A method for normal-mode-based model reduction in nonlinear dynamics of slender structures

This paper introduces a nonlinear reduced-order modelling methodology for finite-element models of structures with slender subcomponents and inertia represented by lumped masses along main load paths. The constructed models have dynamics described by 1-D intrinsic equations of motion, which are further written in modal co-ordinates. This yields finite-dimensional approximations of the system dynamics with only quadratic nonlinearities. Evaluation of the problem coefficients is performed from static condensation of the original model on the lumped masses. The method exploits the multi-point constraints typically used to obtain sectional loads in aircraft aeroelastic analysis. The technique is illustrated on simple 3D structural models built using solid elements.