NONLINEAR FREE VIBRATION OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION UNDER THE STATIC LOADS

In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.

Nonlinear vibration and buckling of circular sandwich plate under complex load

The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.

Performance analysis of high-static-low-dynamic stiffness vibration isolator with time-delayed displacement feedback

The displacement feedback with time delay considered is introduced in order to enhance the vibration isolation performance of a high-static-low-dynamic stiffness(HSLDS) vibration isolator. Such feedback is detailedly analyzed from the viewpoint of equivalent damping. Firstly, the primary resonance of the controlled HSLDS vibration isolator subjected to a harmonic force excitation is obtained based on the multiple scales method and further verified by numerical integration. The stability of the primary resonance is subsequently investigated. Then, the equivalent damping is defined to study the effects of feedback gain and time delay on primary resonance. The condition of jump avoidance is obtained with the purpose of eliminating the adverse effects induced by jumps. Finally, the force transmissibility of the controlled HSLDS vibration isolator is defined to evaluate its isolation performance. It is shown that an appropriate choice of feedback parameters can effectively suppress the force transmissibility in resonant region and reduce the resonance frequency. Furthermore, a wider vibration isolation frequency bandwidth can be achieved compared to the passive HSLDS vibration isolator.

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Analytical and numerical studies on the nonlinear dynamic response of orthotropic membranes under impact load

Orthotropic membrane components and structures are widely used in building structures, instruments and meters, electronic engineering, space and aeronautics, etc., because of their light weights. However, the same lightweight combined with low stiffness make membranes prone to vibration under dynamic loads, and in some cases the vibration may lead to structural failure. Herein, the undamped nonlinear vibration response of pretension rectangular orthotropic membrane structures subjected to impact loading is studied by analytical and numerical methods. The analytical solution is obtained by solving the governing equations by the Bubnov-Galerkin method and the Lindstedt-Poincare perturbation method. Numerical analysis has also been carried out based on the same theoretical model. The analytical and numerical results have been compared and analyzed, and the influence of various model parameters on membrane vibration discussed. The results obtained herein provide some theoretical basis for the vibration control and dynamic design of orthotropic membrane components and structures.

Geometrically Nonlinear Random Responses of Stiffened Plates Under Acoustic Pressure

An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.

低频大幅隔振器设计及实验

为了突破传统隔振器刚度和承载能力之间的矛盾,需要隔振器具有高的静态刚度,低动态刚度的特性.如今的准零刚度隔振器技术可以实现低频微幅隔振,但是对于大幅振动,隔振效果并不明显甚至失效,因此突破宽幅隔振成为隔振领域亟待解决的问题.为此,我们利用多稳态折纸通过并联装配的方式,构造具有宽幅零刚度区间的折纸型隔振器,以解决传统隔振器振动抑制幅值较低的问题.本文建立了宽零刚度隔振器模型,提出宽幅零刚度的设计方法,并通过动力学分析分析了模型的隔振效果.最后搭建试验样机,验证了理论的正确性.这种设计打破了传统准零刚度隔振器单点准零的设计准则,能够在一个大幅范围内保证稳定性,同时实现零刚度,极大拓宽了隔振器的适用范围.这种设计理念能够被用在新隔振材料设计和航空、船舶等大幅低频动态环境中.

落石被动柔性防护网非线性静力设计方法及验证

被动柔性防护网是一种常见的落石灾害防治措施。针对当前落石被动柔性防护网尚无适用的工程化设计方法的现状,以非线性计算过程中结构内能与设计防护能级相等作为加载完成的判别准则,建立了落石被动柔性防护网的非线性静力设计方法。基于LS-DYNA对250~5000 kJ共8种常用能级的被动柔性防护网开展非线性动力分析,明确了冲击力的分布范围及相对大小,形成了适用于不同能级落石被动柔性防护网非线性静力设计的荷载模式。为了有效模拟被动柔性防护网特殊的受力特征,开发了由索单元与受拉弹簧单元组成的非线性耗能单元用于耗能器模拟,开发了内部由多段索单元组成的滑移索单元用于滑移边界以及网环单元模拟。基于对网片冲击试验的反演和3500 kJ被动柔性防护网的设计及足尺冲击试验检验,验证了所提出的落石被动柔性防护网非线性静力设计方法的有效性。

±800kV与500kV混压大跨越钢管混凝土塔等效风荷载分析

大跨越钢管混凝土塔相比于普通钢管塔存在质量、刚度突变的特点。为探究钢管混凝土塔和钢管塔在风荷载作用下的响应规律及设计风荷载的取值,该文以实际工程为例,通过有限元模拟分析了两种塔型的动力特性和风振响应,并将等效静力风荷载与规范结果进行比较。结果表明:钢管混凝土塔的刚度明显高于钢管塔,且前几阶频率相对密集,振型间相互耦合明显;按规范等效风荷载的结构响应大于时程分析响应极值;按规范计算的钢管混凝土塔风振系数在灌入混凝土顶部附近存在突变;钢管混凝土塔顶部位移、加速度响应明显小于钢管塔,且钢管混凝土塔的脉动响应下降更为明显。

基于载荷试验振沉钢管桩承载力计算方法研究

振沉工艺是一种较为新颖的预制桩施工工艺,对于采用这种工艺施工的桩基的桩-土作用研究相对较少,尤其是钢管桩的桩-土作用。针对这一问题,采用慢速单桩竖向抗压静载试验方法获得了一组振沉压入钢管桩的单桩承载力变化规律。随后,根据可能存在的4种桩土作用模式,采用力学平衡法分别计算了桩的竖向极限承载力,并依据规范建议考虑振沉影响对计算结果进行了修正。通过试验结果与理论计算结果的对比,揭示了振沉工艺下钢管桩的桩-土作用特征,研究成果对振沉桩单桩极限承载力的计算具有一定的指导意义。

High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity

High-static-low-dynamic-stiffness(HSLDS) nonlinear isolators have proven to have an advantage over linear isolators, because HSLDS nonlinear isolators allow low-frequency vibration isolation without compromising the static stiffness. Previously, these isolators have generally been assumed to have linear viscous damping, degrading the performance of the isolator at high frequencies. An alternative is to use nonlinear damping, where the nonlinear behavior is achieved by configuring linear dampers so they are orthogonally aligned to the excitation direction. This report compares the performances of single-stage and two-stage isolators with this type of damping with the corresponding isolators containing only linear viscous damping. The results show that both isolators with linear viscous damping and nonlinear damping reduce the transmissibility around the resonance frequencies, but the results show that the isolators with nonlinear damping perform better at high frequencies.

变截面脱硫塔风振效应及等效风荷载研究

变截面是工程设计中常见的结构类型,此类结构风效应在现行规范中受到的关注较少,规定仍较为粗糙。以某高耸脱硫塔为研究对象,综合时、频域数值仿真,详细研究圆柱形分段变截面高耸结构顺、横风向的风致动力响应特性,探讨了横风向涡激共振的判定及计算方法,对比分析变截面圆柱结构常见等效静力风荷载计算方法的差异及结果的可靠性。研究表明,结构第1阶模态是圆柱形变截面脱硫塔风效应的控制振型;应重点关注此类结构上部涡激振动对横风向响应的贡献;鉴于脱硫塔风致振动以共振响应为主,采用惯性力法或三分量(平均、背景和共振)法计算等效风荷载更符合实际分布规律。时、频域分析结果与我国现行规范《建筑结构荷载规范》(GB 50009-2012)计算结果吻合较好,可为分段式变截面高耸结构精细化风振效应研究提供工程参考和依据。

热声载荷环境高速飞行器加筋壁板非线性振动响应特性研究

目的 针对热声载荷环境下高速飞行器排气道加筋壁板结构的大挠度非线性振动响应特性问题展开研究。方法 基于薄壁结构大挠度运动控制方程,开展了加筋壁板结构在热声载荷下的非线性响应仿真计算,给出了加筋壁板结构运动方程,分析了发生热屈曲的临界温度,并运用有限元方法进行数值模拟,计算了加筋壁板结构在不同载荷下的非线性振动响应特性。结果 模态频率的一致性在结果中得到体现。计算了多参数即结构、温度、声压级变化下壁板结构的响应变化。加筋会使壁板结构基频升高,响应降低;屈曲前随温度上升,结构基频不断降低,最低时处于临界温度附近;屈曲后随温度上升,结构基频不断升高。基频幅值在温度上升的过程中先升高后降低。声压级每升高6 dB,等效应力平均升高1.98倍,验证了响应的非线性特性。结论 结构、温度、声压级参数对加筋薄壁结构非线性振动响应有较大影响,加筋壁板结构在温度上升过程中由屈曲前稳定状态变为屈曲失稳状态,又逐步变为屈曲后稳定状态。本文所做的工作可为其他薄壁结构,尤其是加筋壁板结构的非线性振动响应特性计算与分析提供参考依据。

基于等效静载荷法的挤压铝门槛梁非线性结构优化

针对侧面柱碰撞工况下的挤压铝门槛梁截面正向设计问题,分析了基于等效静载荷(ESL)原理的非线性优化技术和传统优化技术的优缺点。研究显示:概念设计阶段基于等效静载荷法的非线性拓扑优化技术相比传统的线性拓扑优化技术,能得到更加贴近碰撞安全结构变形策略要求的拓扑路径;详细设计阶段,基于等效静载荷法的非线性料厚优化技术,在优化效率和优化方案性能方面都优于传统的近似模型数值优化技术。

车桥耦合振动下损伤连续梁桥承载力评定方法研究

【目的】桥梁的安全与承载能力至关重要,为简化试验流程、提高检测效率,以实际工程中一座两跨连续梁桥为研究背景,基于移动车辆进行轻荷载数值分析,探究车桥耦合振动下损伤桥梁承载力评定方法的准确性与可行性。【方法】建立车桥耦合振动模型,提取桥梁结构控制截面的挠度、应变动态时程响应,利用经验模态分解(EMD)和变分模态分解(VMD)去除动力成分并识别准静态响应曲线,分析桥面粗糙度和车速对准静态响应识别精度的影响;通过车辆行驶中控制截面产生的不同响应计算不同加载位置的加载效率,利用“常丁模型”计算轻荷载效率下损伤桥梁控制截面准静态响应的标准校验系数,对损伤连续梁桥的承载力进行评估。【结果】相较于EMD,VMD分解的准静态响应曲线与静态响应曲线吻合程度更好;随着桥面粗糙度、加载车辆移动速度的增大,识别的准静态响应与静态响应的误差也逐步增大;移动车辆加载过程中识别的准静态响应较为精确,可作为静载实测值进行计算;计算的标准校验系数均大于1,准确评估了桥梁的损伤状态。【结论】基于车桥耦合振动评估损伤桥梁承载力的方法具有较强的适用性和可行性。

冲击荷载下岩土介质非线性振动预测方法研究

水利工程作为国家重点保护的民生工程,可能会承受军事打击、恐怖袭击、爆破施工等潜在的冲击荷载,因冲击荷载作用的强非线性,现有振动预测方法均存在不足之处。基于理论分析,提出一种能够精确预测冲击荷载下非线性振动的方法,并建立冲击荷载下岩土介质振动预测模型,通过大量现场实验验证方法及模型的准确性和实用性,为水利工程的安全防护提供理论依据。

单层球面网壳的弹塑性稳定性

为了解和掌握单层球面网壳在静力荷载作用下的弹塑性稳定性能,采用有限元软件ANSYS及自编的前后处理程序对典型单层球面网壳结构稳定性能进行对比分析,初步了解了球面网壳弹性与弹塑性稳定性能的主要差异。在此基础上进行了1000余例K8型单层球面网壳弹性、弹塑性全过程分析,同时考虑竖向均布荷载的不对称分布、初始几何缺陷等因素对球面网壳稳定性能的影响,掌握了以上因素变化对球面网壳弹塑性稳定性能的影响规律,并将其定量化。最后,通过对弹性、弹塑性稳定极限承载力的统计分析,提出适用于K8、K6型球面网壳的塑性折减系数,用以表示材料非线性对极限承载力的影响。这些成果的获得为进一步开展网壳结构的弹塑性稳定性能研究以及工程实践提供了理论依据和技术参考。

爆破振动对建(构)筑物影响数值计算模型及安全判据的研究

针对目前爆破施工对既有建(构)筑物影响的数值分析方法及振动安全判据中存在的爆破荷载施加复杂、计算难以收敛,仅以质点振动速度大小单一指标作为安全判据等问题,利用圣维南荷载等效原理,经过推导提出了数值分析中爆破荷载的等效施加方法,即将作用在炮孔壁上的孔状爆破荷载等效成面荷载,以模拟爆炸作用,这种方法使得数值建模简化且计算容易收敛,同时基于拟静力法给出了新的振动安全判据。最后利用两个具体的工程案例对等效荷载施加方法和新安全判据的合理性进行验证。结果表明,等效荷载施加方法在近区存在一定差异,但在中远区吻合得较好,该方法建模简单,且计算容易收敛;新的爆破振动安全判据考虑了建(构)筑物本身的自振频率和安全储备,能够合理地评价振动荷载对既有建(构)筑物的影响,可供类似工程参考。