Complex motion characteristics of three‐layered Timoshenko microarches

Microstructures of small size are present as the core elements of many micromachines and microdevices (Li et al. 2008, 2016a, b; Rezazadeh et al. 2009; Aboelkassem et al. 2010; Cao et al. 2016; Ouakad 2016; Arani et al. 2016; Xi et al. 2016; Bourouina et al. 2016; Pasharavesh et al. 2016; Tajaddodianfar et al. 2016; Gong et al. 2016; Mukherjee et al. 2016; Tian et al. 2016; Saxena et al. 2016; Liao et al. 2016; Rivadeneyra et al. 2016; Ghayesh et al. 2013) such as micro energy harvesters, biosensors, microactuators, vibration sensors, and airbag accelerometers; between them microbeams and microplates are the most common ones. With the advent of new fabrication techniques, multilayered microbeams and microplates are used as the core elements of microdevices (Li et al. 2014b; Banerjee et al. 2007; Rezazadeh et al. 2012). The small size of these elements affects the deformation/oscillation behaviour of these microstructures; this was first discovered experimentally (Fleck et al. 1994; Lam and Chong 1999; McFarland and Colton 2005). From theoretical perspective, this effect is usually modelled via use of the modified couple stress theory or a strain gradient theory (Wang et al. 2010; Lazopoulos and Lazopoulos 2010; Aghazadeh et al. 2014; Farokhi and Ghayesh 2015b, c; Ansari et al. 2015; Sourki and Hoseini 2016; Ghayesh et al. 2014; Ghayesh and Farokhi 2015). There are many papers in the literature that analysed the static/oscillation behaviour of microbeams. For instance, Mohammad and Ouakad (2016) conducted an investigation into the structural behaviour of an arch-type Abstract Numerical modelling and simulations are carried out on the nonlinear size-dependent motion of threelayered 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