Efficient model order reduction for dynamic systems with local nonlinearities

• A new condensation technique for structural systems with localized nonlinearity is proposed.
• The method reduces the problem size into generalized coordinates of localized nonlinearity.
• Both continuous and discrete systems, including those with internal resonance, are reduced by this method.
• The computational cost is reduced in contrast with harmonic balance method.
• The method has great potentials for identification and health monitoring of nonlinear structures with localized nonlinearity.

In the nonlinear structural analysis, the nonlinear effects are commonly localized and the rest of the structure behaves in a linear manner. Considering this fact, this research work proposes a harmonic balance solution in order to determine the nonlinear response of the structures. The solution is simplified by using an exact dynamic reduction along with the modal expansion technique. This novel approach, which is applicable to both discrete and continuous systems, converts the system equations of motion in each harmonic to a small set of nonlinear algebraic equations. The full set of system equations is reduced to a discrete system with a few generalized degrees of freedom (DOFs) confined to the localized nonlinear regions. The resultant reduced order model is shown to be accurate enough for determining the periodic response. To demonstrate the capability of the proposed method, numerical case studies for continuous and discrete systems, including systems with internal resonance, have been studied and the outcomes are validated with benchmark studies. In addition, the method is applied in the identification process of an experimental test setup with unknown frictional support parameters, and the results are presented and discussed.