Investigation of non-linear free vibrations of fully clamped symmetrically laminated carbon-fibre-reinforced PEEK (AS4/APC2) rectangular composite panels

In an earlier publication, the optimum parameters for ultrasonic welding of carbon-fibre/PEEK (AS4/APC-2) composites have been determined; the physico-chemical properties and fracture surface morphology of modes I and II have been described. The objective of this paper is further to extend our understanding of the dynamic behaviour of the AS4/APC-2 by the theoretical modelling of its geometrically non-linear dynamic behaviour at large vibration amplitudes. In previous work, a theoretical model based on Hamiltonʹs principle and spectral analysis has been used to study the non-linear free vibration of CFRP (carbon-fibre-reinforced plastic) and hybrid composite panels. The present paper investigates the first non-linear mode shape of symmetrically laminated AS4/APC2 composite panels. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. Results are summarised for various plate aspect ratios and vibration amplitudes, giving the dependence of the first non-linear mode shape and associated frequencies on the amplitudes of vibration, and showing higher bending stresses near to the clamps at large deflections, compared with those predicted by linear theory.