Four-Beam Model for Vibration Analysis of a Cantilever Beam with an Embedded Horizontal Crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton＇s principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.

NONLINEAR DYNAMIC MODELING AND PERIODIC VIBRATION OF A CANTILEVER BEAM SUBJECTED TO AXIAL MOVEMENT OF BASEMENT

Dynamic modeling of a cantilever beam under an axial movement ofits basement is present- ed. The dynamic equation of motion for thecantilever beam is established by using Kane's equation first andthen simplified through the Rayleigh-Ritz method. Compared with oldermodeling method, which lineari- zes the generalized inertia forcesand the generalized active forces, the present modeling takes thecoupled cubic nonlinearities of geometrical and inertial types intoconsideration.

Simulation of perforated rectangular cantilever immunosensor for estimation of bacterial pathogens

Micro fabricated and multilayered perforated cantilever beam immunosensor was modeled using CoventorWare for the estimation of bacterial antigens of Bacillus Anthrax, Pseudomonas aeruginosa, Coryne Bacterium Diptheria and Treponema pallidum. A rectangular cantilever beam with perforations was simulated with dimensions as length-200 μm, width-10 μm and thickness-0.5 μm. Each perforation is rectangular with length-10 μm, width-5 μm and thickness-0.5 μm. The theoretical and FEM simulations were carried out with five immunoglobulin antibodies, IgA, IgD, IgE, IgG and IgM for the estimation of bacterial antigens. The effect of perforation in cantilever beam and molecular size of antibody and antigen on the performance of the sensor has been studied. The cantilever beam without perforation showed a deflection of 1.8 e + 02 μm whereas the cantilever beam with perforation showed an increase deflection of 1.9 e + 02 μm. With IgG, the difference between analytical and simulation values is positive and low especially with low molecular weight antigens Pseudomonas aeruginosa and Treponema pallidum. The low molecular weight IgG influences the antigen-antibody interaction more fvourably. The simulated perforated rectangular cantilever beam with IgG antibody is a more promising model for the fabrication of a sensor for the estimation of highly motile Pseudomonas aeruginosa and Treponema pallidum.

Experiment and performance analysis of serpentine-shaped cantilever beam for pipeline vibration-based piezoelectric energy harvester prototype development

Pipelines produce vibrations during fluid or gas transportation.These vibrations are less likely to cause structural failure as they exist with a small magnitude and can be harvested into useful energy.This paper presents a study on the piezoelectric energy-harvesting method converting mechanical energy from pipeline vibration into electrical energy.The performance of the serpentine-shaped piezoelectric cantilever beam was observed to check whether the design can produce the highest output voltage within the allowable vibration region of the pipeline from 10 to 300 Hz through finite element analysis using COMSOL Multiphysics software(Supplementary Material).In addition,this study investigates the energy-harvesting potential of the proposed design under real pipeline vibration conditions through a lab vibration test.The harvested energy output is evaluated based on various vibration frequencies and amplitudes,which gives an idea of the device and its performance under different operating conditions.The experiment result shows that the energy harvester produced an open-circuit voltage of 10.28-15.45 V with 1 g of vibration acceleration.The results of this research will contribute to the development of efficient piezoelectric energy harvesters adapted for pipeline environments.

3D Nonlinear XFEM Simulation of Delamination in Unidirectional Composite Laminates: A Sensitivity Analysis of Modeling Parameters

This article presents a three-dimensional extended finite element (XFEM) approach for numerical simulation of delamination in unidirectional composites under fracture mode I. A cohesive zone model in front of the crack tip is used to include interface material nonlinearities. To avoid instability during simulations, a critical cohesive zone length is defined such that user-defined XFEM elements are only activated along the crack tip inside this zone. To demonstrate the accuracy of the new approach, XFEM results are compared to a set of benchmark experimental data from the literature as well as conventional FEM, mesh free, and interface element approaches. To evaluate the effect of modeling parameters, a set of sensitivity analyses have also been performed on the penalty stiffness factor, critical cohesive zone length, and mesh size. It has been discussed how the same model can be used for other fracture modes when both opening and contact mechanisms are active.

AN ANALYTICAL MODEL OF THE CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT

Oblique impact of projectiles onto structures is of importance in engineering. As thefirst step in the theoretical analysis of this problem, an analytical model is proposed in thispaper for a rigid-linear hardening cantilever beam subjected to oblique impact of a rigidprojectile at its tip. This is a "double-hinge model" combining Parkes’ model and Tailor’smodel; and its response is governed by a system of non-linear algebraical equations. Examplesare given to show the travelling of both hinges and the response history of the velocity atthe tip.

歪闪古建木构架整体纠偏方法与数值模拟

由于环境与人为等因素的长期影响,木结构古建筑普遍存在倾斜歪闪等损伤问题,严重影响了古木建筑的安全,亟需纠偏修复。研究尝试提出一种整体纠偏方法,构建木构架结构纠偏理论计算模型,通过数值模拟方法分析了纠偏过程的可行性,并以某多层木结构建筑的纠偏复位过程为例加以验证。结果表明:纠偏后结构楼层偏移明显减小,纠偏过程中主要结构构件仍然处于弹性范围内,纠偏效果良好,可为同类古建木构架纠偏理论研究提供借鉴。

基于Ansys Workbench的悬臂结构直接优化设计

本文对悬臂梁结构进行了模型数据参数化,利用Ansys Workbench对悬臂梁结构进行直接优化设计,建立以质量最小为最优目标的非线性多约束数学模型。通过计算和分析输入参数对优化目标的敏感性和响应(总变形和等效应力),确定最佳的优化方案。经过直接优化,该悬臂结构质量比原来减轻了47.8%,优化效果良好,达到了最初进行优化的目的,实现利用材料更经济的结果,为类似结构的轻量化设计提供了思路。本方法具有较好的可行性,可优化得到结构性能较好的悬臂结构几何布局方案,可为此类悬臂结构的轻量化优化设计提供技术支撑。

基于力法的格构梁节点荷载分配方法及悬臂段长度优化设计

格构梁节点荷载简化分配方法的不足在于无法考虑2个方向的梁上其他节点荷载的影响且对文克尔(Winkler)地基上梁的类型进行了主观假定。为克服格构梁节点荷载简化分配方法的上述缺点,提出了一种基于力法的格构梁节点荷载分配方法。根据节点静力平衡条件及变形协调条件,新的格构梁节点荷载分配方法通过构建并求解线性方程组,能够合理地将作用在节点的集中力分别分配给2个方向的纵梁和横梁。进一步地,引入一个格构梁边坡锚固案例并等比例地增加纵梁和横梁的悬臂长度。不同基床系数条件下,基于新的节点荷载分配方法将格构梁节点荷载分配给纵梁和横梁,然后对各梁单独进行弯矩计算。以悬臂最大正弯矩与跨中最大负弯矩比值的绝对值接近1为评价指标,对格构梁最优悬臂长度进行了评价。节点荷载分配结果表明,随着悬臂长度的增加,分配给纵梁和横梁的荷载逐渐趋于稳定。弯矩计算结果表明,随着基床系数的增大,悬臂长度对格构梁弯矩的影响逐渐减弱。不同边坡基床系数条件下,当悬跨比在0.2~0.4之间时,悬臂各梁最大正弯矩与跨中最大负弯矩趋于均衡。因此,基于力法理论的节点荷载分配方法的提出为格构梁内力的精确分析及悬臂长度优化设计提供了可靠的理论依据。

大悬臂宽幅混凝土箱梁横隔梁计算方法分析

为研究大悬臂宽幅混凝土箱梁横隔梁的计算分析方法,参照现有混凝土宽箱梁横隔梁计算模式,研究横隔梁杆系单元模型的简化建模方法,重点针对横隔梁两侧的加腋和顶底桥面板的计算长度进行分析,分别取0~10倍顶底板厚度的计算长度,并结合midas Civil分析横隔梁顶部主拉应力和最大负弯矩,探求该类型箱梁断面的最佳顶底桥面板计算长度取值。同时采用Abaqus三维软件建立实体模型,对比杆系单元模型的计算结果,验证建模方式的合理性。结果表明,采用大悬臂宽幅混凝土箱梁横隔梁计算时,断面纵向两侧取4倍顶底板厚度的计算长度最为合理,相对于常规混凝土宽箱梁横隔梁计算方法支座处横隔梁顶部主拉应力减小了7.8%,结果更加安全;根据对比可知,采用该计算方法建立的大悬臂宽幅混凝土箱梁杆系单元横隔梁模型结果与实体模型计算结果基本接近,横隔梁横向主应力和主拉应力仅分别增加了7.7%和2.7%。

轴向运动悬臂梁的独立模态振动控制——Ⅰ近似理论分析

利用Euler Bernoulli梁理论并在低速轴向运动假设的基础上 ,对伸展悬臂梁的独立模态振动控制进行了理论近似解的推导 ,为数值仿真计算结果提供了一定意义下的对照参考模型 。

接触式纱线张力传感器动态测量模型

纱线变化张力的准确测量和有效控制对纺织品质量有重要影响。随着张力变化频率的增高,因悬臂梁机械振动所造成的系统张力误差随之增大。为此,对接触式张力传感器检测单元建立动力学模型,并在此基础上分析振动对张力信号检测的误差影响,进而提出动态张力测量模型以及相应的振动误差抑制算法。通过建立张力测试实验台,对不同条件下的测试结果进行振动误差抑制前后的张力信号对比研究。结果表明,基于动态张力测量模型的误差抑制算法能够有效地消除振动产生的张力检测误差。

基于刚柔耦合的高方平筛动力学建模与振动模态分析

针对高方平筛和其上固结的柔性吊杆组成的动力学系统,进行了刚柔耦合的动力学建模和振动模态分析。将筛体—偏重块系统和吊杆分别作为刚体和弹性的可变形体,建立了筛体稳态圆振动方程和吊杆悬臂梁力学模型,总结出系统固有频率的计算方法。在此基础上,采用有限元方法对系统进行了模态计算和动力学响应分析。结果表明,理论模型能够很好地反映筛体与吊杆之间的动力学耦合关系;以理论分析为基础的载荷和边界条件的设置,使有限元仿真结果较准确地模拟了系统实际的振动特性。

不锈钢和Ti基体上Cu,Ag,Ni膜中的内应力研究

用电镀工艺在不锈钢基体上镀制了Cu,Ag,Ni膜和Ti基体上制备了Ni膜,并用悬臂梁法和X射线法测量了膜中的残余应力。并基于改进的TFD模型,对任意膜厚下由界面电子转移引起的膜内应力作了理论估算。结果表明,理论估算所给出的膜内应力与实验测量值具有可比性。这说明理论计算模型具有较高的准确性和膜内残余应力主要由界面电子转移引起。

悬臂梁易损部件在矩形加速度脉冲激励下的动力学响应与有限元分析

为分析悬臂梁易损部件在矩形脉冲激励下的振动响应,推导出悬臂梁在悬臂端处动态应力的近似解析解,得到最大应力与矩形脉冲峰值之间的关系,分析结果表明:在速度变化量一定时,最大应力随加速度脉冲幅值的增加而增加,但会无限逼近极限值。最后建立了易损件-质量主体在矩形脉冲激励下的有限元模型,并与解析解进行了对比,发现运用2阶振动模态即可得到精确的悬臂梁的应力响应,所取得的研究成果为具有悬臂梁式易损件在蜂窝纸板缓冲作用下的防护提供理论基础。

新型双稳态压电振动俘能系统的理论建模与实验研究

针对线性压电俘能系统的共振频带窄、俘能方向单一、发电效率低等问题,设计了一种双稳态磁力耦合多悬臂梁俘能结构。利用广义Hamilton变分原理建立了系统分布式力-电-磁耦合模型,结合数值计算和实验验证方法揭示了磁铁间距、外界振动激励条件对压电俘能系统响应特性的影响规律。研究结果表明:在合适的磁距和外界振动激励条件下,系统的输出电压可达18V,是线性压电振动俘能系统的3.5倍,有效工作频带是线性压电振动俘能系统的3.1倍,说明双稳态压电振动俘能系统具有明显拓宽有效工作频带和提升发电效率的能力,为压电俘能系统工程化应用提供了理论依据。

大采高放顶煤液压支架围岩耦合三维动态优化设计

分析了大采高综放顶煤破碎规律、直接顶和基本顶的破断规律,揭示了大采高综放开采矿压显现剧烈的原因;建立了大采高放顶煤支架围岩耦合的组合悬臂梁模型,提出大采高综放支架支护强度的确定方法;提出基于支架围岩耦合模型和有限元分析的大采高放顶煤液压支架三维参数优化动态设计方法,发明了大采高放顶煤液压支架新型放煤结构;进行了大采高放顶煤支架总体配套与工作过程仿真研究。

小口径火炮弹炮耦合动态响应有限元时程分析

基于移动荷载思想应用有限单元法和悬臂梁理论研究了小口径火炮弹丸膛内运动过程中的身管振动情况。应用圆柱坐标系将身管结构离散为标准的扇形单元,依据弹带凹槽部和凸起部沿膛线运动过程对各单元进行编号,将弹带视为弹塑性体,凹槽部应用线性简化模型,凸起部应用Dubowsky模型,身管简化为柔性变截面悬臂梁,考虑弹带挤进过程和刚体前定心部对内膛的瞬态碰撞规律,将弹丸膛内运动过程分为三个阶段,根据工程梁理论建立了移动弹丸作用下身管径向振动的时变动力学方程。将计算结果与炮口振动实验数据相比较,可知在忽略火炮后坐、摇架、炮塔等结构影响下,弹炮耦合模型比较准确。

基于各向异性的Galfenol复合悬臂梁三维非线性耦合模型

通过Maxwell方程研究动态条件下三维驱动磁场的非线性分布,利用弱解式方程将Galfenol合金本征非线性模型与复合悬臂梁结构模型进行耦合,得到基于各向异性的悬臂梁磁机耦合非线性模型。模型仿真结果表明,磁感应强度最大的位置出现在靠近悬臂梁固定端的一侧,悬臂梁机械应变的分布结果与磁感应强度类似。分别利用非周期阶跃信号和周期正弦信号对复合悬臂梁进行试验研究。结果表明,所建立的三维非线性耦合模型可以较好地预测试验数据中的死区部分、线性区间以及饱和区间,由于柔性结构中存在的次谐波扰动,阶跃响应中试验曲线出现小幅波动现象,模型可以较好捕捉试验结果中出现的次谐波扰动特征。

压电驱动器非线性模型研究

通过对压电驱动器的软件计算结果与实验结果的差异进行研究总结,利用变形后压电驱动器中各个结构部分的应力应变分布特点,结合复合层合材料力学、梁力学模型和压电材料非线性模型理论构造出压电薄片与基体材料的简化耦合模型,从而建立结构的非线性模型。模型计算结果比软件计算结果更符合实验结果,形式更简单,物理意义更明确。再利用该模型对不同结构参数下的压电驱动器性能进行分析,直观地反应出压电驱动器各结构参数对驱动器性能的影响。