Harmonic Response of Large Engineering Structures with Nonlinear Modifications

In a structural design, the structure may need to be modified and for each modification its dynamic characteristics may need to be determined by reanalyzing the structure dynamically. Since computational time and cost are very critical in design processes, structural modification methods become decisive, particularly for large systems, in predicting the dynamic behavior of modified structures from those of the original and modifying structures. Due to nonlinearity in most engineering structures, linearity assumption may not be applicable to all cases. Then, well known structural modification methods can not be directly used, and it is required to employ a nonlinear structural modification method. In this paper, a structural modification/coupling method proposed in an earlier study is extended for nonlinear modification/coupling. The nonlinearities are quasilinearised using describing function method, and thus nonlinear internal force vector is expressed in terms of a response-dependent matrix which can be regarded as a response level dependent "equivalent stiffness matrix", called "nonlinearity matrix". Then the method developed for linear structural modification/coupling is employed by using an iterative solution procedure. Three case studies are presented in this paper. In the first case study, a nonlinear test structure used in an earlier study is employed and the frequency responses of the system at different forcing levels are calculated by using the approach suggested. Then they are compared with experimental results. Secondly, a simple discrete system is analyzed to demonstrate the accuracy of the approach proposed. Lastly, a large scale model is considered to illustrate the applicability of the approach proposed to large order systems