拱形樑於端點受諧和激振時之折斷式挫曲分析與實驗

Abstract

本文以數值分析與實驗量測驗證拱形樑於端點受諧和激振作用下，將有可能發生折斷式挫曲，並持續在新的平衡位置振動。值得注意的是，我們需將激振器朝拱形樑方向移動些許距離，這是確保拱形樑將產生兩個穩定平衡位置。此外，我們在激振器與拱形樑之間外加一個彈簧做連接，這可使激振器在僅能達到有限的激振振幅下，仍能使拱形樑端點有足夠大的振幅產生，並使之能夠發生折斷式挫曲現象。在實驗方面，首先分別量測拱形樑兩個穩定平衡位置之自然頻率，調整激振頻率分別在兩個平衡位置之第一個自然頻率下做激振，透過適當的控制流經激振器之電流產生施加於激振器中央線圈的簡協磁力，可以發現拱形樑將由初始平衡位置發生折斷式挫曲至另一平衡位置，並會在新的平衡位置持續振盪。這些情況將記錄在實驗數據中，並將此實驗數據與數值模擬做比較。

In this paper we demonstrate, both numerically and experimentally, that it is possible to make a pinned-pinned shallow arch snap to and remain vibrating on the other side by harmonic excitation in the longitudinal direction at the end. One end of the arch is fixed in space, while the other end is attached to a mechanical shaker via a spring. The shaker mount is first moved a small distance toward the arch ends to ensure that the arch possesses two stable equilibrium positions, one on each side of the base line. The spring connecting the arch end and the mechanical shaker is carefully chosen such that small shaker stroke can induce large vibration amplitude of the arch. The natural frequencies of the two (initial and snapped, respectively) positions are measured first. By adjusting the excitation frequency of the mechanical shaker to the first natural frequency of either position of the arch, we demonstrate that the arch can be snapped to and remain vibrating on the other side when the magnitude of the electric current flowing through the shaker is properly chosen. The vibrant snapping action of the arch recorded in the experiment is confirmed by theoretical simulation.