Identification of cubic nonlinearity in disbonded aluminum honeycomb panels using single degree-of-freedom models

Prior work on a disbonded aluminum honeycomb panel showed evidence of a quadratic stiffness nonlinearity, as well as the presence of an unknown cubic nonlinearity. Approximations to higher order nonlinear single degree of freedom (SDOF) models were solved using the method of multiple scales. These approximations were then used to fit displacement data from a sinusoidal excitation test and determine the coefficients of the model as a function of damage size. Confirmation of the quadratic stiffness nonlinearity was achieved through examination of force restoration curves excited at one-half the primary resonance in conjunction with coefficient fitting of the test data to the model. The data were fit against the higher order models to determine whether the cubic nonlinearity could be stiffness or damping related. The coefficient fitting shows that the cubic nonlinearity is a stiffness nonlinearity. This confirmed what was seen in the force restoration curves when the system was excited at one-third the primary resonance. The ability to match the vibratory behavior of the damage to a SDOF model shows that the use of single frequency excitation at lower frequencies can isolate the nonlinear behavior of the damaged area and identify what damage mechanisms may be involved.