Evaluation of static and dynamic responses considering thickness stretching effect for layered composite and sandwich arches using exponential shear and normal deformation theory

Abstract

Present theory investigates the dimensionless vibration frequencies, deformations, and stresses for multilayered and sandwich arches using exponential shear and normal deformation theory (ESNDT). Present studies consider the effect of $\left[1+\left(z/R\right)\right]$radius of curvature while selecting the displacement field of arches under the action of uniform load. It includes the effects of transverse shear $\left({\gamma }_{xz}\ne 0\right)$ and transverse normal deformation$\left({\epsilon }_z\ne 0\right)$ i.e., effect of thickness stretching. The governing relations are obtained using the Navier's method, and Hamilton's virtual work principle. The proposed layered arches are completely free from shear correction, and its top and bottom surfaces is satisfies zero traction free end conditions. Present study obtained very accurate natural frequencies for layered sandwich arches than other theories because, available literature not considered the thickness stretching effect i.e.,$\left({\epsilon }_z=0\right)$. Hence, the present scientific investigation accounts the effect of thickness stretching i.e.,$\left({\epsilon }_z\ne 0\right)$. However, the non-availability of exact elasticity results of bending and dynamic responses for layered sandwich arches. Present theory is obtained vibration frequencies, displacements, and stresses of layered composite and sandwich arches; the results are compared and validates through prior published literature.