Dynamic substructuring using a combination of softening and hardening connecting elements

The dynamic analysis of complex engineering structures represents a challenging task, since the reliability of the results significantly depends on the accuracy of the model. In general, linearized models represent a valid approximation, but in some cases, it is necessary to include also the most significant nonlinearities to obtain reliable results. In the present work, the case in which two beams are jointed together through softening and hardening connecting elements is analyzed. It is possible to account for their presence by modeling them as nonlinear substructures, and the connected subsystems are instead modeled as linear substructures. A Nonlinear Coupling Procedure (NLCP) is defined in the modal domain to analyze the dynamics of these systems. The iterative procedure has been modified with respect to the one used in previous works by selecting a different initial guess and by maintaining the energy of the system constant at each iteration. The theory of Nonlinear Normal Modes (NNMs) is used to account for the presence of the nonlinear connections in the coupled assembly. The NLCP is employed to analyze the effects of modal truncation on the mode shapes and on the resonance frequency.