Mechanical Four-Pole Parameters: Transmission Matrices
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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This report revises and extends an earlier report entitled Mechanical Four-Pole Parameters and their Application Journal of Sound and Vibration, 15, 307-323, 1971. Newly considered are so-called transmission matrices, which enable the transverse vibration response of beams with discontinuities to be analyzed readily. Further, the transmission matrices used in the report result in more concise beam analyses than the matrices generally employed in the literature. Additional examples that are considered here include end-driven cantilever beams or stanchions that are propped by a damped spring or that carry an end mass having a finite moment of inertia or that carry a mass that divides the stanchion into two stages of arbitrary lengths and cross- sectional areas or that carry an end mass and subsequently comprise three stages having arbitrary lengths and cross-sectional areas.