a b s t r a c tLong 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.

An efficient methodology is presented for predicting dynamic response and fatigue life of large-scale nonlinear mechanical models, subjected to random excitation. The methodology developed is based on a combination of techniques leading to a fast and accurate determination of the dynamic response with a method related to an efficient prediction of fatigue life. Specifically, the first step involves application of an appropriate coordinate transformation, causing a drastic reduction in the degrees of freedom. This opens the way to the application of another numerical method, leading to direct determination of periodic steady-state response of nonlinear systems under periodic forcing. This approach provides a solid foundation for the subsequent application of a rainflow stress cycle counting method, leading to prediction of fatigue failure. The computational accuracy and effectiveness of the methodology is illustrated by a quite involved example model, representing a city bus subjected to road excitation. Typical results are presented for both the stochastic response and the fatigue life by considering excitation arising from selected road profiles with known statistical properties. Special attention is paid to assessing the effect of the nonlinearity, by considering profiles of different quality. Moreover, a critical comparison is performed on results referring to the expected fatigue lifetime, obtained by applying methods in both the frequency and the time domain. In this way, the applicability of classical spectral methods in nonlinear models is also investigated.