基于突变理论深埋硬岩隧道的失稳分析

在分析隧道开挖引起围岩扰动和损伤的基础上,运用突变理论探讨了深埋硬岩隧道失稳的机理;基于势能原理,建立了深埋硬岩隧道失稳的尖点突变模型,导出了失稳的力学判据条件。结果表明:深埋硬岩隧道的失稳不仅受岩体特性及所受载荷的影响,而且与围岩中弹性区刚度和塑性区刚度的比值有关;开挖过程中,围岩受扰动和损伤程度越大,岩体完整性系数越小,力学参数指标弱化程度越高,塑性区范围越大,刚度比越小,围岩系统发生失稳的可能性就越大。工程实例分析表明,分析结果与实际经验基本一致;研究成果可为预防隧道失稳、采取合理的施工工艺和支护措施提供参考依据。     

深海采矿柔性立管系统非线性有限元模拟

在海洋环境载荷及集矿机牵引作用下,深海采矿柔性立管系统的动力学响应涉及几何非线性和非保守载荷的双重非线性源.基于三维固体有限变形理论建立数学模型,在完全拉格朗日格式下推导了系统运动平衡方程,针对非保守载荷的等效计算、非线性切线刚度矩阵及非线性方程的数值求解等关键问题提出了有效处理方案.根据处理方案开发了数值计算程序,并...     

Hopf bifurcation analysis of reaction–diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay

The active control approach generally requires power input to suppress vibrations of structures, while the conventional passive manner often causes waste of energy after transferring vibrations of the primary structure to the auxiliary system. In this work, an innovative control strategy based on energy harvesting for efficiently suppressing the cross-flow-induced vibrations such as galloping is proposed. The novel design facilitates the harvester of not only alleviating the oscillation of the primary structure but also seizing the transferred vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler–Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability, and hence, the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control the bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.     

岩体—界面系统剪切不稳定性分析

基于界面的刚塑性应变软化假设，分析了岩体－界面系统在端部剪力和岩体中分布剪切载荷共同作用下的变形、应力和损伤演化。利用位能原理和稳定性的能量准则，得到了岩体界面系统的不稳定性条件。分析结果表明，损伤区达到边界之前，系统可能是稳定的或者是不稳定的。依赖于分布剪切载荷和界面摩擦力的比较，若均布剪切载荷大于界面摩擦力，则系统不稳定，否则系统稳定；当损伤区达到边界之后，系统的不稳定性决定于载荷及界面材料性质，界面软化刚度系数和界面强度对于不稳定性有明显影响。     

基于热固耦合问题的多尺度拓扑优化设计

基于均质材料的拓扑优化逐渐难以适应现代化生产对工业产品高品质、轻量化的需求,同时很多工业设备经常面临着高温和高负载的工作环境.为了提高结构在温度载荷和机械载荷共同作用下的力学性能,本文提出了一种在稳态热源作用下的热固耦合连续体结构并行化拓扑优化方法.以结构刚度作为目标函数,材料的体分比为约束,利用能量均匀化方法预测微结...     

Oil sand deformation under cyclic loading of ultra-class mobile mining equipment

The strain softening of oil sand in the underfoot, due to the loading action of large mobile mining equipment such as trucks and shovels, yields a highly unstable condition for the operation of this ultra-class equipment. High maintenance costs as a result of truck and shovel frame failures are a frequent result of this instability. With the advent of ever larger units as mining operations move towards in-pit extractive technologies, some of these units are now approaching 2800 tons GVW. The ultra class units are able to operate year round, the interactions with the ground conditions have become an integral concern in selection of these units.The scaling approach and multi cycle convergent value approximation allows operations personnel to predict the degree of ground deformation for large mobile mining equipment. Thus enabling the decision of whether to operate equipment in a given soft ground location to be made.A full-scale field test was performed to study the ground stiffness behaviour during ground loading by ultra-class mobile mining equipment. The test involved a P&H 4100 BOSS ultra class shovel, which was tested with respect to its loading and ground response on high-grade oil sand. The field test mimicked real conditions while operating a shovel. This test was the first attempt to measure the stiffness of the oil sand environment by using in-place pressure cells and displacement-measurement tools.The model’s average error for deformation prediction for the shovel underfoot test was approximately 5%. The mining-induced confinement during the plate load test and equipment activities using the elastic model using Boussinesq’s approach was estimated. The Boussinesq’s approach provides a reasonable match between the field shovel test and the model’s outcome.     

Crack growth in concrete slab resting on steel beam: softening and damage accumulation

Analyzed in this work is the four-point bending of a concrete slab supported by a steel beam. An edge crack is assumed to prevail on the tension side of the concrete that would grow gradually while the overall stiffness and local fracture toughness of the concrete would also degrade as damage accumulates. The latter two quantities are assumed to decrease with increasing deflection of the composite system. These effects are incorporated into the strain energy density criterion that can simultaneously predict crack initiation and growth including the event of final termination. Numerical results on load and deflection are obtained for two different composite concrete/steel beam systems such that the prevailing geometric material and loading parameters are accounted for as a combination. The distances between the local and global stationary values of the volume energy density are also determined as an indication of fracture instability. An edge crack tends to extend more stably as the compressive zone ahead increases with deflection of the composite beam.     

部分充液多胞元结构的面内动态力学特性研究

为探究部分充液多胞元结构的抗冲击防护性能,结合充液内凹胞元的落锤冲击试验,建立了充液内凹胞元、部分充液内凹多胞元结构的冲击动态特性二维FEM数值分析,计算得到了部分充液内凹多胞元结构的变形破坏模式,讨论了不同冲击速度下部分充液内凹多胞元结构的动力学响应特性。结果表明:在充液胞元破损后,水介质会流入相邻未充液胞元,形成二次鼓胀吸能效应,从而有效提高结构壁面的变形吸能水平;结构中的充液区域和未充液区域的变形破坏模式分别为鼓胀拉伸和屈曲弯折;随着冲击速度的提高,结构的单位体积应变能以及对初始冲击载荷的削弱作用均得到增强。横向充液方式可以等效为变刚度弹簧的串联布置,该方式仅影响结构的局部刚度,纵向充液方式可以等效为多层变刚度弹簧的并联布置,该方式会影响结构的整体刚度;充液区域与未充液区域的等效刚度呈动态变化,结构变形模式由各区域实时的等效刚度决定。当载荷冲击速度较高时,横向和纵向部分充液内凹多胞元结构对初始冲击载荷的削弱能力均优于未充液内凹多胞元结构。     

Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness

Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models.     

基于分形理论和Mori-Tanaka方法的颗粒土渗透注浆加固体性能预测方法及应用

在注浆加固工程中, 为了避免空间变异性导致的支护结构受力过大而失稳, 提出合理的注浆加固体刚度及强度预测方法十分必要. 本文利用分形理论描述颗粒土类型的隧道围岩的孔隙特征, 基于迂曲度经验公式建立了地层体孔隙率和面孔隙率的转换关系. 以体孔隙率为变量, 结合Mori-Tanaka方法, 提出新的注浆加固体的宏观刚度预测方法. 利用能量法求解连通孔隙不同屈曲半波分布形态下的临界载荷作为加固体的单轴抗压强度, 从而建立了新的注浆加固体的强度预测理论模型. 以玉京山隧道为工程算例, 将本文方法在FLAC3D中进行二次开发, 通过对不同的地层单元随机生成孔隙率, 并利用本文方法计算并赋予地层单元不同的物理力学性质, 实现了围岩空间变异性的模拟, 数值模拟和现场监测得到的隧道洞身水平收敛的最大绝对误差仅为8 mm. 数值模拟结果表明, 对玉京山隧道回填区域进行注浆加固可以降低50%~90%的围岩位移, 极大地降低围岩不良区域对应的支护结构弯矩, 降低支护结构扭矩至0, 并将支护结构变形控制在10 mm以内, 但注浆加固难以改变灰岩和回填体之间的载荷分配规律.      

Usefulness of passive non-linear energy sinks in controlling galloping vibrations

The suppression of vibration amplitudes of an elastically-mounted square prism subjected to galloping oscillations by using a non-linear energy sink is investigated. The non-linear energy sink consists of a secondary system with linear damping and non-linear stiffness. A representative model that couples the transverse displacement of the square prism and the non-linear energy sink is constructed. A linear analysis is performed to determine the impacts of the non-linear energy sink parameters (mass, damping, and stiffness) on the coupled frequency and onset speed of galloping. It is demonstrated that increasing the damping of the non-linear energy sink can result in a significant increase in the onset speed of galloping. Then, the normal form of the Hopf bifurcation is derived to identify the type of instability and to determine the effects of the non-linear energy sink stiffness on the performance of the aeroelastic system near the bifurcation. The results show that the non-linear energy sink can be efficiently implemented to significantly reduce the galloping amplitude of the square prism. It is also shown that the multiple stable responses of the coupled aeroelastic system are obtained as well as the periodic responses, which are dependent on the considered non-linear energy sink parameters.     

Non-conservative stability of intermediate spring supported columns with an elastically restrained end support

The non-conservative stability of an intermediate spring supported uniform column clastically restrained at one end and subjected to a follower force at the other unsupported end is studied. It is found that when the intermediate spring support is far from the unsupported end, the instability mechanism is flutter. As the intermediate spring support approaches the unsupported end, the instability mechanism is changed from flutter to divergence with the increase of intermediate spring stiffness. For the hinged-intermediate and guided-intermediatc spring supported columns, the critical buckling load of flutter instability will first decrease, then increase as the intermediate spring stiffness is increased. Nevertheless, when the instability mechanism is divergence, the critical buckling load depends on the location of the intermediate spring support only, whereas for the clamped-intermediate spring supported column the critical buckling load of divergence instability decreases monotonically to a fixed value as the intermediate spring stiffness is increased. Finally, the influence of elastic end restraints on the stability of the column is also investigated.     

Determination of the critical loads of shells by nondestructive methods

Two methods for determining the location of and load level to produce instability of compressed cylindrical shells are presented. The first relates the variation in the wall normal stiffness as a function of applied compressive force to the critical load. It uses the distribution of stiffness over the surface of the shell as a guide to buckle location. The second method associates the local dynamic mass with instability behavior. The test data presented show that either method will give excellent prediction capability from low-load-level data for shells of orthodox form. Neither method appears to apply to spirally stiffened shells. This is thought to be due to the fact that there is a substantial difference between the buckle pattern under axial compression and the imperfection shape induced by the normal displacement which is used to ascertain the wall stiffness and the dynamic mass.     

磁耦合式双稳态宽频压电俘能器的设计和俘能特性

为了同时提高振动能量俘获系统的效率和实用性, 俘能器主结构的振动特性与环境振动特性的匹配度显得尤为重要. 非线性系统复杂的动力学行为为设计高效的俘能器奠定了基础, 但结构一旦被设计、生成出来, 其工作频率往往是固定的, 无法根据环境中的振动而发生相应的改变. 本文利用可移动铰支座和非线性磁力设计了一种具有双稳态特性的宽频压电俘能器, 通过拓宽压电俘能器的工作频带, 来匹配环境中较宽的振动频率. 为了保证系统低频宽带的俘能效果, 详细分析了结构的长度比、磁间距、负载阻抗、外激励频率和幅值等对系统线性刚度、非线性刚度以及动力学行为的影响, 并进行了实验验证. 首先将系统简化为欧拉-伯努力梁, 利用拉格朗日方程建立系统的非线性动力学方程, 并利用谐波平衡法进行求解. 针对理论分析给出的不同外激励频率下的最优长度比, 搭建了实验平台进行验证. 理论和实验的结果表明: 非线性磁力的引入使系统呈现负刚度特性, 使俘能器能够在单稳态和双稳态之间的变换, 实现低频俘能效果; 通过调节可移动铰支座的位置, 改变系统的长细比, 能够实现从0到16 Hz的宽频俘能效果.      

侵彻过程中弹引螺纹连接结构振动特性研究

针对侵彻过程中的弹引系统,对弹引螺纹连接结构振动特性进行了研究,建立了弹引螺纹连接结构弹性模型。在模型中,充分考虑了螺纹载荷分布不均匀的特性,不但给出了螺纹载荷分布规律,还给出了螺纹连接结构的等效刚度和振动频率;同时,为了验证模型的正确性,对弹引螺纹连接结构的拉伸和冲击过程进行了有限元仿真和试验,分别通过对弹引系统各结构振动特性的计算和对实测过载信号进行时频分析得到了系统的频率特性;将弹引系统的振动频率与实测过载信号的时频分析结果进行了对比。分析计算和试验结果发现:与静载荷时相比,冲击载荷作用下第一扣螺纹承受的载荷更大;螺纹连接结构的刚度明显小于固连结构;增加螺纹材料刚度、增加螺纹旋合长度、减小螺距能够有效增加螺纹连接结构固有频率;在侵彻过载测试信号的时频分析结果中明显存在与螺纹连接结构的振动频率一致的振动信号,并且该频率成分的信号幅值很高,对过载信号影响很大。     

新型负刚度吸能结构力学特性分析

负刚度结构作为一种具有广泛应用前景的力学超材料, 在吸能、减振及降噪等领域呈现出显著的优势, 但传统负刚度结构较低的比能吸收效率以及多稳态非自主回弹等特征, 严重限制了其工程应用. 为解决该问题, 通过单胞构型设计, 提出了一种新型可自主回弹的三维负刚度结构. 该结构利用串联的负刚度单胞在加载?卸载过程中, 曲梁胞元的自主反弹, 实现结构循环加载和多次重复利用; 通过凹槽深度设计抑制单胞多稳态的出现, 并且通过调整侧壁厚度, 控制曲梁屈曲模态的形式, 从而增大负刚度临界载荷差值, 实现吸能效率的显著提升. 随后为实现在复杂载荷环境下的高吸能, 对结构尺寸进行梯度设计, 提出了一种梯度负刚度结构, 利用有限元方法比较分析梯度负刚度结构与均匀负刚度结构在不同载荷作用下的吸能效果. 研究结果表明, 该梯度结构因微结构尺寸的不同, 具有不同的负刚度临界载荷最大值, 从而使其在不同的冲击载荷环境下, 在实现自主回弹的基础上, 均呈现出较好的吸能效率. 该新型负刚度结构为振动控制和结构重组等工程应用提供了技术支持.      

Parametric instability of a Jeffcott rotor with rotationally asymmetric inertia and transverse crack

Both the rotationally asymmetric inertia and transverse crack frequently appear in the rotor system. The parametric excitations induced by this two features cause instability and severe vibration under certain operating conditions. Thus, the parametric instability of a Jeffcott rotor with asymmetric disk and open transverse crack is studied analytically. The vibration equations of four degrees-of-freedom of the system are established, and the stiffness coefficients of cracked rotor shaft are derived based upon the compliance method and strain energy release rate method. Then, utilizing the harmonic balance method and Taylor expansion technique, the unstable widths of simple and combination instability regions (SIR and CIR) are solved approximately. For a practical rotor system, the approximate unstable widths are verified by the Floquet numerical analysis. The effects of crack depth and position upon the unstable widths are discussed, and the conditions for zero unstable points (ZUPs) are given: Besides the asymmetric angle should be π/2 (for SIR) or 0 (for CIR), the relationships between the inertia asymmetry and crack parameters (depth and position) are also presented analytically. These results would be useful for crack detection and instability control of the asymmetric rotor-bearing system.     

超低频振动能量收集器中夹片弹簧结构的建模与验证

针对一类基于夹片弹簧的压电振动能量收集器,利用材料力学莫尔积分理论建立了振荡俘能结构中夹片弹簧的等效刚度模型,通过万能拉伸试验机验证了模型精度.在此基础上,讨论了夹片弹簧刚度线性简化的两种途径:拉伸曲线线性拟合和固有频率修正.研究结果表明,从夹片弹簧拉伸曲线上看,将其等效成线性弹簧具有一定的合理性;而在实际振动能量收集器结构中,若振动加速度相对较小,通过固有频率修正法对夹片弹簧刚度进行线性简化,其幅频响应特性与非线性模型的特性相近.该研究成果为压电振动能量收集器的动力学和机电耦合模型简化提供了理论支撑.     

双联行星轮角度偏差对系统均载特性的影响

为了研究双联行星齿轮在实际设计参数下,其相对角度偏差对复合行星传动系统动力学特性的影响,采用集中参数法建立了3K-I型行星齿轮动力学模型,模型中将双联行星齿轮的相对角度偏差转化为啮合副齿侧间隙的变化,考虑了双联齿轮角度偏差、轮齿侧隙和时变啮合刚度等非线性因素,采用龙格库塔法求解了系统的时域响应并计算其均载系数。分析了不同工况、偏差下系统的动态特性。结果表明,存在双联行星轮角度偏差时,轻载下更容易发生齿轮的脱齿与冲击,系统的均载系数随着双联行星轮角度偏差差值及系统的负载降低而增大,各组行星轮角度偏差分布越集中,角度偏差对系统均载特性的影响越小;角度偏差分布同号时,对系统中某一对齿轮的承载影响明显;角度偏差分布异号时,对系统均载特性的影响最大。     

弯曲衬底上应变异质外延薄膜形态失稳的相场模拟

论文旨在研究弯曲衬底上应变异质外延薄膜的表面非线性演化行为,研究采用了基于Eshelby等效方法的相场微弹性模型来模拟二维应变Si1-xGex/Si薄膜/衬底系统的形态失稳.建立了关于等效特征应变和长程序参量的自由能泛函,数值求解了时间相关的Ginzburg-Landau动力学方程.系统自由能包括化学能,弹性应变能以及薄膜、衬底与真空相两两之界面能.跟踪了全时的形态演化过程,给出了指定时刻的量子点形态轮廓图.结果表明,量子点倾向于沉积在弯曲衬底的波谷处,波谷处是能量有利位置,量子点在此处比在波峰处更加稳定.论文所做的相场模拟可以用来预测量子点形成的轮廓、尺寸和位置,可以为控制和生成周期性自组装表面纳米结构提供理论指导.