Vibration of initially stressed nonlocal irregular nanoplate using wave propagation approach

Abstract

The vibration analysis of pre-stressed nonlocal irregular nanoplate is discussed in this study. To consider the nonlocal effects, Eringen's nonlocal elasticity model are adapted. Biot`s theory is used to generate the new governing equation as well as its closed-form solutions including the initial stress parameter. Governing equations considering small length scale, initial stress, and surface irregularity were solved by the wave propagation approach. A novel frequency equation is explored in relation to a small length scale, initial stress, and surface irregularity. To understand the reactions of the considered nanoplate in terms of natural frequency, the numerical calculations are done and the results are shown graphically. The findings provide a better declaration for vibration analysis of the nonlocal initially stressed irregular nanoplates. It has been observed that, the increase of the small length scale parameter decreasing the natural frequencies and the increase of initial stress and surface irregularity parameters increasing the natural frequencies throughout the computation frequencies of vibrating nanoplate. In addition, the existence of nonlocal, initial stress, and irregularity parameters effect the natural frequency of vibrating nanoplates significantly. Furthermore, the findings obtained could be relevant in designing of nanodevices in which nanoplate are the most common nano element.