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基于虛擬材料復模量非均勻分布的螺栓連接薄板結構半解析建模

Semianalytical modeling of a bolted thin plate structure based on nonuniform distributions of the complex modulus of a virtual material

  • 摘要: 基于非均勻分布的虛擬材料模擬螺栓連接薄板搭接部分的力學特性,其中虛擬材料的材料參數用復模量表示,可直接生成復剛度矩陣以表示搭接部分的剛度及阻尼特性,省卻了常規建模中生成結合部阻尼矩陣的步驟,在保證模型精確性的基礎上簡化了建模流程,以此建立了螺栓連接薄板結構的半解析模型并對其進行了動力學分析。首先描述了建模理念,將虛擬材料分別假定了三種復模量非均勻分布形式模擬螺栓搭接部分的力學特性,提出用反推辨識技術確定虛擬材料儲能模量與耗能模量的方法。接著,基于能量法并用正交多項式假定模態,推導了螺栓連接薄板的半解析分析模型,并創新性地給出了求解半解析模型任意錘擊點與拾振點處頻響函數的公式。最后,以一個具體的螺栓連接薄板結構為對象進行了實例研究,結果表明:用所創建的半解析模型計算出的各階仿真固有頻率與實驗測得的各階固有頻率的誤差均在5%以內,計算得到的各階仿真模態振型以及頻響函數曲線與實測值均較為接近,從而證明了利用復模量非均勻分布的虛擬材料模擬螺栓搭接部分可有效簡化螺栓結合部建模,亦可達到較高的仿真計算精度。

     

    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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