Abstract
The prediction of the modal properties of non-smooth mechanical systems with clearances and prestress presents a computational challenge, since the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. For obtaining nonlinear normal modes (NNMs) of structural systems through modal analysis, a numerical framework that combines numerical integration, the shooting method, and the arc-length continuation scheme is the most widely used approach. This numerical continuation framework computes NNMs through iterative numerical calculations; thus, the computational cost of nonlinear modal analysis of complex nonlinear systems, or non-smooth systems in particular, becomes prohibitively expensive as the model size increases. In this work, a new hybrid continuation framework combining analytic and numerical methods is proposed to efficiently compute the NNMs of non-smooth systems. This new hybrid framework uses a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on a spring-mass oscillator with contact elements, and the NNMs obtained using the new method are validated by those computed using the traditional numerical continuation framework. The modal properties of the system can be computed using the proposed framework with significant computational savings.