Investigations on structural intensity in nanoplates with thermal load

Highlights: • Structural intensity of the nanoplate is studied by nonlocal strain gradient theory. • Higher excitation frequency is more sensitive to the small scale effect. • Thermal load have significant influences on making the energy flow pattern. • The boundary value is found to determine the critical thermal load. The finite element method (FEM) based on the nonlocal Kirchhoff plate theory with second order strain gradient is developed to derive the dynamic equations of nanoplate under thermal load with the small scale effect taken into consideration. The characteristics of transmission and distribution of the steady-state energy flows in the rectangular nanoplate are analyzed based on the structural intensity approach. In the numerical calculation, the natural frequencies of single layer graphene sheets (SLGS) computed by nonlocal FEM agree well with theoretical results of nonlocal strain gradient plate theory, which validate the reliability of the present method. The effects of nonlocal parameters, mechanical load and thermal load on structural intensity are considered. It can be found that the small scale effect is not same for different applying positions and excitation frequencies. The influence of mechanical load on vibration energy flow paths may be cancelled by thermal load, and the effect of thermal load on vibration energy flow paths also may be cancelled by mechanical load. The critical thermal load may be found to determine whether thermal load play a more important role in form energy flow of SLGS than mechanical load.