Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

The free transverse vibrations of two-dimensional functionally graded double Euler–Bernoulli beam system connected through a variable Winkler elastic layer are presented. Modulus elasticity and the density material beams assumed to vary along thickness length according power-law exponential functions, respectively. governing differential equations motion established by means Hamilton’s principle. Chebyshev Spectral Collocation Method (CSCM) is used calculate natural frequencies (2D-FG) beams. effects several parameters such as height ratio beams, stiffness coupling layer, axial indexes, boundary conditions on 2D-FG have been investigated. obtained from CSCM validated comparing them with those available in previous literature.