Power flow between source and passive receiver structures is a common metric for quantifying vibration levels of the coupled system. The objective is generally to reduce the amount of power flow between the structures by means of structural modifications, insofar as to reduce the overall levels of vibration of the coupled system. As such, the sensitivity of power flow to changes in inertial, elastic, and dissipative properties of the structure should be quantified. It is shown that power flow into a receiver is not always directly proportional to the amount of damping in the receiver, but is also dependent on the amount of damping present in the source at a given frequency. The sign of the sensitivity can provide information as to when a change in damping will increase or decrease power flow- positive indicates an increase in power flow, negative indicates a decrease. A similar analysis is performed on changes made to a structure’s mass and stiffness properties.The sensitivity equations are first derived using Wirtinger’s Calculus to differentiate the power flow equation with respect to the receiver impedance. Relationships between power, coupling interface mobility, and receiver impedance are obtained using the Lagrange Multiplier Frequency Based Substructuring method. Since a substructuring method is used, the power flow sensitivity can be determined from a set of frequency response functions of the uncoupled source and receiver structures, making it useful to industries in which multiple contractors have dynamic models for separate components of a larger system to be assembled. Relationships between power flow and power flow sensitivity are shown for a simple single degree of freedom source-receiver coupling. The natural frequencies and damping ratios of the receiver structure are varied to demonstrate how power flow responds to these modifications near resonance of the coupled system, as well as show how the sensitivity behaves as a function of the ratio of the source and receiver coupling impedances.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The general sensitivity equations for multi-degree of freedom systems are then implemented on a coupled beam structure with translational and rotational degrees of freedom to demonstrate the spatial variations of the power flow sensitivity on the receiver structure. It is also shown that the addition of local damping to the structure will increase power flow to the receiver so long as the sensitivity at location of the damping modification is positive. Once enough damping is added to create a local sensitivity of zero, power flow will decrease after larger increases in damping. It is hoped that the power flow sensitivity can be used by a design analyst to select optimal locations for making design modifications so as to reduce power flow to passive receiver structures.

Structure-Borne Power Flow Sensitivity Analysis for General Structural Modifications

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.