Free Vibration of Sandwich and Composite Curved Beam Based on a New Two-Dimensional Refined Higher-Order Theory

In this paper, a new group of two-dimensional (2D) refined higher-order beam theories (RHOBTs) for the free vibration analysis of laminated composite and sandwich curved beams are presented. The proposed full model of RHOBTs 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 curved beams. Also, the present RHOBTs analysis incorporates trapezoidal shape factor of a curved beam element completely. The equations of motion are obtained using Hamilton’s principle.Solutions are obtained in closed-form using Navier’s technique and by solving the eigenvalue equations. Numerical results are presented for the natural frequencies of laminated composite and sandwich thin/thick straight beams and shallow/deep and thick curved sandwich beams. The results of analytical solutions presented herein are compared with the exact 2D elasticity and analytical solutions in the available literature and excellent agreement is obtained.