A Proposition on the Uniqueness of Solutions for Nonlinear Structural Dynamic Models

In nonlinear structural dynamics, in spite of many theorems presenting different sufficient conditions essential for the uniqueness of responses of initial/boundary value problems; there are problems satisfying neither of the conditions. In this paper, the authors pay attention to the importance of structural problems, involved in a special type of nonlinearity, i.e. nonlinearities of the piece-wisely linear type. These problems do not satisfy the existing uniqueness theorems. Considering this, besides the role of nonlinear structural dynamic models, possessing exact closed form solutions, in verifications, and the importance of piece-wisely linear behaviors in structural engineering, in this paper, the uniqueness of the responses of piece-wisely linear dynamic models is demonstrated theoretically. The validity of the achievements is then numerically displayed, via a parametric problem involved in elastic impact, possessing exact closed form solution, analyzed by converging time integration computations.