On the Large Amplitude Forced Vibration Analysis of Composite Sectorial Plates

Abstract

The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinematics of first-order shear deformation theory (FSDT) and employing Hamilton’s principle. The governing equations of motion have been solved in a time domain using a modified shooting method and arc-length/pseudo-arc length continuation technique. The influence of the boundary condition, sector angle, and annularity ratio on the linear as well as nonlinear steady state forced vibration response has been investigated. The strain/stress variation across the thickness of the annular sector plate is presented to explain the reason for a decrease/increase in hardening nonlinear behaviour. The periodic variation of the non-linear steady state stress has also been obtained to throw light into the factors influencing the unequal stress half cycles and multiple cyclic stress reversals, which is detrimental to the fatigue design of laminated composite annular sectorial plates. The frequency spectra of the steady state stress reveals large even and odd higher harmonic contributions for different cases due to changes in the restoring force dynamics. The modal interaction/exchange during a cycle is demonstrated using a deformed configuration of the laminated annular sector plate.