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.     

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.     

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.     

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.     

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.     

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.     

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.     

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。     

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.     

Bending of cross-ply laminated composites: An accurate and efficient plate theory based upon models of Lekhnitskii and Ren

Bending laminated composites results in a distinctive zig-zag shaped deformation pattern, accordingly jumping transverse shear strains at layer interfaces, but continuous courses of transverse shear stresses there. An accurate representation of this laminate-specific mechanical behavior in terms of plate theories is challenging, even more if computational efficiency is aimed for. Here, an axiomatic equivalent single layer plate theory for cross-ply laminated composites is presented, which is based on the work of Lekhnitskii and Ren and delivers accurate deformation and stress prognoses at the cost of six solution variables. Fulfilling transverse stress continuity, the infinitesimal equilibrium equations are considered in order to derive an appropriate ansatz for the transverse shear stresses including the influence of all plane stress reduced stiffness components. However, the effect of the normal stress σ_zz is neglected, and deflection w is assumed constant across the plate thickness. The equilibrium equations and corresponding boundary conditions of the plate theory are derived by application of the principle of virtual displacements. Numerical results for symmetrical and non-symmetrical composites as well as for typical sandwich plates obtained by the present theory show good agreement with corresponding exact elasticity solutions given by Pagano, even for thick plates.     

冲击压缩下氧化铝陶瓷中的延迟破坏实验研究

利用轻气炮对不同厚度的氧化铝陶瓷试件进行了平板冲击实验,并借助激光速度干涉仪（VISAR）测试了试件的自由面速度历程。实验结果显示,自由面速度曲线上存在表征破坏波出现的二次压缩信号。根据实验结果计算获得了破坏波穿过试件的运动进程,并确定了试件中破坏波的运动轨迹近似为一条直线,得出在冲击压力为7.16GPa时试件内破坏波波速约为5.051km/s,破坏延迟时间约为0.105μs。最后简单分析了该现象产生的物理机制。     

Wave propagation and transient response of a FGM plate under a point impact load based on higher-order shear deformation theory

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load are presented. The effective material properties of functionally graded materials (FGMs) for the plate are assumed to vary continuously through the plate thickness and be distributed according to a volume fraction power law along the plate thickness. Based on the higher-order shear deformation theory and considering the effect of the rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived by using the Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Then, using the dispersion relation and integral transforms, exact integral solutions for the functionally graded plate under a point impact load are obtained. The transient response curves of the functionally graded plates are plotted and the influence of volume fraction distributions on transient response of functionally graded plates is analyzed. Finally, the solutions of the higher-order shear deformation theory and the first-order shear deformation theory are studied.     

Recursive formulae for wave propagation analysis of FGM elastic plates via reverberation-ray matrix method

Through a laminated plate model, a recursive formulation for the method of reverberation-ray matrix (MRRM) is proposed for the analysis of free wave propagation in an elastic plate with material properties varying along the thickness direction. In contrast to the traditional MRRM, the present new formulation behaves well for high frequency computation, while the heavy computational cost of storage and memory can also be cut down. Numerical examples are given to analyze dispersion characteristics of waves in FGM plates, and the comparison among traditional MRRM and the recursive formulation demonstrates the significant efficiency of the proposed recursive formula.     

弹丸超高速撞击半无限厚铝板数值模拟

微流星体及空间碎片的超高速撞击威胁着长寿命、大尺寸航天器的安全运行,导致其严重的损伤和灾难性的失效.撞击损伤特性研究是航天器防护设计的一个重要问题.本文采用AUTODYN软件的Lagrange法对半无限铝板的超高速斜撞击和与其具有相同法向速度的正撞击进行了模拟,给出了不同撞击角和不同法向速度下半无限厚铝板弹坑深度、宽度、长度的变化规律及多弹坑的形成过程,并与经验方程进行了比较分析.结果发现:随撞击角的增加,弹坑的深度和宽度减小,而弹坑的长度增加;随撞击速度的增加弹坑的直径和深度增加;在撞击角大于70度时出现多弹坑.     

Bending analysis of functionally graded sectorial plates using Levinson plate theory

Based on the Levinson plate theory (LPT) and the first-order shear deformation plate theory (FST), the bending analysis of functionally graded (FG) thick circular sector plates is presented. The LPT solutions of FG sectorial plates are first expressed in terms of the solutions of the classical plate theory (CPT) for homogeneous sectorial plates and then presented using a direct method. It is assumed that the non-homogeneous mechanical properties of plate, graded through the thickness, are described by a power function of the thickness coordinate. The results are given in closed-form solutions and verified with the known data in the literature.     

Nonlinear vibration of an initially stressed laminated plate according to a higher-order theory

The nonlinear behavior of laminated plates in a general state of non-uniform initial stress was studied at large vibration amplitudes. The nonlinear governing equations of this study were derived using a higher-order theory approach. The results were compared with the Mindlin plate theory’s results. The results showed that the higher-order shear deformation terms had a significant influence on the plate in a large amplitude vibration when the thickness ratio decreases and the plate was stacked with less layers. In addition, the effect of Young’s modulus in the thickness direction on the frequency ratio was significant for the two-layered plate. However, the results of the four-layered plates were not affected too much.     

Low velocity impact analysis of sandwich plates with functionally graded face sheets

This article deals with the study of low velocity impact response on sandwich plates with functionally graded face sheets. High-order sandwich plate theory is improved by considering the in-plane stresses of the core that usually are ignored in the analysis of sandwich structures. A new approach is used to reduce the equations of motion from 27 equations to 15 equations and then solving them for both unsymmetric and symmetric sandwich plates. The model is also checked by finite element simulation and by comparing with other references for validation. A parametric study is done for various geometrical and mechanical properties.     

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

ABSTRACT

This article investigates the nonlinear vibration of piezoelectric nanoplate with combined thermo-electric loads under various boundary conditions. The piezoelectric nanoplate model is developed by using the Mindlin plate theory and nonlocal theory. The von Karman type nonlinearity and nonlocal constitutive relationships are employed to derive governing equations through Hamilton's principle. The differential quadrature method is used to discretize the governing equations, which are then solved through a direct iterative method. A detailed parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, and temperature rise on the nonlinear vibration characteristics of piezoelectric nanoplates.