Tham khảo tài liệu 'volume 08 - mechanical testing and evaluation part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The 1- and 2-wave analyses used to calculate average stress discussed in the theory section implicitly assume that the strain-time pulses measured at the strain gages are identical with those at the ends of the bars in contact with the specimen. This assumption however is not correct because the specimen is normally smaller in diameter than the bar such that the bar ends are not uniformly loaded across their diameter and therefore will indent elastically. In addition as the bars are compressed longitudinally albeit elastically they expand radially in response to the applied force . the Poisson effect . While the exact mathematical descriptions of these effects on the propagation of an elastic pulse through a large elastic rod are very complex the result is that different frequencies of pulses induced in the bars disperse with distance traveled in the bar. The result of this dispersion is such that the pulse induced in the input bar through the impact of the striker bar does not immediately rise into a steady square-wave impulse of fixed amplitude but rather rings up. These end effects quickly dampen after the wave has propagated about ten bar diameters Ref 40 67 . The wave propagation behavior thereafter becomes fully described by the equation of motion in an infinite cylindrical solid. The solution of the equation of motion for these boundary conditions was derived independently during the late 19th century by the mathematicians Pochhammer Ref 70 and Chree Ref 71 . These relations were later specifically applied to address dispersion in the SHPB Ref 12 15 40 72 73 74 . The pressure bars have been determined to vibrate predominantly in a fundamental mode . while there are an infinite number of potential solutions to the equation of motion according to the vibrational mode only one frequency appears to dominate in long elastic bars . This vibration of the bar leads to wave dispersion that can mask resolution of the fine details in the stress-strain data of .
