Extension of Transfer-Matrix Methodology to Nonlinear Problems,
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG
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Transfer matrices have traditionally been used in the solution of linear mechanics problems. They have also been extensively used in the analysis of rotor systems. In current efforts to solve the dynamically-coupled nonlinear rotor mechanics equations, it was necessary to extend the transfer-matrix technology to this class of nonlinear problems. Hibner has shown that transfer matrices can be used on certain classes of nonlinear problems. He incorporated the nonlinear stiffness and damping effects of a fluid-film bearing in the response analysis of rotor systems. However, his approach was essentially to linearize the bearing stiffness and damping about an operating point. Hence, his approach was unable to account for the multifrequency response that arises from certain system nonlinearities. Thus, a technique was sought which solved, in an approximate fashion, for the effects of system nonlinearities on response amplitude and frequency.