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

c_{0}

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