Vibration analysis of viscoelastic functionally graded porous nanoshell

This paper presents dynamic analyses for nanoscale shells with various geometries, utilizing linear standard viscoelastic material properties and functionally graded porous materials. The displacements in Cartesian coordinates for FG porous nanoshell are formulated utilizing a stress and strain shape function based on higher order shear deformation theory, which has been previously employed in the literature. The motion's equations are derived through Hamilton principle, incorporating energy expressions of the system. The forces and moments in motion's equations are expressed with nonlocal terms based on Eringen's nonlocal elasticity theory. Navier method, which allows analytical solutions for simply supported conditions, is employed in the analysis. For the dynamic analysis, dynamic distributed load applied to nanoshell is represented as a trigonometric series. To facilitate the solution, displacements are obtained in Laplace domain and subsequently transformed back into time domain. Material properties in the analysis are represented employing linear standard viscoelastic model. In this context, a computational method is developed utilizing Mathematica, and its accuracy is validated by performing a free vibration analysis. The obtained natural frequencies are compared with values from previous studies in the literature to demonstrate the model's reliability. Subsequently, a series of forced vibration analyses are conducted under dynamic distributed loading as part of parametric study on functionally graded porous viscoelastic nanoshell. The influences of different geometries, geometric properties, nanoscale characteristics, material variations, linear standard viscoelastic coefficients, porosity distributions, and porosity on displacements are investigated.