Steady-State Response of Mechanical Power Flow Due to Structural Modifications

Résumé du livre

In this dissertation, the response of power flow to structural modifications is studied for applications in vibration reduction. Power flow has been used to quantify the vibratory response of mechanical structures for several decades in lieu of force or velocity response, which can become cumbersome to analyze for large structures with many degrees of freedom (DOFs). Alternatively, power flow is a frequency dependent scalar quantity that displays resonant behavior. Most of the existing literature focuses solely on the calculation of power flow, generally from an active source to a passive receiver. Though useful, if the vibration levels of a structure are to be reduced, the response of power flow to structural modifications should be better understood. To address this problem, structural modifications are first characterized in terms of power, a quantity referred to as the Modification Power (MP). This was done by expressing the power input to a structure as a function of impedances. Structural modifications are modeled as perturbations of arbitrary rank to the original structure's impedance matrix, such that matrix sum identities can be used to calculate inverses needed to determine power input. The resulting matrices are better numerically conditioned than a direct inversion, and is valid when representing the structure in both physical and reduced modal coordinates. The resulting MP indicates the magnitude and direction (increase or decrease) of the change in power flow as a function of frequency. An \textit{a priori} approach is then developed to determine how a passive receiver structure should be modified to reduce power transmission between structures. A power flow sensitivity analysis is proposed for single and multi-degree of freedom (SDOF and MDOF) structures which utilizes substructuring methods to perform the analysis using only information regarding the dynamics of the uncoupled source and receiver structures. The sensitivity analysis quantifies the change in active power flow due to perturbations in the real and imaginary parts of the receiver impedance, termed the real and imaginary sensitivities, respectively. These values provide information regarding when maximum power flow occurs, and how and where a structure should be modified to result in narrow-band reductions in power flow. This analysis was then extended to structures whose dynamics are determined experimentally using coupling techniques from experimental substructuring. The resulting sensitivity equations were shown to have frequency dependence similar to those for SDOF and MDOF structures, but require prohibitively precise data inputs to be accurate given the current experimental substructuring techniques available. Finally, the efficacy of using different mode sets obtained from existing substructuring methods to identify ideal locations to modify a structure to reduce power flow is tested. A small piece of software was developed for determining these mode sets. It is shown that the contribution of normal modes tend to dominate the response of the structure at a large number of frequencies resulting in power flow changes that are uncorrelated with the location where the structure is modified.