多梁结构是一种典型的工程结构，该结构在被碰撞过程中，一部分冲击动能会以弹性波的形式被传递到结构中，引起结构振动而耗散冲击能量：比如多梁超材料结构具有优越的抗冲击特性。但这部分能量也会引起结构的破坏：比如在反应堆堆芯结构中，含有大量的细长构件，在动态激励（如地震、碰撞等）下，冲击能量会引起构件的变形，使得内部产生挤压和接触，进而影响核反应堆堆芯的安全性。基于上述研究背景，本文首先分析了小球冲击杆、板、梁等结构动力学行为以及多梁结构抗冲击的研究现状，并针对现有研究的不足，提出了急需解决三个关键问题：梁非线性接触动力学的基本解答，多梁结构抗冲击中多梁接触耦合关系，典型多梁结构（反应堆燃料组件）抗震分析中的接触非线性计算方法。以理论研究为基础，结合数值计算方法与有限元数值模拟方法，本文主要内容和研究成果如下：
梁的非线性接触动力学行为研究：根据碰撞接触的实际应用环境，研究了悬臂梁尖端碰撞、小球与简支梁碰撞以及自由梁与凸起壁面碰撞三种情况。针对悬臂梁的尖端碰撞问题，将快中子反应堆中的燃料棒束管简化为悬臂梁模型，建立其端部存在非线性碰撞引起动力学响应的计算方法；提出了改进的模态叠加法获得动力学响应的计算模型，并与有限元方法对比验证了模型的准确性；研究发现，当弹簧刚度较大时，梁的尖端位移可能会出现过冲现象，导致短期内碰撞力增大，且激发梁的高阶模态振动。对于小球与简支梁的碰撞问题，采用模态叠加法和龙格库塔数值方法分别求解了 Timoshenko 梁和小球的动力学方程；研究讨论了梁长对接触结果的影响，揭示了小球的速度恢复系数 (COR) 与梁长的内在关系，发现冲击引起的高频振动对梁的动态响应有显著影响；此外，对球-梁冲击问题进行了参数敏感性分析，探讨了碰撞速度、小球质量和碰撞刚度等因素对速度恢复系数的影响。最后，研究了自由梁与凸起壁面的碰撞问题，建立了自由梁的动力学方程，通过改进的模态叠加法进行求解，并与有限元方法的结果对比，验证了计算结果的准确性；探讨了碰撞刚度对 COR 、回弹时间和接触次数的影响，发现随着刚度的增加， COR 和回弹时间会发生减小。且接触次数的增加会影响系统的动态响应，但不会导致更高阶振动模态的出现。
多梁结构的非线性接触动力学行为研究：基于发展的多梁系统接触关系，建立了考虑多根燃料棒束管作为多个悬臂梁、间隔垫作为非线性弹簧的力学简化模型。利用 Euler-Bernoulli 梁理论和改进的模态叠加法，研究了冲击工况下的非线性碰撞过程，并与有限元结果对比验证了方法的正确性；揭示了柔性振动在多梁系统中的 “衰减” 效果，获得了多梁系统具有抗冲击能力的力学原理。此外，研究了小球冲击十字堆叠多梁结构的响应，采用数值方法和改进的模态叠加法 (MMSM) 分别求解小球与多梁结构的运动，通过与有限元方法 (FEM)、离散元方法 (DEM) 的比较，验证了MMSM的正确性，揭示了冲击激起多梁结构超过前3阶模态高频率振动的原理；分析了柔性振动对波传播的影响，发现柔性振动在提高能量耗散方面的关键作用，并定量描述了多梁堆叠结构的抗冲击能力，指出了堆叠层数对于实现有效减振的重要性；讨论了梁长和接触点位置对减振效果的影响，为抗冲击结构设计提供了参考。
多梁结构的非线性抗震分析：面对反应堆堆芯全尺度多梁模型计算量过大的问题，建立了非线性双梁力学简化模型，用于模拟压水堆核燃料组件中燃料棒与格架之间的复杂接触关系。该模型通过静态加载实验、横向弹弓实验数据的对比，验证了模型的准确性，揭示了燃料组件结构静态载荷与位移之间的滞回曲线关系，表明模型能够捕捉到摩擦对能量耗散的影响。此外，利用该模型计算了在白噪声激励下燃料组件的动态响应，得到了随着激励幅值增大各阶频率减小的非线性特征。在人工合成地震波激励下结构的抗震分析中，计算出了各碰撞点的最大接触力，与实验结果比较，表明了所建力学模型的正确性。这些研究解决了反应堆组件内部由于复杂接触引起的强非线性问题，为核电站的安全设计提供了科学依据。

Multi-beam structure is a typical engineering structure. During the collision process of this structure, part of the impact kinetic energy will be transferred to the structure in the form of elastic waves, causing structural vibration and dissipating impact energy. For example, multi-beam metamaterial structures have superior impact resistance characteristics. However, this part of energy can also cause structural damage. For example, in reactor core structures, there are a large number of slender components. Under dynamic excitations (such as earthquakes, collisions, etc.), the impact energy will cause deformation of the components, resulting in internal extrusion and contact, which in turn affects the safety of the nuclear reactor core. Based on the above research background, the thesis first analyzes the research status of the dynamic behavior of structures such as a sphere impacting rods, plates, and beams, as well as the impact resistance of multi-beam structures. In view of the deficiencies of existing research, three key issues that need to be urgently solved are proposed: the basic solution of the nonlinear contact dynamics of beams, the multi-beam contact coupling relationship in the impact resistance of multi-beam structures, and the contact nonlinear calculation method in the seismic analysis of typical multi-beam structures (reactor fuel assemblies). Based on theoretical research and combined with numerical calculation methods and finite element numerical simulation methods, the main contents of this paper are as follows:
Research on the nonlinear contact dynamic behavior of beams: According to the actual application environment of collision contact, three situations are studied: tip collision of cantilever beams, collision of small balls with simply supported beams, and collision of free beams with convex walls. For the tip collision problem of cantilever beams, the fuel rod bundle tube in a fast neutron reactor is simplified as a cantilever beam model, and a calculation method for the dynamic response caused by nonlinear collision at the end is established; an improved modal superposition method is proposed to obtain a calculation model for dynamic response, and the accuracy of the model is verified by comparison with the finite element method; it is found that when the spring stiffness is large, the tip displacement of the beam may overshoot, resulting in an increase in the collision force in a short period of time and exciting the high-order modal vibration of the beam. For the collision problem between a small ball and a simply supported beam, the modal superposition method and the Runge-Kutta numerical method are used to solve the dynamic equations of the Timoshenko beam and the small ball respectively; the influence of beam length on the contact result is studied and discussed, and the inherent relationship between the velocity restitution coefficient (COR) of the small ball and the beam length is revealed. It is found that the high-frequency vibration caused by the impact has a significant impact on the dynamic response of the beam; in addition, a parameter sensitivity analysis of the ball-beam impact problem is carried out, and the influence of factors such as collision speed, small ball mass and collision stiffness on the velocity restitution coefficient is discussed. Finally, the collision problem between a free beam and a convex wall is studied, the dynamic equation of the free beam is established and solved by an improved modal superposition method, and the accuracy of the calculation results is verified by comparison with the results of the finite element method; the influence of collision stiffness on COR, rebound time and number of contacts is discussed. It is found that as the stiffness increases, COR and rebound time will decrease, and the increase in the number of contacts will affect the dynamic response of the system, but will not lead to the appearance of higher-order vibration modes.
Research on the nonlinear contact dynamic behavior of multi-beam structures: Based on the developed contact relationship of multi-beam systems, a mechanical simplified model considering multiple fuel rod bundle tubes as multiple cantilever beams and spacers as nonlinear springs is established. Using Euler-Bernoulli beam theory and an improved modal superposition method, the nonlinear collision process under impact conditions is studied, and the correctness of the method is verified by comparison with the finite element results; the "attenuation" effect of flexible vibration in multi-beam systems is revealed, and the mechanical principle of the impact resistance of multi-beam systems is obtained. In addition, the response of a small ball impacting a cross-stacked multi-beam structure is studied. Numerical methods and an improved modal superposition method (MMSM) are used to solve the motion of the small ball and the multi-beam structure respectively. By comparison with the finite element method (FEM) and the discrete element method (DEM), the correctness of MMSM is verified, and the principle of impact exciting high-frequency vibrations of more than the first three modes of the multi-beam structure is revealed; the influence of flexible vibration on wave propagation is analyzed, and the key role of flexible vibration in improving energy dissipation is found. The impact resistance of the multi-beam stacking structure is quantitatively described, and the importance of the number of stacking layers for achieving effective vibration reduction is pointed out; the influence of beam length and contact point position on the vibration reduction effect is discussed, providing a reference for the design of impact-resistant structures.
Nonlinear seismic analysis of multi-beam structures: Facing the problem of excessive calculation amount of the full-scale multi-beam model of the reactor core, a nonlinear double-beam mechanical simplified model is established to simulate the complex contact relationship between fuel rods and grids in a pressurized water reactor fuel assembly. The accuracy of the model is verified by comparison with static loading experiment and transverse slingshot experiment data, revealing the hysteresis curve relationship between static load and displacement of the fuel assembly structure, indicating that the model can capture the influence of friction on energy dissipation. In addition, this model is used to calculate the dynamic response of the fuel assembly under white noise excitation, and the nonlinear characteristic of each order frequency decreasing with the increase of excitation amplitude is obtained. In the seismic analysis of the structure under artificially synthesized seismic wave excitation, the maximum contact force at each collision point is calculated. Compared with the experimental results, the correctness of the established mechanical model is shown. These studies solve the strong nonlinear problem caused by complex contacts inside the reactor fuel assembly and provide a scientific basis for the safety design of nuclear power plants.