| 基于虚拟材料复模量非均匀分布的螺栓连接薄板结构半解析建模 |
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| 作者姓名： | 刘晓峰 孙伟 孙悦 |
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| 作者单位： | 1.东北大学机械工程与自动化学院，沈阳 110819 |
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| 基金项目： | 中央高校基本科研业务费专项资金资助项目（N180312012） |
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| 摘 要： | 基于非均匀分布的虚拟材料模拟螺栓连接薄板搭接部分的力学特性，其中虚拟材料的材料参数用复模量表示，可直接生成复刚度矩阵以表示搭接部分的刚度及阻尼特性，省却了常规建模中生成结合部阻尼矩阵的步骤，在保证模型精确性的基础上简化了建模流程，以此建立了螺栓连接薄板结构的半解析模型并对其进行了动力学分析。首先描述了建模理念，将虚拟材料分别假定了三种复模量非均匀分布形式模拟螺栓搭接部分的力学特性，提出用反推辨识技术确定虚拟材料储能模量与耗能模量的方法。接着，基于能量法并用正交多项式假定模态，推导了螺栓连接薄板的半解析分析模型，并创新性地给出了求解半解析模型任意锤击点与拾振点处频响函数的公式。最后，以一个具体的螺栓连接薄板结构为对象进行了实例研究，结果表明:用所创建的半解析模型计算出的各阶仿真固有频率与实验测得的各阶固有频率的误差均在5%以内，计算得到的各阶仿真模态振型以及频响函数曲线与实测值均较为接近，从而证明了利用复模量非均匀分布的虚拟材料模拟螺栓搭接部分可有效简化螺栓结合部建模，亦可达到较高的仿真计算精度。
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| 关 键 词： | 虚拟材料 复模量 非均匀分布 螺栓连接薄板 半解析建模 |
| 收稿时间： | 2020-04-20 |
Semianalytical modeling of a bolted thin plate structure based on nonuniform distributions of the complex modulus of a virtual material |
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| Authors: | LIU Xiao-feng SUN Wei SUN Yue |
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| Affiliation: | 1.School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China2.Key Laboratory of Vibration and Control of Aero-Propulsion Systems, Ministry of Education of China, Northeastern University, Shenyang 110819, China |
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| Abstract: | The simulation of bolt joints affects the analysis accuracy of the dynamic characteristics of the whole structure in the dynamic modeling of bolted connection structures. In this study, the mechanical properties of the bolted thin-plate lap joint were simulated based on a nonuniformly distributed virtual material. The parameters of the virtual material were expressed based on a complex modulus, and the complex stiffness matrix can be directly generated to express the stiffness and damping characteristics of the lap joint. The steps used to generate a joint damping matrix in conventional modeling were omitted, and the modeling process was simplified to ensure model accuracy. We established a semianalytical model of a bolted thin plate structure to enable its dynamic analysis. In this study, we first described the modeling concept. The virtual material was assumed to have three types of nonuniform complex modulus distributions to simulate the mechanical properties of the bolted lap joint. We proposed a method for determining the storage modulus and energy dissipation modulus of the virtual material using a reverse identification technique. Based on the energy method and the assumed modes of orthogonal polynomials, we derived a semianalytical model of bolted thin plates and develop an innovative formula for solving the frequency response function at any hammering point and the vibration point of the semianalytical model. Finally, we conducted a case study on a bolted thin plate structure. Results show that the deviation between the simulated natural frequencies calculated using the semianalytical model and the experimental natural frequencies are less than 5%. Further, the calculated model shapes and frequency-response-function curves are close to those obtained based on the measured values. These results prove that a virtual material with a nonuniform complex modulus distribution can effectively simplify the modeling of a bolted joint and achieve high simulation accuracy. |
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