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40-Hz square-wave stimulation requires less energy to produce muscle contraction: compared with the TASER® X26 conducted energy weapon

Affiliation

  • 1 General Dynamics Information Technology, 3650 Chambers Pass, Fort Sam Houston, TX, USA.
  • PMID: 23682682
  • DOI: 10.1111/1556-4029.12122

40-Hz square-wave stimulation requires less energy to produce muscle contraction: compared with the TASER® X26 conducted energy weapon

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Authors

Affiliation

  • 1 General Dynamics Information Technology, 3650 Chambers Pass, Fort Sam Houston, TX, USA.
  • PMID: 23682682
  • DOI: 10.1111/1556-4029.12122

Abstract

Conducted energy weapons (CEWs) (including the Advanced TASER(®) X26 model produced by TASER International, Inc.) incapacitate individuals by causing muscle contractions. In this study using anesthetized swine, the potential incapacitating effect of primarily monophasic, 19-Hz voltage imposed by the commercial CEW was compared with the effect of voltages imposed by a laboratory device that created 40-Hz square waves. Forces of muscle contraction were measured with the use of strain gauges. Stimulation with 40-Hz square waves required less pulse energy than stimulation with the commercial CEW to produce similar muscle contraction. The square-pulse stimulation, at the higher repetition rate, caused a more complete tetanus at a lower energy. Use of such a simple shape of waveform may be used to make future nonlethal weapon devices more efficient.

Keywords: Sus scrofa; TASER; conducted energy weapon; electromuscular incapacitation; electronic control devices; forensic science; muscle contraction.

Conducted energy weapons (CEWs) (including the Advanced TASER(®) X26 model produced by TASER International, Inc.) incapacitate individuals by causing muscle contractions. In this study using anesthetized swine, the potential incapacitating effect of primarily monophasic, 19-Hz voltage imposed by the …

Response of circular clamped plates to square-wave stress pulses

Primary object of investigation is to determine the relation between the magnitude of the applied stress pulse and the transient stress and strains

Abstract

An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular stress pulses over a small circular region. The stress pulses were transmitted to the plates through a 1/2-in.-diam shock bar and the strain-time responses of the plates were measured. The stress-wave interactions between the bar and the plates were measured for a number of thicknesses and the effect of the applied stress on the extent of the plastic deformation was determined.

It was found that the elastic response was accurately predicted by the theory of Sneddon and the plastic response behaved according to a simple modification of this theory. The interaction between the stress pulse and plates of various thickness was theoretically predicted and found to be in excellent agreement with experimental measurements. The final plate deflections were theoretically predicted using a rigid viscoplastic theory and was in substantial agreement with the data. From this theory, the data were analyzed to determine the visco-plastic constant or relaxation time of the material. It is proposed that this testing arrangement is a suitable and convenient method for determining dynamic yield properties under biaxial-loading conditions.

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Abbreviations

plate thickness, in.

radius of the unclamped part of the plate, in.

radial and tangential principal stresses, lb-in −2

radial and tangential principal strains

radial and tangential bending moments, lb-in.

radial and tangential curvatures

Young’s elastic modulus, lb-in −2

secant modulus, lb-in −2

uniaxial dynamic yield stress, lb-in −2

uniaxial static yield stress, lb-in −2

duration of the stress pulse, sec

force and stress due to the stress pulse, lb and lb-in −2

actual force and stress acting on the plate due to the pulse, lb and lb-in −2

limit load or static collapse load, lb

dimensionless radial coordinate

deflection of the plate, in

central deflection of the plate, in

radius of the loading area, in

velocity of plate middle surface, in.-sec −1

impact velocity, in.-sec −1

specific density of plate material, lb-in −3

specific density of bar material, lb-in −3

material relaxation time, sec

area of shock bar,P=p/A, in 2

work done on the plate, in.-lb

kinetic energy of the impact bar

length of impact bar, in

longitudinal wave velocity, in.-sec −1

eigen function and eigen value

visco-plastic flexural rigidity

References

Lindholm, U. S. andYeakley, L. M., “A Dynamic Biaxial Testing Machine,” Experimental Mechanics ,7 (1),1–7 (1967).

Boussinesq, J., “Applications des potentials a l’etude et du movement des solides elastiques,” Paris (1885).

Maiden, C. J., “The Stresses Produced in a Thin Elastic Plate by a Transverse Impulsive Force,”Phil. Mag.,3,1413–1423 (1958).

Hopkins, H. G., andPrager, W., “The Load Carrying Capacity of Circular Plates,”Jnl. Mech. Phys. Solids,2,1–13 (1953).

Hopkins, H. G., andWang, A. J., “Load Carring Capacity for Circular Plates of Perfectly Plastic Material with Arbitrary Yield Condition,”-om|Ibid. Jnl. Mech. Phys. Solids,3,117–129 (1954).

Wang, A. J., andHopkins, H. G., “On the Plastic Deformation of Built-in Circular Plates under Impulse Loading,”Ibid.,3,22–37 (1954).

Wang, A. J., “The Permanent Deformation of a Plate under Blast Loading,”Jnl. Appl. Mech.,22,375 (1955).

Hopkins, H. G., andPrager, W., “On the Dynamics of Plastic Circular Plates,”Jnl. Appl. Math. Phys., Zamp,5,317–339 (1954).

Florence, A. L., “Clamped Circular Rigid-plastic Plates under Blast Loading,”Jnl. Appl. Mech.,33,256–260 (1966).

Florence, A. L., “Clamped Circular Rigid-plastic Plates under Central Blast Loading,”Int. Jnl. Solids Structures,2,1–17 (1965).

Wierzbicki, T., “Response of Rigid Viscoplastic Circular and Square Plates to Dynamic Loading,”Ibid.,3,635–647 (1967).

Wierzbicki, T., “Dynamics of Rigid Visco-plastic Circular Plates,”Arch. Mech. Stos.,6,17 (1965).

Sneddon, I. N., “The Symmetrical Vibrations of a Thin Elastic Plate,”Proc. Camb. Phil. Soc.,41,27 (1945).

Rosenfield, A. R., and Hahn, G. T., “Numerical Descriptions of Ambient Low-Temperature, and High Strain-Rate Flow and Fracture Behavior of Plain Carbon Steel,” Battelle Memorial Inst. (1965).

Author information

Affiliations

Acting Assistant Professor, Department of Materials Science, Stanford University, Stanford, Calif

Assistant Professor, Division of Structural Engineering and Structural Mechanics, University of California, Berkeley, Calif

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An account is given of an experimental investigation of the reeponse of clamped circular mild-steel plates of various thicknesses subjected to rectangular