具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学行为研究

弹性梁结构作为一种基本单元被广泛于建筑、航空、航天、船舶等工程领域. 为有效降低弹性梁结构的振动水平, 深刻理解其振动特性、动力学行为显得尤为重要. 本文建立了具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学分析模型, 并采用伽辽金截断法预报梁结构的动力学响应. 在伽辽金截断法的求解过程中, 选取具有弹性边界约束的轴向载荷梁结构的模态振型函数作为伽辽金截断法的试函数与权函数. 首先, 研究截断数对伽辽金截断法稳定性的影响, 并采用谐波平衡法研究伽辽金截断法的可靠性. 在此基础上, 研究谐波激励扫频方向、非线性支撑参数对具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学响应的影响规律. 研究结果表明, 具有非线性支撑和弹性边界约束的轴向载荷梁结构的动力学响应具有初值敏感性且非线性支撑参数对梁结构动力学响应的影响显著. 相关非线性支撑参数使得梁结构出现复杂动力学行为. 合适的非线性支撑参数能够抑制具有非线性支撑和弹性边界约束的轴向载荷梁结构的复杂动力学行为并对梁结构边界处的减振具有有益效果. 

DYNAMIC BEHAVIOR ANALYSIS OF THE AXIALLY LOADED BEAM WITH THE NONLINEAR SUPPORT AND ELASTIC BOUNDARY CONSTRAINTS

As a basic structural member, elastic beam structures are widely used in architecture, aviation, aerospace, shipbuilding, and other engineering fields. To suppress the vibration level of elastic beam structures effectively, it is of great significance to understand their vibration characteristics and dynamic responses. This manuscript establishes the vibration analysis model of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Dynamic behavior of the beam structure is predicted by applying the Galerkin truncated method. Mode functions of the axially loaded beam structure with elastic boundary constraints are selected as the trial and weight function in Galerkin truncated method. Firstly, the influence of the truncated number on the stability of the Galerkin truncated method is studied and the reliability of the Galerkin truncated method is verified by the harmonic balance method. On this basis, the influence of the sweep direction of the harmonic excitation and the parameters of the nonlinear support on the dynamic responses of the axially loaded beam structure with nonlinear supports and elastic boundary constraints is studied. The results show that dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints are sensitive to the initial values of calculation. Parameters of the nonlinear support significantly affect the dynamic responses of the axially loaded beam with the nonlinear support and elastic boundary constraints. In certain parameters of the nonlinear support, the complex dynamic behavior of the beam structure with the nonlinear support and elastic boundary constraints appears. Appropriate parameters of the nonlinear support can suppress the complex dynamic behavior of the axially loaded beam structure with the nonlinear support and elastic boundary constraints. Meanwhile, appropriate parameters of the nonlinear support can also suppress the vibration level at both ends of the axially loaded beam structure with the nonlinear support and elastic boundary constraints.