Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field

摘要

Thermomechanical vibration analysis of axially functionally graded (AFG) nanobeams under nonuniform longitudinal magnetic field is investigated based on nonlocal strain-gradient theory. This theory contains two scale parameters for modeling of size-dependent behavior of AFG nanobeam accurately. This theory takes into account both nonlocal stress field and strain-gradient effects on the response of nanostructures. The nanobeam is subjected to uniform and linear through-the-length temperature distributions. A power-law model is used to describe the distribution of temperature-dependent material properties along the axial direction. A Galerkin-based solution technique is implemented to solve the governing equation obtained from Hamilton's principle. Natural frequencies of functionally graded nanobeam are verified with those of previous articles. It is shown that vibration frequencies of AFG nanobeams are significantly influenced by temperature rise, power-law index, nonlocal parameter, length-scale parameter, magnetic field intensity, and boundary conditions.