Nonlinear structural modification and nonlinear coupling

• An approach for nonlinear structural modification and coupling is proposed.
• Formulations for four nonlinear modification/coupling cases are presented.
• Each nonlinear modification/coupling case is illustrated via example applications.
• A simulated and an experimental case study are presented for the verification.
• Real life application of the proposed approach is demonstrated.

Structural modification methods were proved to be very useful for large structures, especially when modification is local. Although there may be inherent nonlinearities in a structural system in various forms such as clearances, friction and cubic stiffness, most of the structural modification methods are for linear systems. The method proposed in this work is a structural modification/coupling method developed previously, and extended to systems with nonlinear modification and coupling. The method is most useful for large linear structures with nonlinear local modification or coupling. It is based on expressing nonlinear internal force vector in a nonlinear system as a response level dependent “equivalent stiffness matrix” (the so-called “nonlinearity matrix”) multiplied by the displacement vector, through quasilinearizing the nonlinearities using describing functions. Once nonlinear internal force vector is expressed as a matrix multiplication form then several structural modification and/or coupling methods can easily be used for nonlinear systems, provided that an iterative solution procedure is employed and convergence is obtained. In the proposed approach the nonlinear FRFs of a modified/coupled system are calculated from those of the original system and dynamic stiffness matrix of the nonlinear modifying system. Formulations and sample applications of the proposed approach for each of the following cases are given, nonlinear modification of a linear system with and without adding new degrees of freedom, and elastic coupling of a nonlinear subsystem to a main linear system with linear or nonlinear elements. Case studies are given for the verification of the method and then a real life application of the method is presented.