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Research Papers

Dynamic Beam Modification Using Dimples

[+] Author and Article Information
W. N. Cheng

Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621 Taiwan, ROC

C. C. Cheng

Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621 Taiwan, ROCimeccc@ccu.edu.tw

G. H. Koopmann

Department of Mechanical and Nuclear Engineering,Pennsylvania State University

J. Vib. Acoust 130(4), 041007 (Jul 01, 2008) (8 pages) doi:10.1115/1.2890400 History: Received February 06, 2007; Revised December 06, 2007; Published July 01, 2008

In this paper, a design method to modify the vibration characteristics of a beam by creating cylindrical dimples on its surface is investigated. In particular, the vibration response of a beam with several dimples is formulated using the impedance method. The dimpled beam is divided into two kinds of structural segments: one, a curved beam that is modeled as the dimple and the other, a straight beam. The frequency equation is derived by assembling the impedance of each structure segment based on conditions of force equilibrium and velocity compatibility. Then a novel method for shifting the natural frequencies of a beam to preassigned values by creating cylindrical dimples on this structure is introduced. The dimple size and its location on the structure can be determined analytically, so the time consuming process using the traditional optimal search method is thereby avoided. Several examples using this technique are demonstrated.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagrams of dimpled beam

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Figure 2

Impedance model of straight beam

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Figure 3

Impedance model of curved beam

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Figure 4

Schematic diagram of curved beam element

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Figure 5

Schematic representation of dimpled beam

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Figure 6

Percentage change of the first natural frequency by varying the dimple location and the dimple size; (a) influence of dimple location and (b) influence of dimple size

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Figure 7

Schematic representation of simply supported beam with three dimples

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Figure 8

Schematic representation of simply supported beam with two dimples

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Figure 9

Surfaces of Δ(ϕ1,ϕ2,0.9ω1) and Δ(ϕ1,ϕ2,0.9ω2)

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