Mechanical four-pole parameters and their application

Abstract

Analysis of the sinusoidal vibration of damped mechanical systems by the use of four-pole parameter theory is described. Values of the four-pole parameters are derived or stated for lumped systems, such as a dynamic absorber, and for distributed systems, such as a uniform rod in longitudinal vibration. Also stated are the parameters that describe the bending vibrations of a Bernoulli-Euler beam and a thin circular plate, both of which may be envisaged as four-pole systems when they are driven and terminated so that only symmetrical vibrations about their mid-points are excited. Numerical results are plotted for two examples in which four-pole theory is used: (i) to predict the force transmissibility to the clamped boundary of a center-driven circular plate when a dynamic absorber with optimum tuning and damping is attached to its mid-point; (ii) to predict the response ratio and force transmissibility across a two-stage or compound mounting system having a central impedance which ceases to remain masslike at high frequencies.