Periodic steady state response of large scale mechanical models with local nonlinearities

Abstract

Long term dynamics of a class of mechanical systems is investigated in a computationally efficient way. Due to geometric complexity, each structural component is first discretized by applying the finite element method. Frequently, this leads to models with a quite large number of degrees of freedom. In addition, the composite system may also possess nonlinear properties. The method applied overcomes these difficulties by imposing a multi-level substructuring procedure, based on the sparsity pattern of the stiffness matrix. This is necessary, since the number of the resulting equations of motion can be so high that the classical coordinate reduction methods become inefficient to apply. As a result, the original dimension of the complete system is substantially reduced. Subsequently, this allows the application of numerical methods which are efficient for predicting response of small scale systems. In particular, a systematic method is applied next, leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. An appropriate continuation scheme is also applied, leading to evaluation of complete branches of periodic solutions. In addition, the stability properties of the located motions are also determined. Finally, respresentative sets of numerical results are presented for an internal combustion car engine and a complete city bus model. Where possible, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models. Moreover, emphasis is placed in comparing results obtained by employing the nonlinear or the corresponding linearized models.