A new two-dimensional refined higher order theory for in-plane free vibrations of sandwich and composite thick curved beams with flexible cores

Closed-form formulations of two-dimensional refined higher order beam theories and higher order beam theories for the free vibration analysis of simply supported cross-ply laminated composite and sandwich curved beams are presented. The present refined higher order beam theory analysis incorporates a trapezoidal shape factor that arises due to the fact that the stresses through the thickness of the beam are integrated over a curved surface. Therefore, the present theory refines other higher order beam theories established hitherto for free vibration analysis of strongly thick circular curved beams. The stress–strain relationship is derived from an orthotropic lamina in a three-dimensional state of stress. Numerical results are presented for the natural frequencies of laminated composite and sandwich thin/thick straight beams and shallow/deep and moderately/strongly thick curved beams. The closed-form solutions presented herein are compared with the available exact two-dimensional elasticity and analytical solutions in the available literature and excellent agreement is obtained.