Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory

Abstract

The current study aims to analyze the natural frequencies of sigmoid functionally graded (FG) sandwich beams having various configurations employing the high-order shear deformation theory. To do this, three diverse types of sandwich layup schemes have been constructed. The material characteristics of FG components of sandwich beams are presumed to vary continuously along the thickness direction, as indicated by the volume fraction of constituents specified with sigmoid law distribution, whilst the other components are assumed to be isotropic ceramic/metal. The governing equations are derived for higher-order shear deformation theory, i.e., hyperbolic shear deformation theory (HSDT). Navier's method is used to solve the governing differential equations analytically for simply supported boundary conditions at both ends. To show the efficiency of the current theory, the numerical results are obtained not only for HSDT but also for first-order shear deformation theory (FSDT), in the special case. Similarly, power law distributions of FG sandwich beams are also presented for emphasizing the effectiveness of sigmoid law distribution. Detailed comparisons are performed with available results of open literature to confirm the current formulation. Finally, the effects of the HSDT, variations of material properties, layup schemes, and geometrical characteristics of sandwich beams on the non-dimensional natural frequencies are discussed.