Hygrothermally Induced Vibration Analysis of Bidirectional Functionally Graded Porous Beams

In this article, the nonlinear hygrothermally induced vibrational behavior of bidirectional functionally graded porous beams is studied through a numerical approach. Two-dimensional material and temperature distributions, even and uneven porosity distributions, temperature-dependent nature of material properties, and hygroscopic effects are all taken into account in studying beam’s lateral deflection. All material properties are assumed to vary along both thickness and axial directions of beam following a modified power-law distribution in terms of volume fractions of the material constituents, which are considered temperature dependent using Touloukian experiments. Beam's upper surface is subjected to a sudden temperature rise, while its lower surface is kept at reference temperature or is thermally adiabatic; meanwhile, left and right boundaries are thermally insulated. Two-dimensional transient heat conduction equation is solved using generalized differential quadrature (GDQ) method for discretizing spatial derivatives, while time derivatives are approximated using Newmark-beta integration method. Nonlinear sinusoidal moisture concentration is assumed through the thickness direction. Governing equations of motion are derived based on Timoshenko beam theory (TBT) and with the assumption of Von-Kármán geometrical nonlinearity, which is solved afterward using an iterative scheme in conjunction with GDQ and Newmark's method. Finally, the effects of porosity volume fractions, porosity cases, thermal boundary conditions, moisture concentration, FG indexes, slenderness ratio, and temperature rise on maximum non-dimensional lateral deflection are investigated considering various boundary conditions.