Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory

Closed-form formulation of three-dimensional (3-D) refined higher-order shear deformation theory (RHOST) for the free vibration analysis of simply supported–simply supported and clamped–clamped homogenous isotropic circular cylindrical shells is presented. The proposed RHOST accounts for the effects of in-plane and rotary inertias as well as the effects of transverse normal and shear strains on the dynamic response of cylindrical shells. Also, the present analysis incorporates trapezoidal shape factor of a shell element that arise due to the fact that the stresses over the thickness of the shell are to be integrated on a trapezoidal-like cross-section of a shell element to obtain the accurate stress-resultants. Therefore, the present theory refines other HOSTs established hitherto for free vibration analysis of thick circular cylindrical shells. The equations of motion are obtained using Hamilton's principle. Solutions are obtained using the Galerkin method. Numerical results, not hitherto reported in the literature, are presented for the natural frequencies of isotropic long/short and hollow/solid cylinders. Numerical results indicate that for thick cylinders with large length-to-radius ratios, approximate series truncation methods are inadequate for calculating the stress-resultants and just exact integration yields accurate stress-resultants leading to a reliable prediction of natural frequencies. Natural frequencies associated to higher-mode numbers of thick isotropic cylinders, never published in the literature before, are also considered in this paper. It is shown that stress-resultants calculated using exact integration over the cylinder cross-section are necessary to obtain accurate results of the free vibration analysis, especially for higher-mode numbers of thick isotropic cylinders. The closed-form solutions presented herein are compared with the available exact 3-D elasticity and analytical solutions in the available literature and excellent agreement is obtained. Also, the validity of the results is established with the aid of commercial finite element software.

► Closed form 3-D refined HOST with 12 displacement components is used. ► Trapezoidal shape factor of a shell element (1+z/R term) is incorporated exactly. ► Simply supported and clamped homogenous isotropic cylindrical shells are considered. ► Different mode numbers of long/short and hollow/solid cylinders are investigated. ► Among the present theories, the new RHOST12c is the most reliable and accurate theory.