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.
Highlights
Annular sector plates are widely employed as engineering components in civil, defence, biomedical implantation, annular segment cavities in aerospace, rail transport, and terminals of cylindrical vessels, etc
The nonlinear forced vibration analysis of laminated annular sector plates provides insight into the rich dynamic behaviour that is not reflected in the linear analysis
It is revealed from the linear as well as nonlinear response curves that the displacement amplitude is greatest for a laminated annular sector plate with all edges supported and is the minimum for all edges clamped
Summary
Annular sector plates are widely employed as engineering components in civil, defence, biomedical implantation, annular segment cavities in aerospace, rail transport, and terminals of cylindrical vessels, etc. These structural components, when exposed to dynamic loads, may undergo large amplitude vibrations. The nonlinear forced vibration analysis of laminated annular sector plates provides insight into the rich dynamic behaviour that is not reflected in the linear analysis. The free vibration characteristics of isotropic thin sector plates have been investigated based on an extended differential quadrature method [3]. The flexural free vibration frequencies have been obtained for circular and annular sectorial thin isotropic plates using sector
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