Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory

This paper aims to analyze the axial and transverse dynamic response of a functionally graded nanobeam under a moving constant load. The governing equations are obtained using the Hamilton principle and nonlocal Euler–Bernoulli beam theory. The mechanical properties vary in the thickness direction. The simply supported boundary condition is assumed and using the Laplace transform, the exact solution for the transverse and axial dynamic response is presented. Some examples were used to analyze nonlocal parameters such as power law index of FG materials, aspect ratio and the velocity of a moving constant load and also their influence on axial and transverse dynamic and maximum deflections. By obtaining a good agreement between the presented natural frequencies in this study and previous works, the results of this study are validated.