Experimental Mechanics

, Volume 38, Issue 4, pp 242–249

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

  • C. Bacon
Article

DOI: 10.1007/BF02410385

Cite this article as:
Bacon, C. Experimental Mechanics (1998) 38: 242. doi:10.1007/BF02410385

Abstract

An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated.

Key Words

Hopkinson or Kolsky viscoelastic barsgeometric effects due to the radial inertiawave attenuationwave dispersionaccelerometer impedance

Nomenclature

a

bar radius

A

cross-sectional area of the bar

c(ω)

phase velocity

c0

one-dimensional elastic wave speed

d

distance between the strain gage location and the nonimpacted end

E

Young's modulus

E*(ω)

complex Young's modulus

\(\tilde f(x,\omega )\)

Fourier transform of functionf(x, t) at cross sectionx

F

normal force

H*(ω)

strain transfer function

k(w)

wave number

L

bar length

m

accelerometer mass

\(\tilde N(\omega )\)

Fourier transform of the strain atx=0 due to the wave traveling in the direction of decreasingx

\(\tilde P(\omega )\)

Fourier transform of the strain atx=0 due to the wave traveling in the direction of increasingx

t

time

u

axial displacement

v

axial particle velocity

Z*(ω)

mechanical impedance

α(ω)

attenuation coefficient

ε

longitudinal strain

εI(t)

longitudinal strain due to the incident wave

εR(t)

longitudinal strain due to the reflected wave

γ(ω)

propagation coefficient

ν

frequency

ω

angular frequency

ρ

mass density of the bar

σ

normal stress

Copyright information

© Society for Experimental Mechanics, Inc. 1998

Authors and Affiliations

  • C. Bacon
    • 1
  1. 1.Laboratoire de Mécanique PhysiqueUniversité Bordeaux 1Taleuce CedexFrance