Dynamic Instability Of Layered Anisotropic Circular Cylindrical Shells, Part I: Theoretical Development

Abstract

A theoretical development is presented for the parametric resonance of layered anisotropic circular cylindrical shells. The shell's ends are clamped and subjected to axial loading consisting of a static part and a harmonic part. The shell is modelled by using linear shell theory; classical lamination theory is used to determine the stiffness of the overall composite shell structure. The shell's response is divided into a pre-instability (unperturbed) part and an incremental perturbation--which can be dynamically unstable. Rather than assuming the unperturbed state to be a static membrane state of stress, here unperturbed response inertia and spatial variations are retained. A successful solution strategy is developed by employing several Fourier expansions. By means of it, the equations of motion of the perturbed response are reduced to a system of Mathieu equations. The stability of such a system can be determined by known methods. Numerical results are presented in part II.