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Research Papers

Effect of Potential Energy Variation on the Natural Frequency of an Euler–Bernoulli Cantilever Beam Under Lateral Force and Compression

[+] Author and Article Information
B. Béri

Department of Applied Mechanics,
Budapest University of Technology
and Economics,
Budapest 1521, Hungary
e-mail: beri.bence@gmail.com

G. Stépán

Department of Applied Mechanics,
Budapest University of Technology
and Economics,
Budapest 1521, Hungary
e-mail: stepan@mm.bme.hu

S. J. Hogan

Department of Engineering Mathematics,
University of Bristol,
Bristol BS8 1UB, UK
e-mail: s.j.hogan@bristol.ac.uk

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 8, 2017; final manuscript received February 24, 2017; published online March 20, 2017. Assoc. Editor: Nick Aravas.

J. Appl. Mech 84(5), 051002 (Mar 20, 2017) (8 pages) Paper No: JAM-17-1016; doi: 10.1115/1.4036094 History: Received January 08, 2017; Revised February 24, 2017

A cantilever beam is subjected to both lateral force and compression under gravity. By taking into account the potential energy variation of the system, we develop a theoretical result that greatly simplifies the bending vibration frequency calculation in agreement with the experiments.

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References

Figures

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Fig. 3

Mechanical model of a cantilever beam

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Fig. 2

Approximation of the displacement of the end of the cantilever beam

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Fig. 1

The experimental equipment that consists of a rectangular cross rod with length L and a heavy block with mass m = 0.978 kg

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Fig. 4

Fixed-rolling beam under compression

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Fig. 5

(a) Dimensionless relationship between κL and the relative importance of compression/tension given by Eq. (12). (b)Dimensionless relationship between relative importance of spring stiffness and the relative importance of compression/tension given by Eq. (15).

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Fig. 8

Dimensionless connection between the normalized works and the relative importance of compression: (a) case 1 and (b) case 2

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Fig. 9

Dynamical model of the two degrees-of-freedom compressed cantilever beam

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Fig. 7

Works of external forces

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Fig. 6

Displacement analysis. The displacements of d11 and d21 are affected by the lateral force F. The d12 and d22 are due to compression P.

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