New upper bounds for free linear and nonlinear vibration systems with applications of the differential calculus of norms

摘要

In this paper, a new concept is presented to derive upper bounds on the solution of initial value problems for free linear and nonlinear ordinary differential equations representing vibration problems. This concept is based on the idea to associate with the original problem of n degrees of freedom a scalar linear second-order initial value problem modelling an overdamped motion and to take its solution as an upper bound on the solution of the original problem. The best upper bound is computed by applying the differential calculus of norms developed by the author in earlier work.