基于多项式拟合的细长梁结构振动位移重构方法

细长梁结构易受内外因素的干扰而振动,由此引发的疲劳损伤问题不利于结构安全。实时重构结构的振动位移是健康监测和振动智能控制中的关键环节。目前,模态分析法广泛用于细长梁结构的振动位移重构,但对于边界条件复杂的细长梁结构或结构受较强非线性因素干扰时,采用模态分析法重构结构位移将存在诸多不便。针对此问题,提出了基于多项式拟合的细长梁结构振动位移重构方法,并采用延展结构边界的方式有效规避了多项式拟合经常出现的龙格现象。通过有限元模拟和实验数据的对比,验证了基于多项式的位移重构方法的精确性和可行性。结果表明:基于多项式拟合的位移重构方法适用于细长梁结构线性振动和非线性振动的位移重构;延展结构边界可有效规避多项式拟合出现的龙格现象;延展长度为0.875L～1.125L(L为细长梁结构的长度),虚拟测点应变的量级小于等于真实测点应变最大值的量级时,重构得到的结构位移精度较高。

Displacement reconstruction of slender beam based on polynomial fitting method

Vibrations of slender flexible beam are induced easily by the inner and outer interference factors, which may cause severe fatigue damage and threaten the safety of the structure. Real-time reconstruction of structural vibration displacement is the key technology for structural health monitoring (SHM) and intelligent oscillation control. Nowadays, modal analysis approach is widely used in the displacement reconstruction of slender flexible beam. When the slender flexible beam has complex boundary conditions and strong nonlinear factors, modal analysis approach is not convenient to reconstruct the displacement. Hence, displacement reconstruction method for slender flexible beam based on polynomial fitting is put forward. The approach of extending structure boundary is employed to avoid the Runge phenomenon which usually occurs in polynomial fitting. The accuracy and feasibility of displacement reconstruction method based on polynomial fitting are validated by finite element simulation and reconstruction of experimental data. Some conclusions are drawn from the results. The displacement reconstruction method based on polynomial fitting is effective for the displacement reconstruction of linear and nonlinear vibrations of slender flexible beams. Extending structure boundary is useful to reduce the Runge phenomenon caused by polynomial fitting. When the extended length is 0.875L-1.125L (L is the length of slender flexible beam) and the magnitude of strains at the virtual measuring points is less than or equal to the magnitude of the maximum strain at the real measuring points, the reconstructed displacements have high accuracy.