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基于功率密度流的多柔体系统动响应优化

Dynamic Response Optimization of A Flexible Multi Body System Based on Power Density Flow

  • 摘要: 针对柔性结构在复杂载荷作用下能量传播路径识别与结构响应优化的挑战,本文融合功率密度流理论与多柔体系统动力学建模,建立了能量传播分析与动响应优化框架。为准确捕捉局部应力与速度场,并实现功率密度流的可视化与优化,采用具有几何非线性和速度场连续的绝对节点坐标法(Absolute Nodal Coordinate Formulation, ANCF)进行建模。进一步结合Green-Lagrange应变张量与弹性矩阵,推导出薄板结构振动功率密度流的理论表达式,明确应力和振动速度对能量传播路径与分布的影响机制。利用该方法,分别对柔性双连杆机构和卫星本体板结构进行了能量流仿真,发现在连接处及铰支点附近存在显著的能量集中现象。基于此现象,以能量密度分布为优化目标,在保持结构总质量不变的前提下,通过调整单元尺寸参数来抑制能量集中效应。优化结果表明:柔性双连杆机构的能量密度峰值下降了68.5%,其关键部位的位移响应峰值下降约36%,振动水平显著降低;卫星本体板结构的最大能量密度降低了7%,其关键部位的位移响应峰值下降约12%。本文提出的基于功率密度流的结构优化方法为航天器等薄板结构的响应优化提供了新的策略,有效弥补了传统模态分析方法的不足,在复杂载荷环境下的结构动力学设计中具有重要的应用价值。

     

    Abstract: To address the challenges in identifying energy transmission paths and optimizing structural responses of flexible structures under complex loads, this paper integrates power density flow theory with flexible multibody dynamic model to build an analysis and optimization framework. The Absolute Nodal Coordinate Formulation (ANCF), featuring geometric nonlinearity and continuous velocity fields, is employed to accurately capture local stress and velocity distributions and to enable visualization and optimization of power density flow. By combining the Green–Lagrange strain tensor with the elastic matrix, the theoretical expression for the vibration power density flow in a thin plate structure is derived, clarifying how stress and vibration velocity influence the energy propagation path and distribution. Using the power density flow analysis method, energy flow simulations are conducted for a satellite panel structure and a flexible double-link mechanism. A significant energy concentration is observed near connection points and hinge supports. Taking the energy density distribution as the optimization objective and keeping the total mass constant, the element thickness distribution is adjusted to mitigate the energy concentration effect. The optimization results show that the peak energy density of the flexible two-link mechanism is reduced by 68.5%, and the peak displacement response at the key position decreases by approximately 36%. For the satellite panel, the maximum energy density is reduced by 7%, and the peak displacement response at key positions decreases by about 12%, indicating a significant reduction in vibration levels. The proposed structural optimization method based on power density flow provides a new energy-based strategy for vibration suppression of thin-walled structures such as spacecraft, effectively overcoming the limitations of traditional modal analysis and offering important application value in structural dynamics design under complex load environments.

     

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