Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions

This paper presents a method to study the free vibration of a plate with circular holes.The circular hole is regarded as a virtual small plate in which the mass density and Young's modulus are zero.Therefore,the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness.The model is derived from the spectral geometry method(SGM),and the displacement of the plate with circular holes is expanded by the modified Fourier series.Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports.The accuracy of this method is verified by comparison with the finite element calculation results.The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied.

Dynamic stress concentrations in thick plates with two holes based on refined theory

Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

The deformation and failure mechanism of cylindrical shell and square plate with pre-formed holes under blast loading

The deformation and failure mechanism of cylindrical shells and square plate with pre-formed holes under blast loading were investigated numerically by employing the Ansys 17.0 and Ls-Dyna 971.To calibrate the numerical model,the experiments of square plates with pre-formed circle holes were modeled and the numerical results have a good agreement with the experiment data.The calibrated numerical model was used to study the deformation and failure mechanism of cylindrical shells with pre-formed circle holes subjected to blast loading.The structure response and stress field changing process has been divided into four specific stages and the deformation mechanism has been discussed systematically.The local and global deformation curves,degree of damage,change of stress status and failure modes of cylindrical shell and square plate with pre-formed circular holes are obtained,compared and analyzed,it can be concluded as:(1)The transition of tensile stress fields is due to the geometrical characteristic of pre-formed holes and cylindrical shell with arch configuration;(2)The existence of preformed holes not only lead to the increasing of stress concentration around the holes,but also release the stress concentration during whole response process;(3)There are three and two kinds of failure modes for square plate and cylindrical shell with pre-formed holes,respectively.and the standoff distance has a key influence on the forming location of the crack initiating point and the locus of crack propagation;(4)The square plate with pre-formed holes has a better performance than cylindrical shell on blast-resistant capability at a smaller standoff distance,while the influence of pre-formed holes on the reduction of blast-resistant capability of square plate is bigger than that of cylindrical shell.

后路单开门钉板固定结合Key-hole技术在混合型颈椎病患者中的应用效果

目的:分析后路单开门钉板固定结合Key-hole技术在混合型颈椎病患者中的应用效果。方法:采用前瞻性分析法,以随机数表法将2021年6月至2023年6月濮阳市人民医院120例混合型颈椎病患者分为对照组和观察组,各60例。对照组患者采用后路单开门钉板固定治疗,观察组患者采用后路单开门钉板固定结合Key-hole技术治疗。对两组患者术前和术后3个月的JOA评分、JOA评分改善率、Cobb角、ROM、颈椎肌张力及术后3个月的并发症情况进行比较。结果:与对照组相比,术后观察组的JOA评分、JOA评分改善率均升高,术后观察组的Cobb角、ROM、颈椎肌张力均升高,术后3个月观察组的神经根症状总有效率升高,术后3个月内观察组的并发症总发生率降低,差异有统计学意义(P<0.05)。结论:后路单开门钉板固定结合Key-hole技术能够有效缓解混合型颈椎病患者的颈髓、神经根压迫,改善颈髓、神经根功能,且可减少并发症发生。

Computational Complex Method for Finite Elastic Plane Problem with Multiple Elliptical Holes

把多复变量应力函数和边界配点最小二乘法相结合，计算含有任意多个椭圆孔有限大小弹性板的应力场．每个孔的大小、位置为任意．板的边界由下列四种边界条件以及它们的组合所组成：１）已知Ｐｘ和Ｐｙ的应力边界，２）已知Ｖｘ和Ｖｙ的位移边界，３）已知法向位移ＶＮ和切向力ＰＴ的混合边界，４）已知法向力ＰＮ和切向位移ＶＴ的混合边界．编制了相应的ＦＯＲＴＲＡＮ程序，进行考题和算例分析，结果表明本方法行之有效．

Study on the mechanism of near-field underwater explosion on supported thin plates with prefabricated holes

In this study,underwater explosion tests with 2.5 g trinitrotoluene explosive under different fixed plates with prefabricated holes were conducted.The experimental results showed that the air inflow from the prefabricated hole caused the bubble to collapse earlier with an increase in the hole diameter.In addition,the deformation mode of the thin plate transitioned from“convex”to“concave”(up to down).Next,the coupled Eulerian-Lagrangian method was used to perform the corresponding numerical simulation.The accuracy of the numerical simulation method was verified through a comparison with the experimental data.In addition,a series of numerical simulations were conducted with different prefabricated-hole diameters,blast distances,and prefabricated-hole shapes.The results showed that the bubble-pulsating water jet substantially influenced the deformation of the thin plate when the diameter of the prefabricated hole was within the theoretical maximum bubble radius.When the blast distance was within the theoretical maximum bubble radius,the thin plate was subjected to only a single bubble pulsation owing to the air inflow from the prefabricated hole.

SINGULAR SOLUTIONS OF ANISOTROPIC PLATE WITH AN ELLIPTICAL HOLE OR A CRACK

In the present paper, closed form singular solutions for an infinite anisotropic plate with an elliptic hole or crack are derived based on the Stroh-type formalism for the general anisotropic plate. With the solutions, the hoop stresses and hoop moments around the elliptic hole as well as the stress intensity factors at the crack tip under concentrated in-plane stresses and bending moments are obtained. The singular solutions can be used for approximate analysis of an anisotropic plate weakened by a hole or a crack under concentrated forces and moments. They can also be used as fundamental solutions of boundary integral equations in BEM analysis for anisotropic plates with holes or cracks under general force and boundary conditions.

On a Problem of an Infinite Plate with a Curvilinear Hole inside the Unit Circle

In this work, we used the complex variable methods to derive the Goursat functions for the first and second fundamental problem of an infinite plate with a curvilinear hole C. The hole is mapped in the domain inside a unit circle by means of the rational mapping function. Many special cases are discussed and established of these functions. Also, many applications and examples are considered. The results indicate that the infinite plate with a curvilinear hole inside the unit circle is very pronounced.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles

In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat’s function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components σxx, σyy and σxy of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.

STRESS INTENSITY FACTORS OF A PLATE WITH TWO CRACKS EMANATING FROM AN ARBITRARY HOLE

In this paper, Muskhelishvili complex function theory and boundary collocation method are used to calculate the stress intensity factors (SIF) of a plate with two cracks emanating from an arbitrary hole. The calculated examples include a circular, elliptical, rectangular, or rhombic hole in a plate. The principle and procedure by the method is not only rather simple, but also has good accuracy. The SIF values calculated compare very favorably with the existing solutions. A t the same time,the method can be used far different finite plate with two cracks emanating from a hole with more complex geometrical and loading conditions. It is an effective unified approach for this kind of fracture problems.

Simple Proofs of Upper and Lower Envelopes of Van Der Pauw’s Equation for Hall-Plates with an Insulated Hole and Four Peripheral Point-Contacts

For plane singly-connected domains with insulating boundary and four point-sized contacts, C0 …C3, van der Pauw derived a famous equation relating the two trans-resistances R01,23, R12,30 with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.

Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole

The three-dimensional stress concentration factor (SCF) at the edge of elliptical and circular holes in infinite plates under remote tension has been extensively investigated considering the variations of plate thickness, hole dimensions and material properties, such as the Poisson’s coefficient. This study employs three dimensional finite element modeling to numerically investigate the effect of plate width on the behavior of the SCF across the thickness of linear elastic isotropic plates with a through-the-thickness circular hole under remote tension. The problem is governed by two geometric non-dimensional parameters, i.e., the plate half-width to hole radius (W/r) and the plate thickness to hole radius (B/r) ratios. It is shown that for thin plates the value of the SCF is nearly constant throughout the thickness for any plate width. As the plate thickness increases, the point of maximum SCF shifts from the plate middle plane and approaches the free surface. When the ratio of plate half-width to hole radius (W/r) is greater than four, the maximum SCF was observed to approximate the theoretical value determined for infinite plates. When the plate width is reduced, the maximum SCF values significantly increase. A polynomial curve fitting was employed on the numerical results to generate empirical formulas for the maximum and surface SCFs as a function of W/r and B/r. These equations can be applied, with reasonable accuracy, to practical problems of structural strength and fatigue, for instance.

沿空留巷密集钻孔切顶机理及关键参数确定方法

为实现密集钻孔切顶条件下沿空留巷顶板结构安全稳定,研究正常情况与密集钻孔条件下顶板岩层结构受力状况,基于岩石断裂理论和弹性理论分析回采前后顶板密集钻孔孔间围岩受力分布及其破断过程,明确密集钻孔切顶机理及相邻钻孔的孔间集中应力相互作用机制,推导工作面端头弧形三角板结构巷道侧边界密集钻孔孔间围岩的拉剪应力计算公式。在此基础上,分析不同参数对孔间围岩所受拉剪应力的影响作用,提出沿空留巷密集钻孔切顶关键参数确定方法。研究表明:密集钻孔主要通过回采前后钻孔周围应力条件改变来增加钻孔围岩拉剪应力集中程度,引起孔间裂隙扩张联通,形成切缝线破断关键岩层。回采前钻孔主要受水平挤压应力影响,回采后钻孔受力逐渐转变为采空区顶板回转下沉产生的拉剪应力为主,钻孔孔间围岩状态随之由孔间围岩弱化阶段过渡到孔壁裂纹成形阶段,再转变为孔间围岩破断阶段。密集钻孔孔间围岩所受拉剪应力大小主要取决于关键岩层厚度及钻孔孔径与孔间距之比,与钻孔高度及间距成负相关,与角度及直径正相关。据此提出了密集钻孔关键参数确定方法,并根据龙滩矿3124 N工作面坚硬顶板条件设计了密集钻孔切顶留巷方案,确定钻孔长度为8.3 m,角度为15°,钻孔直径为48 mm,间距为500 mm。留巷后巷道顶帮变形可控且整体稳定性较好,由此可证明密集钻孔布置参数较为合理,密集钻孔关键参数确定方法有效可行。

高寒区隧道洞口段覆雪波纹钢棚洞减载方法研究

高寒区隧道洞口段易受上方覆雪及落石影响,采用现有大跨径波纹钢棚洞会产生较大变形和失稳,影响边疆公路运行安全。为此,依托某线路隧道洞口段波纹钢防雪棚洞项目,从拱效应及加筋桥减载原理出发,运用有限元软件构建了EPS板、EPS板+加筋雪、EPS板+加筋冰等10种减载方案的三维波纹钢棚洞模型,研究不同减载方案对棚洞应力、棚洞变形和覆雪压力的影响,对比分析棚洞受力变形特征及减载效果,筛选出最优减载方案。结果表明:施加减载材料后,棚洞上方覆雪压力均不同程度分散到棚洞两侧,减小了棚洞结构的受力;随着覆雪高度增加,减载效果更显著,其中30 cmEPS板+加筋冰组合式方案的减载效果最佳,棚顶应力减少32.72%,棚顶位移减小22.63%;针对波纹钢棚洞的减载问题,建议隧道洞口30 m范围内采用30 cmEPS板+加筋雪方案,距隧道口30 m以外范围可采用30 cmEPS板+加筋冰方案。

玉米大豆兼用腔盘组合孔式排种盘设计与充种性能试验

针对玉米大豆带状复合种植条件下传统机械式排种器不易实现二者兼用精量排种要求、现有气力式排种器排种速度提高因型孔漏充存在漏播断条等问题,设计了一种具有腔盘组合孔结构的排种盘,分析确定了排种盘关键结构参数,构建了吸附过程和吸运过程力学模型。应用EDEM离散元仿真与台架试验相结合的方法进行了排种盘型式优选试验,结果得出:腔盘组合孔式排种盘具有提高充种室种群定向运移平均速度和增大拖拽充种角的作用,有效抑制了型孔漏充率。以安装优选种盘的玉豆兼用排种器为对象,以机组前进速度和工作负压为试验因素,以漏充率和充种合格率为试验指标,采用二因素全因子试验设计开展了充种性能试验,结果表明:当机组前进速度为4.0~7.0 km/h、工作负压在3.0~4.0 kPa时,玉米和大豆种子漏充率均小于3.6%、充种合格率均不小于96%。田间验证试验表明,在机组前进速度为4.0~7.0 km/h、工作负压为3.0~4.0 kPa条件下,腔盘组合孔式排种盘的排种器播种玉米和大豆漏充率分别不大于3.8%、4.2%;当工作负压为3.0 kPa、机组前进速度为7.0 km/h时,自扰动腔盘组合孔式排种盘相比无扰动平面排种盘,播种玉米和大豆漏充率分别下降14.8、12.6个百分点。

附加式声学黑洞对悬臂板振动寿命影响研究

结构在振动条件下的疲劳破坏对其自身的使用寿命以及使用者的人身安全均带来了隐患,目前对于解决结构振动疲劳有添加加强筋、敷设大量阻尼材料等方法,但往往效率较低,附加质量过大。为解决上述问题,提出将附加式声学黑洞(ABH)安装在结构上,通过降低结构响应达到降低应力幅值,延长使用寿命的目的。以悬臂板为基准结构,利用有限元方法进行了稳态动力学分析。结果表明,在附加矩形声学黑洞(RABH)后,悬臂板缺口处的应力响应明显降低。通过应力实验以及疲劳实验,验证了附加RABH可以降低结构危险点处应力响应,并延长悬臂板结构的振动疲劳寿命。

叠合板式综合管廊侧墙连接节点面外抗震性能试验研究

叠合板式综合管廊属于半装配式结构,其接缝数量少,抗渗性能优越,应用前景广泛。为了研究采用灌浆套筒连接和浆锚搭接连接两种连接方式的叠合板式综合管廊侧墙在面外荷载作用下的抗震性能,该文开展了采用两类连接方式的足尺侧墙模型的面外低周反复试验,并与管廊现浇侧墙构件作对比。通过分析试件破坏模式、裂缝分布以及受力性能指标,初步揭示了不同连接方式对叠合板式侧墙面外抗震性能的影响。研究表明:叠合板式试件与现浇试件抗震性能基本一致,滞回曲线均较饱满,极限承载力与刚度退化规律基本一致,满足装配式结构等同现浇的抗震设计要求;两类叠合板式管廊侧墙试件延性系数分别为7.05和8.50,均具有良好的面外延性,满足我国抗震设计规范中变形能力要求;采用浆锚搭接连接的叠合板式试件与采用灌浆套筒连接的叠合板式试件相比,滞回曲线更加饱满,变形能力好,但峰值抗侧承载力低,相同侧向位移下损伤破坏严重;两种连接方式的均可有效传递钢筋应力直至构件破坏。

带温度梯度的钴基高温合金蠕变性能研究

二元隔热衬套是航空发动机高温燃气尾喷管的关键部件,在服役状态下承受非均温、蠕变等复杂环境与载荷。开展了二元隔热衬套钴基高温合金材料GH5188在温度梯度下的蠕变性能研究,设计了具有二元衬套孔结构特征的平板模拟件,开发了带温度梯度的蠕变加载试验装置,进行了内外壁温度差为200℃(760/560℃)以及760、980℃均温条件下带孔与不带孔二元隔热衬套模拟件的蠕变试验。研究表明:在均温与温度梯度环境下带孔模拟件蠕变寿命均高于无孔试样的,带孔试样的蠕变变形显著低于无孔试样的。

带孔形状记忆合金薄板弹热性能的实验和理论研究

NiTi形状记忆合金因其优异的弹热效应在新兴固态制冷领域具备广阔的应用前景.然而,该类合金较高的相变临界应力使得其弹热效应需要很高的机械载荷来驱动,对固态制冷器件的小型化和大规模应用带来了挑战.文章通过在NiTi形状记忆合金薄板上引入孔洞,揭示了孔洞体积分数、分布形式对薄板弹热性能的影响.结果表明,孔洞造成的应力集中效应能够在显著降低薄板相变驱动力的同时,有效增加薄板的整体制冷温度和吸热量.薄板在变形过程中的整体力-位移响应和温度演化强烈依赖于孔洞体积分数,孔洞分布形式仅仅影响薄板的局部应力-应变-温度场,而对整体的热-力响应影响较小.进一步地,基于应力对数客观率,在不可逆热力学框架下建立了形状记忆合金有限变形热-力耦合本构模型,并完成了模型的有限元移植.通过与实验结果的对比发现,提出的本构模型能够很好地预测孔洞对NiTi形状记忆合金薄板变形行为和弹热性能的影响,从而为该类合金带孔薄板的设计提供理论工具.