Vibration analysis of a cylindrical shell by using strain gradient theory via a moving Kriging interpolation-based meshfree method

Abstract

The strain gradient theory is introduced into the Donnell shell model to investigate the vibration characteristics of a thin-walled cylindrical shell under classical and elastic boundary conditions. An energy equation concurrently involving the in-plane shell displacements and out-plane shell deflections is constructed. Meshfree discretization scheme is adopted, in which the moving Kriging interpolation, possessing C2 continuum and the Kronecker delta function property, is used to formulate the shape functions. The accuracy of the proposed method is first validated, and then parametric studies in terms of small-scale parameters, boundary conditions and the length-to-radius and thickness-to-radius ratios on the frequencies and mode shapes are carried out in detail. Natural frequencies evaluated by strain gradient elasticity theory are found to be lower than those of the classical Donnell cylindrical shell model. Some lower natural frequencies corresponding to ultrahigh-order mode shapes appear. This demonstrates that the size effect has a significant influence on the vibration of the thin-walled cylindrical shell. Five types of elastic boundary conditions are listed to illustrate the effect on the natural frequency. Meanwhile, it is concluded that the mesh-free moving Kriging interpolation method has high precision and good stability in dealing with strain gradient Donnell cylindrical shells.