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Research Papers

Optimal Design of an Intermediate Support for a Beam With Elastically Restrained Boundaries

[+] Author and Article Information
D. Wang1

Department of Aeronautical Structural Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P.R. Chinawangdng66@yahoo.com.cn

1

Corresponding author.

J. Vib. Acoust 133(3), 031014 (Mar 31, 2011) (8 pages) doi:10.1115/1.4003204 History: Received January 11, 2010; Revised July 27, 2010; Published March 31, 2011; Online March 31, 2011

A straight, slender beam with elastically restrained boundaries is investigated for optimal design of an intermediate elastic support with the minimum stiffness for the purpose of raising the fundamental frequency of the beam to a given value or to its upper bound. Based on the optimality criterion of the support design, the characteristic frequency equation can readily be formulated. Then, a closed-form solution is presented for estimating the minimum stiffness and optimum position of the intermediate support such that the analysis of the various classical boundary conditions is only a degenerate case of the present problem. With the procedure developed, the effects of the general cases of the beam restraint boundaries on the optimal design of the intermediate support are studied in detail. Numerical results show that the optimum position will move gradually apart from the end with the degree increment of the boundary restraints. Moreover, it is also observed that the rotational restraint affects the optimal design of the support more remarkably than the translational one at the lower values of the restraint constants, but becomes less effective at the higher constants.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A generally restrained slender beam with an intermediate elastic support

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Figure 2

The first natural frequency of a beam, clamped at the left end and elastically restrained at the right end of the stiffness constants T2=R2=200, raised with an intermediate support of different stiffnesses γ at various positions

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Figure 3

The vibration modes of the beam related to the first natural frequency parameter λ1=6.1427 with an intermediate support of stiffness γ=785.71 at position b=0.6311

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Figure 4

Variation in the original second natural frequency (or maximum of the first natural frequency with an intermediate support) of the general beam unsupported with various sets of the elastically restrained boundaries at the right end

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Figure 5

Variation in the minimum stiffness of the intermediate support for maximizing the first natural frequency of the general beam with various sets of the elastically restrained boundaries at the right end

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Figure 6

Variation in the optimum position of the intermediate support for maximizing the first natural frequency of the general beam with various sets of the elastically restrained boundaries at the right end

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Figure 7

Variation in the minimum stiffness of the intermediate support for raising the first natural frequency parameter to a specific value 5.5 with various sets of the elastically restrained boundaries at the right end

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Figure 8

Variation in the optimum position of the intermediate support for raising the first natural frequency parameter to a specific value 5.5 with various sets of the elastically restrained boundaries at the right end

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