On the role of surface stress tensor in the nonlinear response of time-dependent mechanical actuated nanoplate-type energy piezo-harvesters
Muhammad Atif Shahzad, Saeid Sahmani, Babak Safaei, Mohammed Salem Basingab, Abdul Zubar Hameed
Abstract
In the present exploration, the role of surface stress tensor as one of the most important size effects at nanoscale in the nonlinear dynamical behavior of nanoplate-type energy piezo-harvesters under a time-dependent mechanical actuation is investigated. The general form of the energy functional associated with a quasi-3D nanosize energy piezo-harvester incorporating the surface Lame constants and the residual surface stress is derived. After that, by taking the Hamilton’s principle into consideration, the weak form of the surface continuum mechanics-based governing equations for a nanoplate-type energy piezo-harvester is achieved. Afterwards, the meshless collocation strategy is utilized to numerically solve the established coupled electromechanical surface elastic-based nonlinear problem with the aid of implementing a combined form of the polynomial-kind and radial-kind basis functions to eliminate any singularity which may be observed for the associated moment matrices. One can find that for the nanoplate-type energy piezo-harvesters under simply edge supports owning the thickness of 10, 20, and 50 nm, the average value of the achieved voltages are equal to 84.7140, 169.4280, and 423.5701 μv, respectively. However, by taking the role of surface stress tensor into consideration, these values in order reduce to 48.7650 μv (−42.44%), 126.8687 μv (−25.12%), and 386.3565 μv (−8.79%). Moreover, for the nanoplate-type energy piezo-harvesters under clamped edge supports owning the thickness of 10, 20, and 50 nm, the conventional average values of the attained voltages are, respectively, 71.9994,143.9989, and 359.9973 μv. However, by taking the role of surface stress tensor into consideration, these values in order decrease to 27.1823 μv (−62.25%), 83.0573 μv (−42.32%), and 328.9342 μv (−8.63%), respectively. Therefore, it is deduced that the role of surface stress tensor in the nonlinear dynamical behavior of nanoplate-type energy piezo-harvesters owing lower thickness is more prominent.