Dynamic stability of piezoelectric laminated cylindrical shells with delamination

The dynamic stability of a composite laminated cylindrical shell containing a throughout delamination along circumferential direction integrated with piezoelectric layers at both inner and outer surfaces is investigated in this article. The Heaviside step function is used to describe the displacement components in the regions with and without delamination. Based on the classical shell theory, linear piezoelastic constitutive relationship, and variational principle, the governing equations of motion are derived and then solved by employing Rayleigh–Ritz method and Bolotin method to obtain the principal unstable region. Numerical results are presented in both tabular and graphical forms to show the effects of the piezoelectric layer; the length, depth, and location of the delamination; and the static axial force on the resonance frequency and the principal unstable region of the delaminated piezoelectric laminated shell.