In-Plane Vibrations of Deep Sandwich Arches with Different End Conditions Based on a Logarithmic Shear Deformation Theory

Abstract

This paper deals with the vibrational frequencies of deep sandwich arches to enhance their application domain and possibly use them for energy harvesting. The circular arch with porous nanocomposite core and titanium alloy face sheets having different end conditions is numerically analyzed. The middle core of the sandwich arch is made of a six-layered porous aluminum reinforced with graphene nanoplatelets. The kinematic equations are formulated in this study based on the higher-order shear deformation theory using a logarithmic function of radius. The effective properties of the nanocomposite media are modeled by employing the Halpin–Tsai modified rule. The equations of motion are determined by applying the principle of virtual displacement. The partial differential equations are reduced using the generalized differential quadrature technique to solving an algebraic eigenvalue problem. Novel numerical results are given to show the effects of geometrical parameters, material properties, and boundary conditions on the vibrations of deep sandwich arch.