振动冲击能量发生器的后掠动力学
Post-grazing dynamics of a vibro-impacting energy generator
摘要：
研究了受迫振动冲击倾斜能量采集器在设备底部和顶部冲击次数不对称的参数范围内的运动。这种运动发生在掠射分叉之外，在掠射分叉处，交替的顶部和底部撞击由与装置底部的零速度撞击补充。对于周期性强迫，我们得到了半解析表达式的非对称周期性运动的比例为2：1的影响，在设备底部和顶部，分别。这些表达式是通过一组非线性映射之间的不同对的影响，结合影响条件，提供跳跃的速度不连续性。分岔图的分析解决方案的线性稳定性分析周围的2：1非对称周期解的补充，并进行了数值验证。对于较小的倾斜角，第二个擦边分叉的数值检测，导致3：1的不对称性。对于较大的倾斜角，倍周期分叉先于此分叉。对于非对称运动，每次冲击的转换电能减少，因此在该度量下不太理想。
英文摘要：
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 this bifurcation. The converted electrical energy per impact is reduced for the asymmetric motions, and therefore less desirable under this metric.
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