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TECHNICAL PAPERS

Steady-State Dynamic Response of a Kirchhoff’s Slab on Viscoelastic Kelvin’s Foundation to Moving Harmonic Loads

[+] Author and Article Information
Lu Sun

Transportation College, Southeast University, Nanjing 210096, China; Department of Civil Engineering, The Catholic University of America, Washington, DC 20064e-mail: sunl@cua.edu

J. Appl. Mech 74(6), 1212-1224 (Apr 27, 2007) (13 pages) doi:10.1115/1.2744033 History: Received May 08, 2005; Revised April 27, 2007

In this paper, fast Fourier transform and complex analysis are used to analyze the dynamic response of slabs on a viscoelastic foundation caused by a moving harmonic load. Critical speed and resonance frequency of the slab to a moving harmonic load are obtained analytically. It is proved that there exists a bifurcation in critical speed. One branch of critical speed increases as load frequency increases, while the other branch of critical speed decreases as load frequency increases. There are two critical speeds when the load frequency is low, but only one critical speed exists when the load frequency is high. A parametric study is also performed to study the effect of load speed, load frequency, material properties of the slab and the damping coefficient on dynamic response. It is found that the damping coefficient has significant influence on dynamic response. For small damping, the maximum response of the slab increases with increased load speed and frequency. However, for large damping, the maximum response of the slab decreases with increased load speed and frequency.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

An infinite slab on a viscoelastic foundation subjected to a moving load

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Figure 2

Critical speed versus moving load frequency

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Figure 3

Peak displacement of a slab to a moving constant load at different speeds (Ω=0Hz)

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Figure 4

Peak displacement of a slab to a moving load with different load frequencies (v=30m∕s)

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Figure 5

Dynamic responses of a slab to a moving load with large damping C=107Ns∕m3 and different load frequencies (left column: v=10m∕s; right column: v=30m∕s)

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Figure 6

Dynamic responses of a slab to a moving load at different speeds with large damping C=107Ns∕m3 (left column: Ω=0Hz; right column: Ω=50Hz)

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Figure 7

Dynamic responses of a slab to a moving load at speed v=30m∕s with different damping coefficients (left column: Ω=0Hz; right column: Ω=50Hz)

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Figure 8

3-D dynamic responses of a slab to a moving load at speed v=30m∕s with large damping C=107Ns∕m3 (left column: Ω=0Hz; right column: Ω=50Hz)

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Figure 9

Effect of damping coefficient on dynamic coefficient

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Figure 10

Dynamic coefficient as a function of various parameters (C=1×105Ns∕m3)

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Figure 11

Dynamic coefficient as a function of various parameters (C=1×107Ns∕m3)

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