Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis

A higher-order mathematical formulation with applications is presented in this paper for the free vibration analysis of arches and beams made of composite materials. Higher-order shear deformation theories are required to capture accurately the three-dimensional behavior of these structures through a one-dimensional scheme. Several orders of kinematic expansion are investigated and compared. In addition, the so-called zig–zag theories obtained through the use of the well-known Murakami's function are employed. Their effectiveness is extremely clear when laminates with inner-soft cores are analyzed. A set of numerical applications is presented to prove the accuracy of the current methodology. In particular, the comparison with exact solutions and results available in the literature or obtained through three-dimensional finite element commercial codes justifies the use of higher-order models, in which the displacement field is defined through the arbitrary choice of the maximum order of kinematic expansion. The in-plane vibrational modes of arches and beams, as well as annular ring structures, are computed and presented, discussing also the Poisson effect on the solutions.