Dynamics of nonuniform deformable AFG viscoelastic microbeams

Abstract

This paper analyses the coupled dynamics of nonuniform deformable axially functionally graded (AFG) viscoelastic microbeams with special consideration to a Kelvin–Voigt type viscosity in the FGM system. When modelling AFG viscoelastic systems, linear assumptions are commonly utilised to simplify numerical or analytical calculations. Another important factor which is usually neglected in the literature on AFG systems is to ignore in-plane/axial displacements/inertia. Viscosity between infinitesimal elements of AFG systems is also usually neglected to simplify calculations. This paper is the first to analyse the viscosity on the dynamical behaviour of AFG microbeams with the help of the Kelvin–Voigt method of viscosity, and the Euler–Bernoulli beam theory. The size dependence in the model and numerical simulations is incorporated via the modified version of the couple stress theory. Viscous stress-components of the Kelvin–Voigt model incorporated via their negative work contribution. The use of an energy balance generates the continuous model of the AFG system in the longitudinal as well as transverse directions. There are both nonlinear and linear couplings between elastically generated and viscous related terms. The nonuniform shape of the microbeam is incorporated via an axial-coordinate-dependent width. A truncation/discretisation for the coupled nonlinear model is performed using Galerkin’s method. The couplings between the dynamics of the AFG viscoelastic microbeam is examined through analysing the influence of various microsystem parameters (e.g. gradient index, viscosity coefficient, and the taper ratio of the microbeam).