【作者】 李媛萍；

【导师】 张卫；

【作者基本信息】 暨南大学 ， 工程力学， 2010， 博士

【摘要】 大跨空间结构多用于具有特殊用途的重要公共建筑中,除了造型和工艺比普通建筑更加复杂之外,建筑物内部使用的电力、热力设施亦非常复杂,而且人员相对密集,一旦发生破坏,造成的经济损失和社会后果将尤为严重,因此,在设计这类结构时更应该充分地考虑其在服役期间可能遇到的各种极端状况并予以防止或加强,以确保其经济合理及安全可靠。大跨空间结构往往跨度大、厚度薄、重量轻,因此其几何非线性问题较突出,另外,大跨空间结构用材多为钢或铝合金,在高温环境或爆炸、冲击荷载作用下以及在采取一些减震控制措施之后,材料的时间相关性将大大增强而实质上成为一种粘弹性或粘弹塑性材料。基于以上原因,本文以非线性粘弹性结构的动态行为作为研究重点,并考察了大跨空间结构中较有代表性的单层球面网壳的减震控制问题。首先,本文利用分数算子能够较好地描述材料的时间和频率效应这一优点,根据不同应力状态下金属材料的应力应变关系,推导了适用于金属材料的分数导数型粘弹性和粘弹塑性本构模型并进行了实验验证,结果证明该本构模型不仅能较好地与实验数据相吻合,而且能较好地预测材料长时间蠕变行为。针对Riemann-Liouville分数导数定义中积分内核函数的奇异性问题,本文利用分段处理的方法成功地予以解决并建立了线性和非线性分数导数的数值计算格式,算例表明,本文所建立的算法不仅成功地解决了被积函数的奇异性问题,而且具有收敛快,精度高,稳定性好的优点。在第4章中,通过调节系统的特征参数,探讨了自治和非自治分数阶Ver Del Pol-Duffing耦合系统的动态行为,研究发现,该系统不仅具有与经典Van der pol-Duffing耦合系统相似的振动特性,而且可以额外地通过调节分数导数阶值来调节系统的自振特性；分数算子在振动控制问题中具有极大的优越性。第5章所探讨的两端铰接扁拱的无量纲化动力学方程复杂且无法直接求解,本文分别对其进行了1阶和2阶Galerkin截断简化,并分别探讨了两类截断系统的动力学行为随阻尼系数、分数导数阶值以及外激励幅值的变化,对比分析表明：两种简化系统中都普遍存在着倍周期分岔和阵发性混沌现象,定性性质基本一致,但1阶Galerkin系统中还存在多解共存现象,系统的振动状态对初始条件非常敏感；调节分数导数阶值可以唯一确定地改变系统的振动特性。再次证明了分数算子在振动控制系统中具有重要作用。在第6章对两杆平面桁架结构动态行为的研究中,本文对比了系统在垂直、水平以及复合加载方式下的平衡路径,研究发现：复合加载方式相当于在垂直加载时施加了水平扰动而导致系统的运动发生分歧,平衡路径变得复杂,系统的极限承载力变小。本章还利用相图的概念将结构的动力极限承载力与分岔、混沌现象成功地联系起来,并提出：分岔意味着动力加载的临界状态,混沌意味着动力加载已超过系统的极限承载力,在实际工程中可以取系统从周期运动突变为混沌时所对应的外激励幅值作为系统的动力极限承载力。本文第7、8章为工程应用部分。在第7章中,在对ANSYS软件进行二次开发的基础上对比了弹性和粘弹性材料特性下具有相同跨度、相同矢跨比以及相同杆件截面的单层球面网壳动态行为的差异,对比分析发现,考虑材料的时间相关性之后,网壳的自振频率减小；材料自身的阻尼导致网壳振动特性发生明显改变；在高温、受控等特殊情况下材料的时间相关性成为影响结构动态性能的重要因素,必须予以考虑。在第8章中,将粘弹性阻尼器引入某单层球面网壳中进行减震控制,对受控前后球壳的动态行为进行了对比分析,提出了阻尼器的最佳布置方式以及阻尼器参数的最佳取值范围,为相关工程提出了参考意见。更多还原

【Abstract】 Long span space structures are widely used in important public buildings. They are complex not only on architectural modeling and construction technology but also on inner facilities of electricity, thermal and water supply. The geometrically nonlinear problems of long span space structures are very conspicuous because of their large span, thin thickness and light weight. In addition, long span space structures are often made by steel or aluminum alloy materials, the viscosity of materials will be greatly enhanced in high temperature environment or under an explosion, impact load or after being taken some vibration control measures. The structures essentially become a kind of viscoelastic or visco-elastic plastic structures on condition of mentioned above. The main motivation of this dissertation is to study the dynamic behaviors of several kinds of viscoelastic structures and the seismic control of long span space shell.Firstly, fractional derivative viscoelastic and visco-elastic plastic constructive model of steel and aluminum alloy material are proposed, which provided with strongpoint to describe the time and frequency effects. Subsequently in chapter 2, the creep experiment of aluminum alloy material and dynamic characteristic experiments of three polymeric materials are made to prove the advantage of fractional constructive model. Then, numerical computation schemes for fractional derivative are deducted in chapter 3. The results of silmulation sample shows that the proposed method possesses the advantages of fast convergence, higher accuracy and better stability.In chapter 4, the dynamic characteristics of autonomy and non-autonomy fractional Van Der Pol-Duffing system are discussed based on the numerical scheme proposed in chapter 3 and Runge-Kutta method. The results show that the responses of this fractional system are similar to classical Van Der Pol-Duffing system. Moreover, the order of fractional derivative can change the oscillation period and nonlinearity of the system greatly. In additional, the output energy under seismic loads can be varied by changing the fractional order, which can be used to seismic control.In chapter 5, the first and second order Galerkin methods are used to simplify the flat hinged shallow arch structure. The dynamic responses with varyiance of damping coefficient, fractional order and excitation amplitude are illustrated. The results show that this nonlinear system has complex dynamics phenomena such as period doubling bifurcation and chaos. In additional, there is coexistence of solutions found in the first order Galerkin system.In chapter 6, comparison is made to exposure the balance route of a two-bar plane truss structure under vertical loads, horizontal loads or compound loads. The research results show that balance route of the compound loads is more complex than the others, which is equivalent to vertical loads with horizontal disturbance, and the support capacity decreases under compound loads. Then, based on the phase portrait definition, the relationship of ultimate bearing capacity of structure with bifurcation and chaos is built. In this theory, bifurcation means critical condition and chaos means ultimate bearing capacity.The final part of this dissertation is engineering application. In chapter 7, the difference of dynamic characteristics between an elastic single-layer spherical shell with a viscoelasticity aluminum alloy single-layer spherical shell on condition of same span, same rise-span ratio and same member sections. The results show that the time-dependence of the material may affect the structure’s dynamic behaviors greatly. In chapter 8, viscoelastic dampers are introduced into a single-layer spherical shell for seismic control and the dynamic performances of controlled shell and uncontrolled shell are contrasted. Parameter analyses are performed to investigate the influence of dampers’positions and parameters on seismic control effort. The results show that it is feasible to seismic control by viscoelastic dampers, but the control effort is greatly influenced by the dampers’location and parameters.更多还原