Viscoelastic nonlinear dynamic behaviour of Timoshenko FG beams

Retaining rotary-inertia terms and translation/rotation, a nonlinear analysis is conducted on the dynamic behaviour of Timoshenko functionally graded (FG) beams. The shear/normal strain field components are formulated using the Timoshenko theory. The elastic/viscous stress components are related to the strain components, using the Kelvin-Voigt scheme, and the strain components to translation/rotation terms using the Timoshenko beam theory. The viscous effects are incorporated using a negative work expression. The through-thickness gradual changes in the properties are modelled using the Mori-Tanaka technique. Energy-loss/work/energy Hamilton's principle for system's energy balance is utilised and the coupled nonlinear sets of equations of motion are obtained. Reduced-order motion models are obtained using Galerkin's discretisation method. Numerical simulations are conducted via a parameter-continuation method and the dynamical behaviour is examined.