Post-grazing dynamics of a vibro-impacting energy generator
Post-grazing dynamics of a vibro-impacting energy generator
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DOI：
10.1016/j.jsv.2020.115811
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Larissa Serdukova;R. Kuske;D. Yurchenko
中科院分区：
文献类型：
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作者：
Larissa Serdukova;R. Kuske;D. Yurchenko
在设备底部和顶部的冲击次数不对称的参数范围内研究强制振动冲击倾斜能量采集器的运动。这种运动发生在掠过分叉之外，在该分叉处，交替的顶部和底部冲击由与设备底部的零速度冲击来补充。对于周期性力，我们获得了不对称周期性运动的半解析表达式，其对设备底部和顶部的影响分别为 2:1。这些表达式是通过不同冲击对之间的一组非线性映射，并结合提供速度跳跃不连续性的冲击条件而得出的。解析解的分岔图由围绕 2:1 非对称周期解的线性稳定性分析进行补充，并经过数值验证。对于较小的倾斜角度，可以通过数值方式检测到第二个掠分叉，从而导致 3:1 的不对称性。对于较大的倾斜角，倍周期分岔先于掠线分岔。对于不对称运动，每次冲击所转换的电能会减少，因此在此指标下不太理想。
The motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. This motion occurs beyond a grazing bifurcation, at which alternating top and bottom impacts are supplemented by a zero velocity impact with the bottom of the device. For periodic forcing, we obtain semi-analytical expressions for the asymmetric periodic motion with a ratio of 2:1 for the impacts on the device bottom and top, respectively. These expressions are derived via a set of nonlinear maps between different pairs of impacts, combined with impact conditions that provide jump discontinuities in the velocity. Bifurcation diagrams for the analytical solutions are complemented by a linear stability analysis around the 2:1 asymmetric periodic solutions, and are validated numerically. For smaller incline angles, a second grazing bifurcation is numerically detected, leading to a 3:1 asymmetry. For larger incline angles, period doubling bifurcations precede grazing bifurcations. The converted electrical energy per impact is reduced for the asymmetric motions, and therefore less desirable under this metric.