Transient dynamic, energy absorption and out-phase/in-phase vibration response of coupled annular/circular SMA nanoplates assuming surface effects on frictional substrates

Shape and size are two important factors that affect the mechanical properties of nanostructures. Therefore, various forms of nano-scaled structures such as annular and circular ones have been applied in the engineering fields. Shape Memory Alloy (SMA), which can be used as the actuator because of its ability to change shapes, has potential applications in nano-electro mechanical system (NEMS). Dynamic behavior and the ability to absorb energy are two critical characteristics of advanced structures that are under static or various forms of dynamic loadings to be specific, this research numerically examined the in-phase/out-phase vibration, transient dynamic behavior under impulse load, and energy absorption in SMA annular/circular nanoplates with ferroelastic and pseudoelastic effects coupled together via damper and spring, placed between two frictional layers. In addition, an assumption of the Kuhn-Tucker phase transformation conditions was made. Moreover, the governing equations were derived based on Hyperbolic Higher Order Shear Deformation Theory (HHSDT) and solved using Differential Cubature Method (DCM). The constitutive equation of SMA proposed by Brinson was employed to model the pseudo-elastic behavior of SMA. Besides, Gurtin-Murdoch and modified couple stress theories were employed to calculate surface and micro-scale effects. As revealed by numerical achievements, under out-phase vibration mode, by increasing the surface effect coefficient to 0.4 when the annular nanoplate inner to outer radius ratio was 0.35, the natural frequency enhanced about 174%. As the material length scale parameter to thickness ratio was increased to 0.3 and the surface effects were considered, the energy absorption capacity was enhanced by nearly 28% and 23%, respectively.