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An experimental study of bending impact waves in beams

Investigation covers the propagation of flexural waves in an elastic beam of circular cross section subjected to an approximate step-function bending moment

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Abstract

An experimental study of the propagation of flexural waves in an elastic beam of circular cross section subjected to an approximate-step-function bending moment is given. The test beam was a low-carbon-steel bar 2 in. diam × 30-ft long and was suspended in a vertical position by a pin located near the upper end. The step moment was applied at the upper pinned end of the bar by an arrangement of two high-pressure, nitrogen-operated cylinders. The strains were measured with strain gages located at eight stations along the bar.

The experimental results are compared with results obtained from a solution of the “Timoshenko” beam by W. Flügge and E. E. Zajac for a semi-infinite pinned-end beam subjected to a suddenly applied bending moment at the pinned end. The experimental results are correlated with the predictions of the theoretical solution.

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Abbreviations

A :

cross-sectional area, in.2

A s :

effective shear area, in.2

C m =C b :

propagation velocity of a discontinuity in bending=\(\sqrt {E/\rho } \), fps

C v :

propagation velocity of a discontinuity in shear=\(\sqrt {GA_S /\rho A} \), fps

E :

Young's modulus, psi

G :

shear modulus, psi

I :

area moment of inertia of cross section, in.4

M 0 :

moment input, ft-lb

a :

radius of bar, in.

ω:

deflection normal to axis of bar, in.

x :

space coordinate

t :

time, sec

λ:

wave length, in.

ξ:

space coordinate, dimensionless

ρ:

mass density at beam, mass per unit volume

τ:

time, dimensionless

K :

physical constant=ρA/EI

Bibliography

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Authors and Affiliations

  1. Mechanical Engineering Dept., Rice University, Houston, Texas

    J. G. Stephenson (Candidate for M.S. degree)

  2. Rice University, Houston, Texas

    J. C. Wilhoit Jr. (Associate Professor of Mechanical Engineering)

Authors
  1. J. G. Stephenson
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  2. J. C. Wilhoit Jr.
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Additional information

at time that paper was prepared; is now Mechanical Research and Development Engineer, Hallibuton Co., Duncan, Okla.

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Stephenson, J.G., Wilhoit, J.C. An experimental study of bending impact waves in beams. Experimental Mechanics 5, 16–21 (1965). https://doi.org/10.1007/BF02320899

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