Nonlinear Normal Modes of a Curved Beam and Its Response to Random Loading

Abstract

Hypersonic vehicles are exposed to high amplitude, random, broadband loading and so, in order to predict the life of the system, the geometrically nonlinear response of certain skin panels must be computed for a long time duration. This is a costly procedure when using the finite element (FE) method due to large mesh sizes and small time step requirements. Nonlinear Reduced Order Models (NLROMs) provide an accurate and computationally efficient alternative to compute the response of such structures. The NLROMs still require computationally expensive validation that is conventionally done by comparing responses with the full FE model. An alternative approach to validating NLROMs is to compute their Nonlinear Normal Modes (NNMs), which are independent of the loading scenario and provide information regarding the system’s response over a range of energy or response amplitude. This work investigates the relationship between the NNMs and response of a curved beam to random inputs. The structure contains quadratic and cubic nonlinearities that produce both a softening and hardening behavior of the beam as the system energy is increased. A connection is made between the accuracy of NNMs computed from NLROMs and their random response predictions.