Monday  |  Salon 8  |  04:30 PM–04:50 PM

#16511–Guaranteeing Real Positive Modal Frequencies in Experimental Substructure Uncoupling of a Transmission Simulator

Experimental dynamic substructure elastic modal parameters are often measured with free boundary conditions
because very good estimates are practically achievable with soft suspension systems like bungee cords. However,
the free basis vectors for component mode synthesis of multiple substructures may not be very accurate. The error is due to modal truncation aggravated by the unloaded free interfaces, which do not even exercise the significant joint stiffness or dissipation. A method that attaches a fixture, known for many years as the transmission simulator, has the advantage of improving the modal basis by loading the interface, including the joint stiffness, joint damping and accounting for rotations in the connection. When the experimental substructure is coupled to another substructure, the transmission simulator must be uncoupled and subtracted from the new system. Due to some approximations, the uncoupling sometimes leads to non-positive definite mass or stiffness matrices, which then yield negative eigenvalues and complex modal frequencies in the final eigensolution. The reason for the ill-conditioned mass or stiffness matrix is reviewed. Previous work is extended to guarantee positive definite or semi-definite mass and stiffness matrices and real positive modal frequencies after the uncoupling of the transmission simulator. An analytical example chosen with a transmission simulator design that exacerbates the ill-conditioned uncoupling demonstrates the mitigation technique.

Randy Mayes   Randall L Mayes Consulting