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TECHNICAL PAPERS

Snapping of a Shallow Arch With Harmonic Excitation at One End

[+] Author and Article Information
Jen-San Chen1

Department of Mechanical Engineering,  National Taiwan University, Taipei, Taiwan 10617jschen@ccms.ntu.edu.tw

Der-Wei Chang

Department of Mechanical Engineering,  National Taiwan University, Taipei, Taiwan 10617

1

Corresponding author.

J. Vib. Acoust 129(4), 514-519 (Apr 16, 2007) (6 pages) doi:10.1115/1.2748479 History: Received December 23, 2006; Revised April 16, 2007

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 to ensure that the arch assembly 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 a small shaker stroke can induce a large vibration amplitude in 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 numerical simulation.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of a shallow arch with one end attached to a mechanical shaker. The shaker-mount is moved toward the arch a distance a to induce initial compression in the arch.

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Figure 2

The boundary separating the domains of two stable equilibrium positions and one stable equilibrium position in the k‐a plane. Point A represents the design parameters we choose in our experimental setup.

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Figure 3

The relation between spring constant k and the ratio ẽs∕ẽ. Only the spring constant k on the right-hand side of the vertical dashed line can guarantee the existence of two stable equilibrium positions. Point A represents the design parameters we choose in our experimental setup.

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Figure 4

Photograph of the experimental setup. (a) The initial unstressed position before the shaker-mount movement. (b) The P0 position after the shaker-mount movement. The arch is bent more compared to (a). (c) The snapped position P1− indeed exists.

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Figure 5

Measured frequency response functions of the assembly in (a) the initial prestressed position and (b) the snapped position

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Figure 6

Experimental (solid curve) and theoretical (dashed curve) lateral displacement history at the middle point of the arch. The arch starts at the initial prestressed position.

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Figure 7

Replot of Fig. 6 by shifting the numerical simulation result (dashed curve) to the right 0.13s such that the instants of the last peaks before snapping are aligned

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Figure 8

The measured longitudinal displacement history of the end slider (solid curve) and the shaker (dashed curve) in the experiment described in Fig. 6

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Figure 9

Experimental (solid curve) and theoretical (dashed curve) lateral displacement history at the middle point of the arch. The arch starts at the snapped position. The dashed curve is shifted to the right 0.14s such that the instants of the last peaks before snapping back are aligned.

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