Complex motion characteristics of three-layered Timoshenko microarches

Abstract

Numerical modelling and simulations are carried out on the nonlinear size-dependent motion of three-layered Timoshenko microarches. At the first step, the theoretical model of the three-layered microsystem is obtained based on an energy method. The second step involves the numerical simulations on the linear part of the dynamical model of the system in order to examine the possibility of internal energy transfer and modal interactions in the system dynamics. The third step is to analyse the nonlinear motion characteristics of the cases with internal energy transfer via constructing frequency–responses and force–responses. The size effects are modelled via use of the modified couple stress theory. Hamilton’s principle is used for the dynamic energy balance. The geometric imperfection is included in the model by an initial deflection in the transverse direction. The theoretical models developed for all the longitudinal, transverse, and rotational motions involve all the inertial terms. The numerical simulations are performed via a continuation method in conjunction with a direct time-integration technique for the nonlinear analysis and an eigenvalue extraction method for the linear analysis. The main aim is to analyse the level and mechanism on which the energy transfer occurs; it is also examined that how the energy transfer changes the resonant response of the microsystem and if these changes cause drastic influences.