Investigation of the Effect of Viscosity and Density on the Wave Propagation of a Nonlocal Porous Beam Submerged in Fluid using Bernstein Polynomials

This study investigates the effect of viscosity and density on the free vibration characteristics of a homogeneous porous Euler nanobeam submerged in fluid, incorporating the governing equations from Eringen’s nonlocal elasticity theory. To enhance computational efficiency in our analysis, we employ the Rayleigh-Ritz method, utilizing computationally efficient Bernstein polynomials as shape functions. Furthermore, we explore a range of classical boundary conditions tailored to address the specific problem at hand. In order to validate our findings, we conduct a comparative analysis against existing literature, thereby underscoring the effectiveness and robustness of our proposed methodology. Our research also places a significant emphasis on elucidating the impact of nonlocal parameters, non-dimensional amplitude, thickness, density, viscosity and porosity on non-dimensional frequency across various boundary conditions, including simply-supported (S-S), clamped-simply supported (C-S), and clamped-clamped (C-C) configurations.