Modal energy exchanges in an impulsively loaded beam with a geometrically nonlinear boundary condition: computation and experiment
Modal energy exchanges in an impulsively loaded beam with a geometrically nonlinear boundary condition: computation and experiment
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具有几何非线性边界条件的脉冲加载梁中的模态能量交换：计算和实验
DOI：
10.1007/s11071-020-06156-7
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发表时间：
2021
影响因子：
5.6
通讯作者：
Vakakis, Alexander F.
中科院分区：
文献类型：
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作者：
Mojahed, Alireza;Liu, Yang;Bergman, Lawrence A.;Vakakis, Alexander F.
几何非线性边界条件的能力，即，研究了悬臂Euler-Bernoulli梁振动模态间宽带输入能量（由脉冲载荷产生）“再分配”的一种强局部非线性。结果表明，这种模式的能量重新分配增加了被动耗能悬臂梁的固有能力。非线性边界条件是通过一个倾斜的线性弹簧-阻尼器对实现接地的自由端的悬臂梁的中性轴，而在休息时的初始倾角。对于，倾斜弹簧-阻尼器对是几何非线性的，而在极限情况下边界条件是线性的。为了研究悬臂梁的非线性模态能量再分配，采用多步系统识别方法来识别实验夹具的未知参数;这通知夹具的计算降阶有限元（FE）模型。首先，采用多输入多输出频域识别（MFDID）技术对无边界条件的“基底”线性悬臂梁的实验频响函数进行分析，识别出其模态参数。其次，施加极限角的边界条件，从而再次得到线性夹具。通过调和计算和实验测量，（线性）刚度和阻尼系数的边界，以及确定。最后，通过改变倾斜角度的范围内，非线性边界条件的识别的有限元模型的非线性瞬态响应的计算和投影到线性化的模态基础的系统在零能量的限制。有限元计算结果与实验测量结果进行了比较。在此之后，计算系统的时间平均模式能量，并用于估计分配给每个模式的光束的总能量的部分。此外，通过使用这些模态能量，可以研究和跟踪非线性边界附着的不同初始倾角的模态子集之间的非线性能量交换。通过实验测量验证了计算结果，从而突出了计算有限元模型的预测能力。在最后一步中，通过计算每个瞬时模态能量的百分比中的最大波动来定义模态能量交换的标量测量，该最大波动是由模态交换的能量的最大百分比。这个措施被证明是依赖于初始能量和初始倾角。同样，实验测量有利地比较计算FE模拟。
The capability of a geometrically nonlinear boundary condition, i.e., a strong local nonlinearity, in “redistributing” a broadband input energy (generated by an impulsive load) among the vibration modes of a cantilever Euler–Bernoulli beam is investigated. It is shown that this modal energy redistribution increases the inherent capacity of the cantilever for passive energy dissipation. The nonlinear boundary condition is realized by grounding the free end of the cantilever through an inclined linear spring–damper pair with initial angle of inclinationrelative to the neutral axis of the beam while at rest. For, the inclined spring–damper pair isgeometrically nonlinear, whereas in the limiting casethe boundary condition becomeslinear. To study the nonlinear modal energy redistribution in the cantilever, a multi-step system identification method to identify the unknown parameters of the experimental fixture is employed; this informs a computational reduced-order finite element (FE) model of the fixture. First, the Multi-input Multi-output Frequency Domain Identification (MFDID) technique to analyze the experimental frequency response functions of the “base” linear cantilever without the boundary condition is employed and its modal parameters are identified. Next, the boundary condition for the limiting angleis imposed, so that again a linear fixture is obtained. Through reconciliation of computational and experimental measurements, the (linear) stiffness and damping coefficients of the boundary are identified, as well. Finally, by varying the angle of inclination in the range, the nonlinear transient responses of the identified FE model with the nonlinear boundary condition are computed and projected onto the linearized modal basis of the system in the limit of zero energy. The computational FE results favorably compare with experimental measurements. Following this, the time-averaged modal energies of the system are computed and used to estimate the portion of the total energy of the beam allocated to each mode. Additionally, by employing these modal energies one may study and track the nonlinear energy exchanges between subsets of modes for different angles of initial inclinationof the nonlinear boundary attachment. The computational results are validated by experimental measurements, thus highlighting the predictive capacity of the computational FE model. In the last step, a scalar measure for modal energy exchange is defined by computing the maximum fluctuation in the percentage of each of the instantaneous modal energies that is the maximum percentage of energy being exchanged by the modes. This measure proves to be dependent on both the initial energy and the initial angle of inclination. Again, experimental measurements favorably compare to computational FE simulations.
局部非线性存储在实验模型平面中引起全局动态效应
影响因子：
2.5
作者：
K. Moore;A. Mojahed;L. Bergman;A. Vakakis
通讯作者：
A. Vakakis
双稳态非线性能量吸收器的频率与能量依赖性
影响因子：
--
作者：
M. Al;Adnan S. Saeed
通讯作者：
Adnan S. Saeed