Filtering characteristics of a long cylindrical steel bar with discontinuities in cross sectional area

When a continuous longitudinal wave is propagated along the length of a finite cylindrical steel bar the frequency of maximum response of the propagated wave depends on the length of the bar. This is due to the reflections of acoustic energy which occur at the ends. Any other abrupt change in cross sectional area is also a point of energy reflection and if there are several area discontinuities spaced along the bar length the possibility of acoustic resonances exists. Typically, such a system is analyzed by means of mechanical-electrical analogies. A four-terminal electrical network is synthesized which has the characteristics of the mechanical system. The result is a Pi-section band pass filter composed of passive, non-dissipative components. These components are functions of the physical characteristics of the mechanical system and take into consideration such parameters as distance between discontinuities and area ratios at discontinuities. A computer program is given by means of which quantitative information is obtained and discussed. The attenuation is presented as a function of frequency for a typical physical model. The pass and stop bands for this system are discussed.