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TECHNICAL PAPERS

# Vibration and Stability of a Shallow Arch Under a Moving Mass-Dashpot-Spring System

[+] Author and Article Information
Jen-San Chen

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

Min-Ray Yang

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

J. Vib. Acoust 129(1), 66-72 (May 21, 2006) (7 pages) doi:10.1115/1.2345673 History: Received December 26, 2004; Revised May 21, 2006

## Abstract

In this paper we study the dynamic behavior of a shallow arch under a moving load system containing two masses, a dashpot, and a suspension spring. It is assumed that the masses in the load system are under the action of gravity. This paper is an extension of a previous publication in which the arch is loaded by a moving point force. The emphasis of the paper is placed on finding out how the inertia effect of the load system affects the dynamic response of the arch. It is found that the point-force model is a good approximation only when the arch is slender and the moving speed of the load system is low. The boundary of a dangerous speed zone is defined based on the comparison of the total energy gained by the arch and an energy barrier. It is observed that the suspension model predicts a considerably different dangerous speed zone from the one predicted by the point-force model, especially in the high-speed range.

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## Figures

Figure 3

External force F as a function of load position e for the arch-mass system in Fig. 2

Figure 4

Effects of slenderness ratio ε on α1(e) for arches with h=20, v=0.5. (a)Qg=40, (b)Qg=50.

Figure 9

Effects of suspension (with critical damping) on the total energy of the arch for v=1. (a)Qg=40. (b)Qg=50. Other parameters are h=20, m=0.5(ε=1000).

Figure 10

The crosshatched area represents the dangerous speed zone for an arch with h=20 and μ=0.001

Figure 1

(a) Schematic diagram of a shallow arch under a moving mass-dashpot-spring system. (b) The free body diagram of the load system.

Figure 2

Convergence test on (a)α1, (b)Harch. The parameters of the arch-mass system are h=20, Qg=40, ε=1000, and v=0.5. The corresponding mass parameter m1=1.

Figure 5

Components of total energy for an arch-mass system with h=20, v=0.5, Qg=50, and ε=2154(m1=0.1). (1) Kinetic energy and (2) strain energy of the arch. (3) Kinetic energy and (4) potential energy of the mass m1.

Figure 6

Vertical component Q(e) of the dynamic force applied by the load system on the arch with h=20, Qg=40, ε=1000, and v=0.5

Figure 7

Effects of moving speed v on α1(e) for an arch with h=20 and m1=0.5. (a)Qg=40, (b)Qg=50.

Figure 8

Effects of suspension (with critical damping) on the total energy of the arch for v=0.5. (a)Qg=40. (b)Qg=50. Other parameters are h=20, m=0.5(ε=1000).

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