Static and vibration analysis of sandwich beam with FGM core and viscoelastic interface using differential quadrature method

Functionally graded (FG) beams are critically important in advanced engineering applications due to their ability to tailor material properties for improved performance under extreme conditions. This study investigates the static and vibration behaviors of a sandwich beam with a functionally graded material (FGM) core and viscoelastic interfaces based on the twodimensional theory of elasticity. Young's Module and material density of functionally graded material (FGM) core is assumed to vary exponentially in thickness direction and the Poisson's ratio is held constant. In bending analysis, the sandwich beam is subjected to uniform pressure at the top surface whereas the bottom surface is traction-free. State space differential equations are derived using differential equations of motion as well as stress-displacement relations. For simply supported boundary conditions, these equations are solved analytically by using Fourier series expansion along the longitudinal direction, and other boundary conditions are solved semi-analytically using one-dimensional differential quadrature method (DQM) along the axial direction and state space across the transverse direction. Imperfect interfaces are modeled by the Kelvin-Voigt viscoelastic law. Time-dependent behavior is specified by dissolving the first-order differential equation of sliding displacement at the viscoelastic interfaces. Moreover, the influence of solid/elastic/ viscoelastic interfaces, different boundary conditions, length-tothickness ratio, elastic spring coefficient, and time passing on the static and vibration behavior of the beam are investigated. Major insights include the significant impact of imperfect bonding on vibration and bending behavior, discontinuity in transverse displacement for elastic and viscoelastic models, and higher transverse stresses in solid interfaces compared to viscoelastic ones.