A nonlinear joint model for large-amplitude vibrations of initially curved panels: Reduced-order modelling and experimental validation

This study conducts an extensive theoretical-experimental investigation into the nonlinear dynamical response of a base-excited initially curved panel clamped at two ends via bolted joints. A new distributed nonlinear joint stiffness model is proposed capable of exhibiting interconnected effects at various states of the contact interface. More specifically, the proposed model allows the control of the nonlinear softening behaviour of the panel through controlling the displacement threshold for micro-slip and new stick states, as well as the rate at which the micro-slip region develops. Due to the inclined angle of the clamping supports, the panel is slightly curved in its fastened arrangement. Hence, the panel is modelled as a shallow shell using Donnell’s nonlinear shallow shell theory, taking into account von Kármán strain nonlinearities, while retaining all in-plane and out-of-plane displacements. Structural damping is considered via use of the Kelvin–Voigt model. Taking into account the work of the nonlinear joint stiffness model, the partial differential equations governing the in-plane and out-of-plane motions of the panel are derived using the generalised Hamilton’s principle, which are then discretised into a reduced-order model using a two-dimensional Galerkin modal decomposition approach. For the experimental part, two nominally identical panels are considered and several tests are conducted through base excitation in the primary resonance region and the backbone curves are obtained directly via the Phase Lock Loop method. Extensive comparisons are conducted between experimental results and theoretical predictions for both backbone curves and time histories of the panel midpoint velocity and displacement. It is shown that the theoretical predictions are in very good agreement with the experimental results, with the proposed joint stiffness model being capable of predicting the significant variability in the experimental results.