Coupled efficient layerwise and smeared third order theories for vibration of smart piezolaminated cylindrical shells

Abstract

The improved third order zigzag theory and its smeared counterpart (without the zigzag effect), recently developed by the authors for static analysis of piezoelectric laminated cylindrical shells, are extended to dynamics. The piezoelectric layers are considered as radially polarized to make use of the extension actuation mechanism that is best suited for effective actuation and sensing. The zigzag theory accounts for the layerwise variation of inplane displacements and includes the transverse normal extensibility under electric field, and also satisfies the conditions on transverse shear stresses at the layer interfaces and at the inner and outer surfaces of the shell. Yet, the number of primary displacement variables is only five, same as its smeared counterpart. The two theories are critically assessed for their accuracy by direct comparison with the three dimensional piezoelasticity solutions for free and forced vibration response of simply supported smart angle-ply infinite-length and cross-ply finite-length shells, with a variety of heterogeneous composite and sandwich laminates. It is shown that the zigzag theory, in spite of being computationally efficient, is very accurate even for shells with highly inhomogeneous laminates. In contrast, the smeared third order theory is grossly inadequate for smart shells made of inhomogeneous composite and sandwich substrates.