Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One Dimensional Analysis

Abstract

The free vibration analysis of thinand thickwalled layered structures via a refined onedimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higherorder 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing halfwave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higherorder terms is fundamental especially to capture vibrational modes that require warping and inplane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with threedimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thinand thickwalled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobetype modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.