Nonlocal elasticity theory for radial vibration of composite nanoscale spherical shells via wave approach

Abstract

In this work, the wave approach is combined with nonlocal elasticity theory to address the problems of mechanics of composite nanoscale spherical shells. To the authors’ knowledge, many published literature primarily concentrate on investigating the nonlocal frequencies of nanoscale spherical shells by utilizing conventional method. Currently, no such work has been carried out on the nanoscale spherical shells from wave standpoint, particularly for the laminated nanocomposites. In this work, the characteristic determinant corresponding to composite laminated nanoscale spherical shells is formulated mathematically by incorporating general solution and transfer matrix into the conventional method. Based on wave propagation, the propagation, reflection, and coordination matrices are derived and assembled to capture the nonlocal frequencies. With respect to the composite laminated nanoscale spherical shells, the nonlocal frequencies predicted by wave approach are compared with the conventional solutions to demonstrate the validity of the proposed wave approach. Additionally, the accuracy and validity of the present method for single nanoscale spherical shells are simultaneously confirmed and examined by the available published data. Finally, the illustrative parametric studies are further scrutinized to exhibit the mechanical properties of spherically composite nanostructures.