LetterAnalysis of wave propagation in a functionally graded nanobeam resting on visco-Pasternak's foundation

•Wave propagation velocity in terms of non-homogeneous index and nonlocal parameter.•Decreasing phase velocities with increasing the nonlocal parameter.•Decreasing phase velocities with increasing non-homogeneous index and wave number.

Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak's foundation is studied in this paper. Timoshenko's beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton's principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.