAT feature resulted in the highest accuracy, making a relative decrease in error of 42.06 and 81.04% compared to PAT and TC cases, respectively. A consistency measurement scheme has been developed as well, which indicated that MAT is more consistent than PAT and TC for a particular pair of impact-sensor location, and hence a more accurate localization of impact can be obtained.     

多壁碳纳米管横向扰动波传播的研究

将N层碳纳米管模拟成N层连续弹性壳模型，研究横向扰动波在单个多壁碳纳米管中轴向传播问题。研究表明，当扰动频率低于多壁碳纳米管的临界频率时，振动模态是同轴的；如果扰动频率至少高于多壁碳纳米管的一个临界频率时，振动模态是非同轴的，并以不同的波速传播，或低或高于单壁连续弹性壳模型的波速。因此，多壁碳纳米管的THz高频波存在着复杂现象，振动基本是不同轴的。特别是当多壁碳纳米管THz高频波以不同的速度传播时，传播速度不仅依赖于频率，而且依赖于非同轴的振动模态。