Analytical method for free-damped vibration analysis of viscoelastic shear deformable annular plates made of functionally graded materials. Issue 4 (4th July 2019) - Alavi, Seyed Hashem; Eipakchi, Hamidreza
Abstract: This contribution aims to study the free vibrations behavior of viscoelastic functionally graded (VFGM) annular plates using the first-order shear deformation theory . The Zener three-parameter model is employed to model the time-dependent behavior of the plate which is assumed viscoelastic in shear and elastic in bulk. The functionally graded material properties vary through the thickness of the plate with a power law function and exponential distribution. Hamilton's principle is utilized to derive the governing equations which are three coupled partial differential equations with variable coefficients . The equations of motion are solved analytically using the perturbation technique. The natural frequencies of the plate are determined with different combinations of boundary conditions including simply supported, clamped and free. In addition, the effects of different viscoelastic and geometric parameters on the results are studied. The results are compared with those obtained from the literatures and the finite-element package. Investigation of the gradient index effect on the damping properties of VFGM plate shows that an increase in gradient index tends to decrease the damping behaviors of the VFGM plate. Highlights: First-order shear deformation theory is used for ANALYTICAL investigation of the vibrations and damping behaviors of VFGM annular plates with various combinations of boundary conditions. For more exact modeling of viscoelastic materials, we separated the bulk and shear behavior of the structure which is closer than to the behavior of a variety of viscoelastic structures. The plate properties are variable with time and space simultaneous. The perturbation technique in conjunction with a special variable change can convert the governing equations which are a system of coupled partial equations with variable coefficients to a system with constant coefficients so that each order of equations has an Cosed-form solution. A sensitivity analysis is performed and the results are compared with the three-dimensional theory of elasticity using FE method.