A dual Craig-Bampton substructuring method for nonlinear systems using nonlinear normal modes

Flores P.A. · Communications in Nonlinear Science and Numerical Simulation (2026) · DOI: 10.1016/j.cnsns.2026.110173

Resumen

In flexible mechanical systems, nonlinearities frequently arise in the equations of motion due to factors such as large deformations, nonlinear force interactions, or material behavior. When transient dynamic analysis is performed using the finite element method (FEM), these nonlinearities can significantly increase computational cost. Model order reduction techniques that preserve essential nonlinear dynamics are thus critical for efficient simulation. This paper proposes a nonlinear extension of the Dual Craig-Bampton (DCB) substructuring method for systems with non-classical damping. The approach incorporates nonlinear normal modes (NNMs), constructed via invariant manifold theory, into the dynamic component of the reduction. Two numerical case studies are presented: a cantilever Bernoulli beam with cubic stiffness at its support, and a planar truss structure with nonlinear springs, both subjected to harmonic loading. The proposed method achieves excellent agreement with full-model simulations using the Hilber-Hughes-Taylor (HHT) method, while significantly reducing the number of degrees of freedom. Results demonstrate the method’s potential for accurate and efficient nonlinear transient analysis in structural dynamics.

Instituciones: Pontificia Universidad Católica del Perú