In-plane free vibration of functionally graded circular arches with temperature-dependent properties under thermal environment

Analysis of in-plane free vibration of functionally graded (FG) thin-to-moderately thick deep circular arches in thermal environments is presented based on first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. Hamiltonʹs principle is employed to derive the equations of motion and the related boundary conditions including the effects of initial thermal stresses. The temperature is assumed to be uniform through the arch surface and varied through the thickness. The initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. The differential quadrature method (DQM) as an efficient numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The numerical solutions are validated by comparing to the solutions of the limited cases for isotropic arches, as well as by examining the solutions convergence behavior. Parametric studies are also conducted to study the effects of the temperature rise, boundary conditions and the material graded index on the frequency of the FG arches. Also, the impact of geometrical parameters such as the thickness-to-mean radius ratio and the opening angle are examined.