Dynamic Analysis of a Piezoelectrically Layered Perforated Nonlocal Strain Gradient Nanobeam with Flexoelectricity

This study presents a mathematical size-dependent model capable of investigating the dynamic behavior of a sandwich perforated nanobeam incorporating the flexoelectricity effect. The nonlocal strain gradient elasticity theory is developed for both continuum mechanics and flexoelectricity. Closed forms of the equivalent perforated geometrical variables are developed. The Hamiltonian principle is exploited to derive the governing equation of motion of the sandwich beam including the flexoelectric effect. Closed forms for the eigen values are derived for different boundary conditions. The accuracy of the developed model is verified by comparing the obtained results with the available published results. Parametric studies are conducted to explore the effects of the perforation parameters, geometric dimensions, nonclassical parameters, flexoelectric parameters, as well as the piezoelectric parameters on the vibration behavior of a piezoelectric perforated sandwich nanobeam. The obtained results demonstrate that both the flexoelectric and piezoelectric parameters increased the vibration frequency of the nanobeam. The nonlocal parameter reduced the natural vibration frequency due to a decrease in the stiffness of the structures. However, the strain gradient parameter increased the stiffness of the structures and hence increased the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the ration of the value of the nonlocal parameter to the strain gradient parameter. This model can be employed in the analysis and design of NEMS, nanosensors, and nanoactuators.