A new higher order shear and normal deformation theory for the free vibration analysis of sandwich curved beams

Abstract

The free vibration analysis of functionally graded sandwich beams curved in elevation is presented in this paper using a fifth-order curved beam theory accounting for the effects of transverse shear and normal strains i.e. thickness stretching effects. The theory assumes higher-order variations of axial (tangential) as well as transverse (radial) displacements. Equations of motion are derived from the dynamic version of the principle of virtual work and solved analytically by using Navier’s technique. The present theory is applied for the free vibration analysis of sandwich curved beams with functionally graded face sheets and the homogenous core. The material properties of face sheets are graded in the thickness direction according to the power law. The non-dimensional fundamental frequencies are obtained for different parameters such as radius of curvature, the power-law index, and lamination scheme and compared with previously published results wherever possible and found in good agreement with those. It is observed that as the radius of curvature is decreased keeping length and thickness constant the value of non-dimensional fundamental frequency increases. It is also observed that as the power-law index increased the non-dimensional frequency decreases for all length to thickness ratios.