Influence of active stiffening on dynamic behaviour of piezo-hygro-thermo-elastic composite plates and shells

The active stiffening and active compensation analyses are carried out to present the influence of active stiffness on the dynamic behaviour of piezo-hygro-thermo-elastic laminates. A coupled piezoelectric finite element formulation involving a hygrothermal strain field is derived using the virtual work principle and is employed in a nine-noded field consistent Lagrangian element. The closed-loop system is modelled with elastic stiffness, active stiffness introduced by isotropic actuator lamina and geometric stiffness due to stresses developed by hygrothermal strain. Through a parametric study, the influence of active stiffening and active compensation effects on the dynamics of cross-ply and angle-ply laminated plates and shells are highlighted. The active stiffening on thin shells is significantly influenced by boundary effects and the actuator efficiency further decreases with increase in curvature. The reduction in natural frequencies of cross-ply laminates due to hygrothermal strain is actively compensated by active stiffening; however, it is observed that the actuator performance reduces significantly with increase in curvature particularly in angle-ply laminates, which demands the use of directional actuators. The active stiffening and active compensation effects are low in moderately thick piezo-hygro-thermo-elastic plates and shells, which are less influenced by boundary conditions.