Off-campus Michigan Tech users: To download campus access theses or dissertations, please use the following button to log in with your Michigan Tech ID and password: log in to proxy server

Non-Michigan Tech users: Please talk to your librarian about requesting this thesis or dissertation through interlibrary loan.

Date of Award


Document Type

Master's report

Degree Name

Master of Science in Mechanical Engineering (MS)

College, School or Department Name

Department of Mechanical Engineering-Engineering Mechanics

First Advisor

James DeClerck


Jason Blough


A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion.

The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction.

The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.